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Asked/Added Questions From NCERT: Mathematics


Question 1. Asked on :24 June 2022:09:05:48 PM

 There are is a pleace value of two 40.02

-Added by yash chaurasia Mathematics » Fraction And Decimal

Answer:

yash chaurasia

 There are place value of two in 40.02 is hundredth place 

-Answered by yash chaurasia On 24 June 2022:09:11:03 PM


Question 2. Asked on :20 June 2022:11:50:10 AM

Write 267962433 in international number system and separate them using commas. 

-Added by Master Mind Mathematics » Know Your Numbers

Answer:

yash chaurasia

 267,962,433

Twenty six million seven hundred nine sixty two thousand four hundred thirty three  

-Answered by yash chaurasia On 24 June 2022:08:51:03 PM


Question 3. Asked on :09 June 2022:11:09:09 AM

 If the 1st term of a series is 7 and 13th term is 35. find the sum of 13 terms of the sequence.

-Added by Master Purushottam Mathematics » Arithmetic Progressions

Answer:

Master Purushottam

 a= 7 , a13 = 35 
   

Sn = n2 (a + l)

S13 = 132 (7+35)

      = 132 x 42

      = 13 x 21 

      = 273

Hence, the sum of the first 13 term of the sequence is 273.

-Answered by Master Purushottam On 09 June 2022:11:19:25 AM


Question 4. Asked on :09 June 2022:10:56:24 AM

Value of the roots of the quadratic equation, 

x-x-+=0 are.................

-Added by Master Purushottam Mathematics » Quadratic Equations

Answer:

Master Purushottam

 CORRECT EQUALTION 

x-x- 2 =0 

=> x - x - 6 =0

=> x-3x + 2x - 6 =0

=> x(x-3) + 2(x-3) = 0

=> (x - 3) (x+2) = 0

=> x = 3 , x = -2 


-Answered by Master Purushottam On 09 June 2022:10:57:52 AM


Question 5. Asked on :09 June 2022:10:42:27 AM

 solve for x (in term of a and b):

a/x-b + b/x-a = 2, x≠ a,b

-Added by Master Purushottam Mathematics » Algebra Expression

Answer:

Master Purushottam

 a(x-a) + b(x-b) 
(x-b) (x-a)
 = 2

cross multiplying both the sides 

a(x-a) + b(x-b) = 2[x2-(a+b)x+ ab]

ax- a2 + bx -b2  = 2x2 -2(a+b)x + 2ab

2x2 -3(a+b)x + (a+b)2 = 0 

2x2 -2(a+b)x -(a+b)x + (a+b)2 = 0

[2x- (a+b) ] [x-(a+b)] = 0

        

x = a + b, a + b2 

-Answered by Master Purushottam On 09 June 2022:10:46:59 AM


Answer:

Shruti Srivastva
A.P. 23,21,19.....5

a=23, d= -2

an =5

=>a+(n-1)d=5

=>23+(n-1)-2=5

=>(n-1)-2=5-23

=>(n-1)=-18/-2

=>n=9


-Answered by Shruti Srivastva On 01 June 2022:06:01:47 PM


Question 7. Asked on :01 June 2022:05:25:29 PM

If sn, the sum of first n terms of an A.P. is given by sn=3n2-4n, find the nth term.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

s1=a1=3(1)2-4(1)

=> 3-4

=> -1

s2=3(2)2-4(2)

=>12-8

=>4

s2-s1=a2 

a2=4-(-1)

a2=5

d=a2-a1

d=5-(-1)

d=6


an = a+(n-1)d

=> -1+(n-1)6

=> -1+6n-6

=>6n-7


-Answered by Shruti Srivastva On 01 June 2022:05:28:25 PM


Question 8. Asked on :01 June 2022:05:16:00 PM

Which term of the A.P. 3,15,27,39..... will be 120 more than its 21st term?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=3, d=12, n=21

an = a+(n-1)d

=> 3+(21-1)12

=> 3+(20)12

=> 3+240

=> 243


120 more than 21st term =243+120=363


an = 363

=>a+(n-1)d=363

=>3+(n-1)12=363

=>(n-1)12=363-3

=>(n-1)=360/12

=>n=30+1

=> n=31

-Answered by Shruti Srivastva On 01 June 2022:05:19:13 PM


Question 9. Asked on :01 June 2022:04:22:08 PM

The sum of 5th term and 9th term of an A.P is 30. If its 25th term is three times its 8th term, find the A.P.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions


Question 10. Asked on :01 June 2022:04:12:59 PM

Find the number of natural numbers between101 and 999 which are divisible bu both 2 and 5.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

Number which are divisible by 2 and 5

=> number which are diisible by 2×5=10


A.P. 110,120,130.....990

a=110, d=10


an = 990

=>a+(n-1)d=990

=> 110+(n-1)10=990

=> (n-1)10=990-110

=> (n-1)10=880

=> (n-1)=880/10

=> n=88+1

=> n=89

-Answered by Shruti Srivastva On 01 June 2022:04:16:31 PM


Question 11. Asked on :01 June 2022:03:56:13 PM

The sum of 5th and 9th terms of an A.P. is 72 and the sum of 7th and 12th term is 97. Find the A.P.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a5+a9 =72

=> a+4d+a+8d=72

=> 2a+12d=72

=> a+6d=36

=> a=36-6d----(1)


a7+a12 = 97

=> a+6d+a+11d=97

=> 2a+17d=97----(2)


putting eq(1) in eq(2)

=>2a+17d=97

=>2(36-6d)+17d=97

=>72-12d+17d=97

=>5d=97-72

=>5d=25

=>d=25/5

=>d=5


putting d in eq.(1)


a=36-6d

a=36-6(5)

a=36-30

a=6


A.P. 6,11,16,21....



-Answered by Shruti Srivastva On 01 June 2022:03:58:33 PM


Question 12. Asked on :01 June 2022:03:44:51 PM

Find the sum of integers between 10 and 500 which are divisible by7.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P., 14,21............497

a=14, d=7

an = 497

=>a+(n-1)d=497

=>14+(n-1)7=497

=>(n-1)7=497-14

=>(n-1)=483/7

=>(n-1)=69

=>n=69+1

=>n=70


sn = n/2[2a+(n-1)d]

=> 70/2[2×14+(70-1)7]

=> 35[28+483]

=> 35[511]

=> 17885

-Answered by Shruti Srivastva On 01 June 2022:03:46:36 PM


Question 13. Asked on :01 June 2022:03:33:05 PM

Find the middle terms of the A.P. 7,13,19...241.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions


Question 14. Asked on :01 June 2022:03:22:54 PM

Which term of the A.P. 121,117,113.... is the first negative terms?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
Let an<0

a=121, d=-4

=>a+(n-1)d<0

=>121+(n-1)-4<0

=>121-4n+4<0

=>125-4n<0

=>n<125/4

n=32

32th term 

-Answered by Shruti Srivastva On 01 June 2022:03:26:08 PM


Question 15. Asked on :01 June 2022:03:09:13 PM

Which term of the A.P. 3,7,11,15.... is 79? Also find the sum 3+7+11+15+.....79?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=3, d=4

an = 79

=> a+(n-1)d=79

=> 3+(n-1)4=79

=> (n-1)4=79-3

=> (n-1)=76/4

=> (n-1)=19

=> n=19+1

=> n=20


sn = n/2[2a+(n-1)d]

=> 20/2[2×3+(20-1)4]

=> 10[82]

=> 820

-Answered by Shruti Srivastva On 01 June 2022:03:14:54 PM


Question 16. Asked on :30 May 2022:05:15:32 PM

In an A.P. find Sn , where an = 5n-1. Hence find the sum of the first 20 terms.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
an =5n-1

putting n=1

a1 = 5(1)-1

=> 5-1

=> 4

a2 = 5(2)-1

=> 10-1

=> 9

a=4,d=5


sn = n/2[2a+(n-1)d]

=> 20/2[2×4+(20-1)5]

=> 10[8+95]

=> 10[103]

=> 1030

-Answered by Shruti Srivastva On 30 May 2022:05:30:09 PM


Question 17. Asked on :30 May 2022:04:54:10 PM

Find the middle term of an A.P. ,-6,-2,2,........58.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a=-6, d=4

an = 58

=> a+(n-1)d=58

=> -6+(n-1)4=58

=> (n-1)4=58+6

=> (n-1)=64/4

=> n=16+1

=> n=17


Middle term = (n+1/2)th term

=> (17+1/2)

=> (18/2)

=> 9th term


a9 = a+8d

=> -6+8(4)

=> -6+32

=> 26

-Answered by Shruti Srivastva On 30 May 2022:04:59:07 PM


Question 18. Asked on :30 May 2022:04:36:38 PM

Find How many two digit numbers are divisible by 6?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P.:- 12,18,........ 96

a=12, d=6

an=96

=>a+(n-1)d=96

=>12+(n-1)6=96

=>(n-1)6=96-12

=>(n-1)6=84

=>(n-1)=84/6

=>n=14+1

=>n=15

15 two digit number are divisible by 6


-Answered by Shruti Srivastva On 30 May 2022:04:48:34 PM


Question 19. Asked on :30 May 2022:04:28:45 PM

Find whether (-150) is a term of A.P. 11,8,5,2,........?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=11, d=-3

an = -150

=> a+(n-1)d = -150

=> 11+(n-1)-3=-150

=> 11-3n+3=-150

=> 14-3n=-150

=> -3n=-150-14

=> -3n=-164

=> n= 164/3

 

-150 is not a term of this A.P.

-Answered by Shruti Srivastva On 30 May 2022:04:43:23 PM


Question 20. Asked on :30 May 2022:04:15:01 PM

Solve 1+4+7+10+.....+x=287

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P. :- 1,4,7,10.....

a=1, d=3

sn = 287

=> n/2[2a+(n-1)d]=287

=> n/2[2×1+(n-1)3]=287

=> n/2[2+3n-3]=287

=> n/2[3n-1]=287

=> 3n2-n = 287×2

=> 3n2-n-574=0

=> 3n2-42n-41n-574=0

=> 3n(n-14)-41(n-14)=0

=> (3n-41)(n-14)=0

=> 3n-41=0, (n-14)=0

=> n=41/3(not possible), n=14

ans.14

-Answered by Shruti Srivastva On 30 May 2022:04:18:48 PM


Question 21. Asked on :30 May 2022:04:07:43 PM

If 10 times of 10th term is equal to 20 times of 20th term of an A.P. Find its 30th term.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

 10(a10)=20(a20)

=> 10(a+9d)=20(a+19d)

=> 10a+90d=20a+380d

=> 20a+380d=10a+90d

=> 20a-10a = 380d-90d

=> 10a=290d

=> a=29d

=> a-29d=0

a30 = 0

30th term of this A.P. is 0


-Answered by Shruti Srivastva On 30 May 2022:04:10:31 PM


Question 22. Asked on :30 May 2022:04:00:17 PM

How many terms of the A.P. 22,20,18, ...... should be taken so that their sum is zero.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=22, d=-2

sn = 0

=> n/2[2a+(n-1)d]=0

=> n/2[2×22+(n-1)-2]=0

=> n/2[44-2n+2]=0

=> n/2[46-2n]=0

=> 46-2n=0

=> -2n=-46

=> n=46/2

=> n=23

23 terms should be taken

-Answered by Shruti Srivastva On 30 May 2022:04:01:52 PM


Question 23. Asked on :30 May 2022:03:44:56 PM

If 4m+8, 2m2+3m+6, 3m2+4m+4 are three consecutive terms of an A.P. find m.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a3-a2 = a2-a1 

=> 3m2+4m+4-(2m2+3m+6)=2m2+3m+6-(4m+8)

=> 3m2 +4m+4-2m2-3m-6 = 2m2+3m+6-4m-8

=> m2-m-2 = 2m2-m-2

=> 2m2-m2 =0

=> m2=0

=> m=0


-Answered by Shruti Srivastva On 30 May 2022:03:47:24 PM


Question 24. Asked on :30 May 2022:03:36:59 PM

Find the sum of even positive integers between 1 and 200.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P.:- 2,4,6......198

a=2, d=2

an =198

=>a+(n-1)d=198

=>2+(n-1)2=198

=>2+2n-2=198

=>2n=198

=>n=198/2

=>n=99


sn = n/2[2a+(n-1)d]

=> 99/2[2×2+(99-1)2]

=> 99/2[4+(98)2]

=> 99/2[4+196]

=> 99/2[200]

=> 99[100]

=> 9900


-Answered by Shruti Srivastva On 30 May 2022:03:37:55 PM


Question 25. Asked on :30 May 2022:03:32:01 PM

Find the sum of first 15 multiples 8.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P. :- 8,16,24.....

a=8, d=8, n=15


sn = n/2[2a+(n-1)8]

=> 15/2[2×8+(15-1)8]

=> 15/2[16+112]

=> 15/2[128]

=> 15[64]

=> 960

-Answered by Shruti Srivastva On 30 May 2022:03:32:47 PM


Question 26. Asked on :30 May 2022:03:24:37 PM

The first term, common difference and last term of an A.P. are 12,6 and 252 respectively, find the sum of all terms of this A.P.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=12, d=6, 

an=252

=> a+(n-1)d=252

=> 12+(n-1)6=252

=> (n-1)6=252-12

=> (n-1)6=240

=> (n-1)=240/6

=> (n-1)=40

=> n=40+1

=> n=41


sn =n/2[2a+(n-1)d]

=> 41/2[2×12+(41-1)6]

=> 41/2[24+240]

=> 41/2[264]

=> 41[132]

=> 5412


-Answered by Shruti Srivastva On 30 May 2022:03:26:13 PM


Question 27. Asked on :30 May 2022:03:17:29 PM

Which term of the A.P. 5,15,25... will be 130 more than its 31st term?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a=5, d=10, n= 31

an = a+(n-1)d

a31 = 5+(31-1)10

a31 = 5+(30)10

a31 = 5+300

a31 = 305


130 more than 31st term = 305+130 = 435


an = 435

=>a+(n-1)d=435

=>5+(n-1)10=435

=>(n-1)10=435-5

=>(n-1)=430/10

=>(n-1)=43

=>n=43+1

=>n=44

ans. 44th term

-Answered by Shruti Srivastva On 30 May 2022:03:19:21 PM


Question 28. Asked on :28 May 2022:05:58:48 PM

Show that (a-b)2 , (a2-b2) and (a+b2) are in A.P.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions


Question 29. Asked on :28 May 2022:05:53:39 PM

Is 144 a term of the A.P. 3,7,11,...? Justify your answer

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a=3, d=4

an = 144

=> a+(n-1)d = 144

=> 3+(n-1)4 = 144

=> (n-1)4 = 144-3

=> (n-1)4 = 141

ans. 144 is not a term of this A.P.

-Answered by Shruti Srivastva On 28 May 2022:05:55:54 PM


Question 30. Asked on :28 May 2022:05:37:41 PM

State true/false and justify

Sum of first 20 natural numbers is 410.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P.:- 1,2,3....20

a=1, d=1

sn = 410

=> n/2 [2a+(n-1)d] = 410

=> 20/2 [2(1)+(20-1)1]=410

=> 10[2+19]=410

=> 10 [21] = 410

=> 210≠410

ans. false

-Answered by Shruti Srivastva On 28 May 2022:05:39:58 PM


Question 31. Asked on :28 May 2022:05:35:14 PM

2,5,9,14 .... is an A.P.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a3 -a2 = a2 -a1 

9-5 = 2-5

4≠-3


ans. false

-Answered by Shruti Srivastva On 28 May 2022:05:36:22 PM


Question 32. Asked on :28 May 2022:05:30:23 PM

State true/False and justify

301 is a term of an A.P. 5,11,17,23...

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=5, d=6


an = 301

a+(n-1)d = 301

5+(n-1)6 = 301

(n-1)6 = 301-5

(n-1)6 = 296

(n-1) = 296/6

n-1 = 49.66


ans. false


-Answered by Shruti Srivastva On 28 May 2022:05:32:00 PM


Question 33. Asked on :28 May 2022:05:27:45 PM

The first term of an A.P., is p and the common difference is q, then its 10th term is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

 p+9q

-Answered by Shruti Srivastva On 28 May 2022:05:29:59 PM


Question 34. Asked on :28 May 2022:05:23:53 PM

What is the common difference of an A.P. in which a18 -a14 =32?

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a18 - a14 = 32

=>(a+17d)-(a+13d) = 32

=>a+17d -a -13d = 32

=>4d = 32

=>d = 32/4

=>d= 8

-Answered by Shruti Srivastva On 28 May 2022:05:25:22 PM


Question 35. Asked on :28 May 2022:05:21:44 PM

The fampus mathematician associated with finding the sum of the first 11 natural numbers is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

Gauss

-Answered by Shruti Srivastva On 28 May 2022:05:23:38 PM


Question 36. Asked on :28 May 2022:05:15:32 PM

The 11th term from the last term of an A.P. 10, 7, 4,..., -62 is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P.:- 10,7,4......-62

reversing the A.P.

A.P., -62,-59,........4,7,10

a= -62, d=3


an = a+(n-1)d

a11 = -62+(11-1)3

a11 = -62+(10)3

a11 = -62+30

a11 = -32


-Answered by Shruti Srivastva On 28 May 2022:05:17:07 PM


Question 37. Asked on :28 May 2022:05:13:49 PM

The list of numbers -10,-6,-2,2,....is 

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
An A.P.,  with d=4

-Answered by Shruti Srivastva On 28 May 2022:05:14:37 PM


Question 38. Asked on :28 May 2022:05:09:18 PM

The first three terms of an A.P. respectively are 3y-1, 3y+5 and 5y+1 then y equals:

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a3-a2 = a2-a1 

=> 5y+1-(3y+5) = 3y+5-(3y-1)

=> 5y+1-3y-5 = 3y+5-3y+1

=> 2y-4 = 6

=> 2y = 6+4

=> 2y = 10

=> y = 10/2

=> y = 5

-Answered by Shruti Srivastva On 28 May 2022:05:10:46 PM


Question 39. Asked on :28 May 2022:05:03:02 PM

In an A.P., if d=-4, n=7, an =4, then a is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

an = a+(n-1)d = 4

=> a+(7-1)-4 = 4

=> a+(6)-4 = 4

=> a-24 =4

=> a = 4+24

=> a= 28


-Answered by Shruti Srivastva On 28 May 2022:05:06:16 PM


Question 40. Asked on :28 May 2022:04:52:32 PM

11th term of anA.P., -3, -1/2,,...... is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=-3, d=-5/2


an = a+(n-1)d

a11 = -3+(11-1)-5/2

a11 = -3+(10)-5/2

a11 = -3+25

a11 = 22

-Answered by Shruti Srivastva On 28 May 2022:04:53:35 PM


Question 41. Asked on :28 May 2022:04:45:37 PM

30th term of the A.P. 10,7,4.... is

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=10, d=-3, n=30


an = a+(n-1)d

a30 = 10+(30-1)-3

a30 = 10+(29)-3

a30 = 10-87

a30 = -77


-Answered by Shruti Srivastva On 28 May 2022:04:46:32 PM


Question 42. Asked on :28 May 2022:04:34:57 PM

Find the missing term

__, 38, __, __, __, -22

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a2 = 38

a+d = 38

d = 38-a -----(1)


a6 = -22

a+5d = -22 ----(2)


putting eq.1 in eq.2

a+5d = -22

a+5(38-a) = -22

a+190-5a = -22

-4a = -22-190

-4a = -212

a = 212/4

a = 53

putting a in eq.1

d = 38-a

d = 38-53

d = -15


a3 = a+2d 

=> 53+2(-15)

=> 53-30

=> 23


a4 = a+3d 

=> 53+3(-15)

=> 53-45

=> 8


a5 = a+4d

=> 53+4(-15)

=> 53-60

=> -7


A.P.:- 53,38,23,8,-7 

-Answered by Shruti Srivastva On 28 May 2022:04:35:47 PM


Question 43. Asked on :28 May 2022:04:28:41 PM

Find the missing term 

-4,__,__,__,__,6

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a6 = 6

a+5d = 6

-4+5d = 6

5d = 6+4

5d = 10

d= 10/5

d = 2


a2 = a+d

=>-4+2 

=> -2


a3 = a+2d

=> -4+2(2)

=> -4+4

=> 0


a4 = a+3d

=> -4+3(2)

=> -4+6

=> 2


a5 = a+4d

=> -4+4(2)

=> -4+8

=> 4

-Answered by Shruti Srivastva On 28 May 2022:04:30:32 PM


Question 44. Asked on :28 May 2022:04:20:40 PM

Find the missing term

5,__,__,19/2

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a4 = 19/2

5+3d = 19/2

3d = 19/2-5

3d = 9/2

d = 9/2 ÷3

d = 3/2


a2 = a+d

a2 = 5+3/2

a2 = 13/2


a3 = a+2d

a3 = 5+2×3/2

a3 = 8

-Answered by Shruti Srivastva On 28 May 2022:04:23:23 PM


Question 45. Asked on :28 May 2022:04:11:02 PM

Find the missing term

__, 13, __, 3

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a2 = 13

a+d = 13 

a = 13-d----(1)


a4 = 3

a+3d = 3 -----(2)


from eq. (1) and (2)


a+3d = 3

(13-d)+3d = 3

13+2d = 3

2d = 3-13

2d = -10

d= -10/2

d=-5


putting d in eq. 1 

a=13-(-5)

a=13+5

a=18


a3 = a+2d

a3 = 18+2(-5)

a3 = 18-10

a3 = 8




-Answered by Shruti Srivastva On 28 May 2022:04:11:58 PM


Question 46. Asked on :28 May 2022:04:05:19 PM

Find the missing term

2,__,26

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a3 = 26

a+2d = 26

2+ 2d = 26

2d = 26-2

2d = 24

d = 24/2

d = 12


a2 = a+d

a2 = 2+12

a2 = 14

-Answered by Shruti Srivastva On 28 May 2022:04:08:33 PM


Question 47. Asked on :28 May 2022:04:02:03 PM

3,k-2,5 are in A.P. find k.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a2-a1 = a3-a2 

k-2-3 = 5-(k-2)

k-5 = 5-k+2

k-5 = 7-k

k+k = 7+5

2k = 12

k = 12/2

k = 6

-Answered by Shruti Srivastva On 28 May 2022:04:03:09 PM


Question 48. Asked on :28 May 2022:03:54:37 PM

What is the value of a=16 for the following A.P., -10,-12,-14,-16,..........

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a=-10, d=-2,n=16


an = a+(n-1)d

a16 = -10+(16-1)-2

a16 = -10 -32+2

a16 = -42+2

a16 = -40

-Answered by Shruti Srivastva On 28 May 2022:03:58:32 PM


Question 49. Asked on :28 May 2022:03:47:39 PM

What will  be the value of a8 - a4 for the following A.P.

4,9,14,.............,254

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

a=4, d=5, an =254

an = a+(n-1)d

a4 = 4+(4-1)5

a4 = 4+(3)5

a4 = 4+15

a4 =19


an = a+(n-1)d

a8 = 4+(8-1)5

a8 = 4+(7)5

a8 = 4+35

a8 = 39


a8-a4

=> 39-19

=>20

ans.=20

-Answered by Shruti Srivastva On 28 May 2022:03:49:21 PM


Question 50. Asked on :28 May 2022:03:42:20 PM

Write the common difference of A.P. whose nth term is an = 3n+7.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

an = 3n+7

putting n=1

a1 = 3(1)+7

a1 = 10

putting n=2

a2 = 3(2)+7

a2 = 6+7

a2 = 13


d= a2-a1

d= 13-10

d=3

-Answered by Shruti Srivastva On 28 May 2022:03:45:13 PM


Question 51. Asked on :28 May 2022:03:37:24 PM

Find the nth term of the A.P. -10,-15,-20,-25...........

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
a=-10, d=-5


an = a+(n-1)d

an = -10+(n-1)-5

an = -10-5n+5

an = -5n-5

an = -5(n+1)

-Answered by Shruti Srivastva On 28 May 2022:03:39:48 PM


Question 52. Asked on :28 May 2022:03:30:35 PM

Write the sum of first n even numbers.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
A.P.:- 2,4,6....

a=2, d=2


sn = n/2[2a+(n-1)d]

sn = n/2[2×2+(n-1)2]

sn = n/2[4+2n-2]

sn = n/2[2n+2]

sn = n/2×2[n+1]

sn = n[n+1]

-Answered by Shruti Srivastva On 28 May 2022:03:34:02 PM


Question 53. Asked on :28 May 2022:03:23:46 PM

Write the sum of first n natural numbers.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

 A.P. :- 1,2,3......

a=1, d=1


sn = n/2[2a+(n-1)d]

sn = n/2[2×1+(n-1)1]

sn = n/2[2+n-1]

sn = n/2[n+1]

-Answered by Shruti Srivastva On 28 May 2022:03:33:13 PM


Question 54. Asked on :28 May 2022:03:18:06 PM

Write the nth term of odd numbers.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

A.P.:- 1,3,5.....

a=1, d=2


an = a+(n-1)d

an = 1+(n-1)2

an = 1+2n-2

an = 2n-1

-Answered by Shruti Srivastva On 28 May 2022:03:20:23 PM


Question 55. Asked on :28 May 2022:03:11:29 PM

Find the sum of first 10 even numbers.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
A.P. :- 2,4,6.....

a=2, d=2, n=10


sn = n/2 [2a+(n-1)d]

sn = 10/2[2×2+(10-1)2]

sn = 5[4+9(2)]

sn = 5[4+18]

sn = 5[22]

sn = 110

-Answered by Shruti Srivastva On 28 May 2022:03:12:05 PM


Question 56. Asked on :28 May 2022:03:07:18 PM

Find 5th term of an A.P. whose nth term is 3n-5.

-Added by Shruti Srivastva Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

n=5

=>3n-5

=>3(5)-5

=> 15-5

=> 10

5th term is 10

-Answered by Shruti Srivastva On 28 May 2022:03:10:21 PM


Answer:

Shruti Srivastva
Let radius of cone = x cm

and height of cone = 3x cm

=>12×volume of 1 toy = volume of solid cylinder

=>12×[2πr3 +⅓r2 h]

=>12×[2πx3 +⅓x2 3x]

=>π(6)2×15

=>x = 27

=>x=3cm


∴Radius of hemisphere = 3cm 

 and total height of toy = 3+(3×3)

=3+9

=12cm

-Answered by Shruti Srivastva On 27 May 2022:05:51:12 PM


Answer:

Shruti Srivastva

Radius of hemisphere = 21/2 cm = 10.5cm


Volume of remaining block = (21)3 - 2/3 × 22/7 × (10.5)3 

= 6835.5 cm3

-Answered by Shruti Srivastva On 27 May 2022:05:45:18 PM


Answer:

Shruti Srivastva

Height of sone = 9.5-3.5 6cm


Volume of solid = 2/3πr3+⅓πr2 h

=> 2/3×22/7×(3.5)3 + ⅓×22/7×(3.5)2 ×6

=> 166.83 cm3 approx.

-Answered by Shruti Srivastva On 27 May 2022:05:36:10 PM


Answer:

Shruti Srivastva

h=21cm, R=20cm, r=10cm


Volume of bucket = ⅓πh[r2+R2+r×R]

=> ⅓×22/7×21×[(10)2+(20)2+10×20]

=> 15400 cm3 

=> 15.4 litre 


Cost of milk @ rupee 40 per litre = 15.4 ×40 

=rupees 616

-Answered by Shruti Srivastva On 27 May 2022:05:20:32 PM


Answer:

Shruti Srivastva
Let inner and outer radius of hollow cylinder be r cm and R cm respectively.


Difference between Outer and inner CSA = 88cm2 

=> 2πh[R-r] = 88

=> 2×22/7×14×[R-r]=88

=> 88×[R-r]=88

=> [R-r]=1        -----(1)


Volume of hollow cylinder = 176cm3 

=> πh[R2-r2]=176

=> 22/7×14×[R2-r2]=176

=> R2-r2 =4

=> (R+r)(R-r)=4       ----(2)[from-(1)]


From (1) and (2), we get 

R=2.5cm and r=1.5cm


∴Outer and inner diameter are 5cm and 3 cm respectively.

-Answered by Shruti Srivastva On 27 May 2022:04:54:54 PM


Question 62. Asked on :27 May 2022:04:30:25 PM

The rain water from a roof 22m×20m× drains into a cylindrical vessel having diameters of base 2m and height 3.5m. If the vessel is just full, find the rainfall in cm.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes

Answer:

Shruti Srivastva

Rainfall = Volume of cylindrical vessel/Area of roof

=> πr2h/l×b

=> 22/7×(1)2 ×3.5/22×20

=>1/40


=> 1/40×100cm

=> 2.5cm

-Answered by Shruti Srivastva On 27 May 2022:04:33:26 PM


Answer:

Shruti Srivastva
Slant height 
=> h2+r2
=> √(14)2+(10.5)2 
=> √196+110.25
=> √306.25
=> 17.5 m

Surface area of tent = 2πrh+πrl
=> 2×22/7×3×14+22/7×14×17.5
=> 1034m2 

Cost of cloth = 1034×80
=>rupeee 82720

-Answered by Shruti Srivastva On 27 May 2022:04:24:49 PM


Answer:

Shruti Srivastva

 Volume of toy = Volume of cylidrical part + Volume of hemispherical part + Volume of conical part

=> πr2 h+2/3πr3 +⅓πr2 h

=> 22/7×(2.1)2 ×12+⅓×22/7×(2.1)2 ×7+2/3×22/7×(2.1)3 

=> 218.064 cm3

-Answered by Shruti Srivastva On 27 May 2022:04:21:26 PM



Answer:

Shruti Srivastva
Surface area of the remaining block = TSA of cuboidal block+CSA of cylinder- Area of two circular bases 

=> 2(lb+bh+hl)+2πrh-2πr2 

=> 2(15×10+10×5+15×5)+2×22/7×7/2×5-2×22/7×(7/2)2 

=> 583 cm2

-Answered by Shruti Srivastva On 27 May 2022:03:43:29 PM


Answer:

Shruti Srivastva

radius = 3.5 cm


Volume of toy=166 5/6 cm3  = 1001/6cm 

=> 2/3πr3 +⅓πr2 h = 1001/6

=> 2/3×22/7×(7/3)3 +⅓×22/7×(7/2)2 ×h =  1001/6

=> h=6cm


Area of hemispherical part of toy

=> 2πr2 

=> 2×22/7×(7/2)2 

=> 77cm2 


Cost of paining = 77×10= rupees 770

-Answered by Shruti Srivastva On 27 May 2022:03:32:11 PM


Answer:

Shruti Srivastva

Radii of frustum are 6cm and 2cm.

Height of frustum = 12-4=8cm


Slant height = √(8)2+(6-2)2 

√64-16

√48

= 4√5 cm


Total surface area of frustum

= πl(R+r)+π(R2+r2)

= 22/7×4×2.236×[6+2]+22/7×(6)2+22/7×(2)2 

= 350.592 cm2 approx.

-Answered by Shruti Srivastva On 27 May 2022:03:21:42 PM


Answer:

Shruti Srivastva
h=24cm, R=45/2 cm, r= 25/2 cm 


slant height = √(24)2+(45/2-25/2)2 

= 26cm


Surface area of bucket = πl(R+r)+πr2 

=> 22/7×26(45/2+25/2)+22/7×25/2×25/2

=>3351.07 cm2approx.


Volume of bucket = ⅓πh[R2+r2+R×r]

=>⅓×22/7×24×[(45/2)2+(25/2)2+45/2×25/2]

=> 23728.57 cm3 approx.

-Answered by Shruti Srivastva On 26 May 2022:05:14:03 PM


Answer:

Shruti Srivastva
R=20cm, r=12cm, h=16cm


Volume of container = ⅓πh(R2+r2+R×r)

=> 3.14×16/3 [(20)2+(8)2+20×8]

=> 10450 cm3approx. 

=> 10.45 litres


Cost of milk = 10.45×50 = 522.50 


Slant height = √h2+(R-r)2

=20cm

Surface area of conatiner 

=3.14×20(20+8)+3.14×(8)2

= 1959.36 cm2 

Cost of metal sheet = 10/100 × 1959.36 

= 195.94 rupees


-Answered by Shruti Srivastva On 26 May 2022:04:57:20 PM


Answer:

Shruti Srivastva
Let radius of conical section be r cm.

∴ Height of conical section be 4r cm.


A.T.Q.,


=>10×Volume of ice-cream in 1 cone = Volume of cylindrical container

=>10[⅓πr2h+2/3πr3] = πr2h

=> 10[⅓πr2×4r+2/3πr3] = π(6)2h

=>r=3 cm

-Answered by Shruti Srivastva On 26 May 2022:04:45:27 PM


Answer:

Shruti Srivastva

R=12cm, H=220cm 

r=8cm, h= 60cm


Volme of solid = πR2H+πr2h

=> 3.14×(12)2×220+3.14×(8)2×60

=> 111532.8cm3 


Mass of the pole 

=> 111532.8×8/1000

=>892.2624 kg

-Answered by Shruti Srivastva On 26 May 2022:04:36:20 PM


Answer:

Shruti Srivastva
R=20cm

r=12cm


Volume of bucket=12308.8cm3 

=>⅓×πh[R2 +r2 +R×r] = 12308.8

=>⅓×3.14×h[(20)2 + (12)2 +20×12] = 12308.8

=> h=15cm


slant height,

l=√h2-(R-r)2 

l = √(15)2 (20-12)2 

l = 17cm


Surface area of metal sheet used 

=> π×l×(R+r)+π×(r)2 

=> 3.14×17×(20+12)+3.14×(12)2 

=> 2160.32 cm2

-Answered by Shruti Srivastva On 26 May 2022:04:21:21 PM


Question 74. Asked on :26 May 2022:04:11:18 PM

A cone of base radius 4cm is divide into two parts by drawing a plane through the mid-point of its height and parallel to its base. Compare the volume of the two parts.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes


Question 75. Asked on :26 May 2022:04:01:49 PM

A solid metallic cuboid of dimensions 24cm×11cm×7cm is melted and recast into solid cones of base radius 3.5cm and height 6cm. Find the number of cones so formed.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes

Answer:

Shruti Srivastva
dimension of cuboid = 24cm×11cm×7cm


radius of cone = 3.5cm

height of cone = 6cm


Number of cones = Volume of cuboid / Volume of cone

=> l×b×h/⅓πr2h

=> 24×11×7 / ⅓×22/7×(3.5)2 ×6

=>24


ans. 24 cones

-Answered by Shruti Srivastva On 26 May 2022:04:05:14 PM


Answer:

Shruti Srivastva

Volume of raised water in tank  = 50×44×7/100 = 154 m3

 Volume of water flown in 1 hr = 22/7 × (7/100) × (7/100) × 5000 = 77

Time taken = 154/77 = 2 hours

-Answered by Shruti Srivastva On 26 May 2022:03:57:10 PM


Answer:

Shruti Srivastva

height of conical heap = 24cm


radius of cylindrical bucket = 18cm

height = 32cm


A.T.Q.,


Volume of conical heap=Volume of cylindrical bucket

=> ⅓πr2 h = πr2h

=> ⅓r2 ×24 = (18)2 ×32

=> r = 36cm


slant height,

l = √(36)2 + (24)2

l = 43.27 cm approx.

-Answered by Shruti Srivastva On 26 May 2022:03:43:24 PM


Answer:

Shruti Srivastva
Radius of cylindrical part = 5/2 cm

Height of cylindrical part = 10cm


Radius of hemispherical part = 5/2 cm


Apparent capacity = Volume of cylindrical part = πr2h

=> 3.14×(5/2)2 ×10

=> 196.25 cm3


Actual capacity = Volume of cylindrical part - Volume of hemispherical part

=> πr2h - 2/3 ×πr3

=> 196.25 - 2/3 ×3.14 ×(5/2)3

=> 163. 54cm3approx

-Answered by Shruti Srivastva On 26 May 2022:03:33:36 PM


Answer:

Shruti Srivastva

Tiime to fill tank = Volume of cylindrical tank / Volume of water flown in 1 hour

=> πr2h/πR2H

=> (5)2 ×2/ (1/10)2 ×3000

=> 100


ans. 100 minutes or 1 hour and 40 minutes

-Answered by Shruti Srivastva On 26 May 2022:03:25:21 PM


Answer:

Shruti Srivastva

Radius of cone = 6cm

Height of cone = 24cm


Volume of sphere = Volume of cone

=> 4/3πr3 = ⅓πr2h

=> 4/3πr3 = ⅓π(6)2 ×24

=> 4/3r3 = 36×8

=> r3 = 36×8 ×3/4

=> r= 216

=> r = 324

=> r = 6cm

-Answered by Shruti Srivastva On 26 May 2022:03:15:38 PM


Answer:

Shruti Srivastva

radius of first sphere = 3cm

Let densiy of metal be d kg/cm3

∴  4/3π(3)3 ×d =1

Let radius of second sphere be r cm.

∴ 4/3πr×r×r×d =7

From(1) and (2), we have

r3= 7(3)3

Let the radius of new sphere by R cm. 


A.T.Q

4/3πR3=4/3π(3)3+4/3πr3

R3=(3)3+7(3)3

R=6cm


∴Diameter of new sphere = 2×6 = 12cm.

-Answered by Shruti Srivastva On 25 May 2022:05:51:46 PM


Answer:

Shruti Srivastva

Cylinder

radius = 3.5 cm

height = 20-3.5-3.5 = 13cm

radius of hemisphere = 3.5cm


Volume of sollid = volume of cylindrical part + 2×Volume of hemispherical part

=> 22/7×(3.5)2 ×13+2×2/3×22/7(3.5)3

=> 4040/6 cm3

-Answered by Shruti Srivastva On 25 May 2022:05:43:51 PM


Question 83. Asked on :25 May 2022:05:35:43 PM

Water in a canal, 6m wide and 1.5m deep, is flowing with a speed of 10 km/hour. How much area will it irrigate in 30 minutes; if 8cm standing water is needed?

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva

Length of canal covered in 30 mins = 5000m

b=6m, h=1.5m

Volume of water flown in 30 mins = 6×1.5×5000


Area irrigated = 6×1.5×5000/0.08 

= 562500m2


-Answered by Shruti Srivastva On 25 May 2022:05:39:06 PM


Question 84. Asked on :25 May 2022:05:26:14 PM

A petrol tank is a cylinder of bas diameter 28cm and length 24cm fited with conical ends each of axis length 9cm. Determine the capacity of the tank.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes

Answer:

Shruti Srivastva

 Capacity of tank = Volume of cylindrical part + 2×Volume of conical part

=> πr2h + 2×⅓πr2h

=> 22/7 × 142 ×24 + 2 × ⅓ × 22/7 × 142 × 24

=> 18480 cm2

-Answered by Shruti Srivastva On 25 May 2022:05:28:38 PM


Answer:

Shruti Srivastva

ΔOABΔOCD

AB/CD = OA/OC

∴ AB = 4cm 

Volume of conical part/Volume of frustum part 

=> ⅓π(4)2×6/ ⅓π×6[(8)2+(4)2+8×4]

=> 1/7


Required ratio=1:7 or 7:1

-Answered by Shruti Srivastva On 25 May 2022:05:20:01 PM


Question 86. Asked on :25 May 2022:05:04:41 PM

Find the depth of a cylindrical tank of radius 10.5 cm, if its capacity is equal to that of a rectangular tank of size 15cm × 11cm × 10.5 cm.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva

Capacity of cylindrical tank = Capacity of recatngular tank

22/7 × (10.5)2 × h = 15 × 11 × 10.5

h = 5cm

-Answered by Shruti Srivastva On 25 May 2022:05:08:37 PM


Question 87. Asked on :25 May 2022:04:56:38 PM

Three cubes of a metal whose edge are in the ration 3:4:5 are melted and converted into a single cube whose disgonal is 12√3 cm. Find the edge of three cubes.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes

Answer:

Shruti Srivastva

Let the edges of three cubes be 3x cm, 4x cm and 5x cm

Volume of single cube = Sum of volume of three cubes 

(side)3= (3x)3+(4x)3+(5x)3

Side = 6x cm 


Diagonal of single cule = 12√3 cm

√3(6x) = 12√3

x=2

hence edge of three cubes are 6cm, 8cm and 10 cm

-Answered by Shruti Srivastva On 25 May 2022:05:00:07 PM


Answer:

Shruti Srivastva

Volume of bucket = 28490 cm3

=> ⅓πh(r2R2Rr) = 28490

=>  ⅓ × 22/7 × h [(28)2+(21)2+28×21] = 28490

=> h=15cm

-Answered by Shruti Srivastva On 25 May 2022:04:53:13 PM


Question 89. Asked on :25 May 2022:04:43:10 PM

 The volume of a right circular cylinder with its height equal to the radius is 175/7 cm3. Find the height of the cylinder.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva
Let the height and radius of cylinder be x cm and x cm respectively.

Volume of cylindr = 176/7 cm3

=> 22/7 x (x)2 × x = 176/7

=> x3=8

=> x=2cm

-Answered by Shruti Srivastva On 25 May 2022:04:45:51 PM


Question 90. Asked on :25 May 2022:04:35:43 PM

The diameters of the two circlar ends of the bucket are 44 cm and 24 cm. The height of the bucket is 35cm. Find the volume of the bucket.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva
Volume of bucket = ⅓πh(r2R2Rr)

=> ⅓ x 22/7 x 35 [(22)2+(12)2+22 x 12]

=> 327062/3 cm3

-Answered by Shruti Srivastva On 25 May 2022:04:39:55 PM


Question 91. Asked on :25 May 2022:04:29:17 PM

Twelve solid sphere of the same sizes are made by meltig a solid metallic cylinder of base diameter 2cm and height 16cm. Find the radius of each sphere.

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva

Volume of 12 spheres = volume of cylinder

12 x 4/3 πr= πr2h

12 x 4/3 πr3 = π(1)216

r3 = 1

r = 1 cm

-Answered by Shruti Srivastva On 25 May 2022:04:32:48 PM


Question 92. Asked on :25 May 2022:04:18:31 PM

Two identical cubes each of volume 216 cm3 are joined together end to end. What is the surface area of the resulting cuboid?

-Added by Shruti Srivastva Mathematics » Surface Areas And Volumes.

Answer:

Shruti Srivastva

volume of 1 cube =s3= 216 cm3

=> s = 3√216

=> 6cm


∴ length, breadth and height are 12cm, 6cm, 6cm respectively


Surface area of cuboid = 2(lb+bh+hl)

=> 2(12 x 6 + 6 x 6 + 6 x 12)

=> 2(72+36+72)

=> 2(180)

=> 360 cm2

-Answered by Shruti Srivastva On 25 May 2022:04:21:19 PM


Question 93. Asked on :25 May 2022:04:08:54 PM

Find the height of largest right circular cone that can be cut out of a cube whosevolume is 729 cm3.

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva
volume of cube =s3= 729 cm3


s3= 729

s =3√729

s = 9 cm

hieght of largest right circular cone is 9 cm. 

-Answered by Shruti Srivastva On 25 May 2022:04:13:23 PM


Question 94. Asked on :25 May 2022:04:02:47 PM

 How many cubes of side 2 cm canbe cut from a cuboid measuring (16cm x 12cm x 10 cm)?

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

side of cuboid = 16 x 12 x 10


volumeof cuboid = l x b x h

=> 16 x 12 x 10

=> 1920 cm3


side of cube = 2cm


volume of cube = s3

=> 23

=> 8 cm3


Number of cubes can be cut from the cuboid = volume of cuboid / volume of cube

=> 1920/8

=> 240

ans. 240 cubes

-Answered by Shruti Srivastva On 25 May 2022:04:05:00 PM


Question 95. Asked on :25 May 2022:03:58:35 PM

 If the volume of a cube is 1331 cm3, then find the lenth of its edge.

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

Volume of cube = s3=1331

s= 3√1331

s= 11cm

-Answered by Shruti Srivastva On 25 May 2022:04:00:24 PM


Question 96. Asked on :25 May 2022:03:54:03 PM

Find total surface area of a solid hemi-sphere of radius 7cm.

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

total surface area of hemisphere = 3πr2

=> 3x22/7x7x7

=> 462 sq. cm




-Answered by Shruti Srivastva On 25 May 2022:03:55:16 PM


Question 97. Asked on :25 May 2022:03:52:38 PM

 What cross section is made by a cone when it is cut parallel to its base?

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

Circle.

-Answered by Shruti Srivastva On 25 May 2022:03:53:47 PM


Question 98. Asked on :25 May 2022:03:51:27 PM

A solid shape is converted from one form to another. What is the change in its volume?

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

The volume will remain same.

-Answered by Shruti Srivastva On 25 May 2022:03:52:20 PM


Question 99. Asked on :25 May 2022:03:34:44 PM

The surface area of a sphere if 616 cm2. Find its radius?

-Added by Shruti Srivastva Mathematics » Surface Ares And Volumes.

Answer:

Shruti Srivastva

Surface area of sphere = 4πr2=616cm2


=> 4πr2=616

=> 4x22/7xr2=616

=> r2= 616x7/22x¼

=> r2=49

=> r=√49

=> r=7cm


ans. 7cm

-Answered by Shruti Srivastva On 25 May 2022:03:35:54 PM


Question 100. Asked on :25 May 2022:03:27:09 PM

The next term of the A.P. √8, √18, √32, ____

-Added by Jyoti Srivastva Mathematics » Arithmetic Progressions

Answer:

Jyoti Srivastva

 

√50

-Answered by Jyoti Srivastva On 25 May 2022:03:29:33 PM


Question 101. Asked on :24 May 2022:04:40:48 PM

 Which one is stronger acid 

(a) ph = 5

(b) ph = 2

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Manisha Kumari

 ph = 2

-Answered by Manisha Kumari On 24 May 2022:04:50:59 PM


Question 102. Asked on :24 May 2022:04:38:16 PM

 A compound x in aqueous solution turns red liymus solution into blue identify 'x'.

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Manisha Kumari

 hydochloric acid

-Answered by Manisha Kumari On 24 May 2022:04:40:32 PM


Question 103. Asked on :24 May 2022:04:08:23 PM

If roots of 4x2-2x+c=0 are reciprocal of each other them the value of c is ______ .

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

c=4

-Answered by Shruti Srivastva On 24 May 2022:04:21:11 PM


Question 104. Asked on :24 May 2022:04:04:12 PM

The value of k for which the roots of quadratic equations x2+4x+k= are real is ______ .

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

k will be equal or more the four

-Answered by Shruti Srivastva On 24 May 2022:04:21:52 PM


Question 105. Asked on :24 May 2022:03:57:37 PM

 The quadratic equation x2-5x-6=0 i expressed as (x+p)(x+q)=o then value of p and q respectively are ____ and ____ .

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

p=6 q=1

-Answered by Shruti Srivastva On 24 May 2022:04:23:20 PM


Question 106. Asked on :24 May 2022:03:52:33 PM

 If px2+qx+r = 0 has equal root then value of r will be____.

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

q2/4p

-Answered by Shruti Srivastva On 24 May 2022:04:23:46 PM


Question 107. Asked on :24 May 2022:03:46:59 PM

 The value(s) of k for which the quadratic equation 2x2+kx+2=0 has equal root is

(a) 4

(b) ∓4

(c) -4

(d) 0

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

(b)

-Answered by Shruti Srivastva On 24 May 2022:04:24:28 PM


Question 108. Asked on :24 May 2022:03:41:22 PM

Roots of quadratic equation x2-7x=0 will be

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

0 & 7

-Answered by Shruti Srivastva On 24 May 2022:04:24:52 PM


Question 109. Asked on :24 May 2022:03:42:34 PM

 Evaluate: tan 60./cot 25.

-Added by Manisha Kumari Mathematics » Trignometry

Answer:

Shruti Srivastva

 tan 60./cot 25

=1

-Answered by Shruti Srivastva On 24 May 2022:04:25:17 PM


Question 110. Asked on :24 May 2022:03:39:40 PM

 Find the number of terms in the A.P:18,31/2,13,.......,-47.

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva
the number of terms in the A.P:18,31/2,13,.......,-47 =27

-Answered by Shruti Srivastva On 24 May 2022:04:26:04 PM


Question 111. Asked on :24 May 2022:03:37:27 PM

 Every quadratic equation have at most

(a) 3 roots

(b) 1 root

(c) 2 roots

(d) any number of roots

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva
(c) 2 roots

-Answered by Shruti Srivastva On 24 May 2022:04:26:26 PM


Question 112. Asked on :24 May 2022:03:33:08 PM

 Find the value of k which the quadratic kx (x-2) +6=0 has two equal roots. 

-Added by Manisha Kumari Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

the root is 6

-Answered by Shruti Srivastva On 24 May 2022:04:26:43 PM


Question 113. Asked on :24 May 2022:03:33:53 PM

If 1/2 is a root of x2+px-5/4 =0 then value of p is 

(a) 2

(b) -2

(c) 1/4

(d) 1/2

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

 (a) 2

-Answered by Shruti Srivastva On 24 May 2022:04:27:28 PM


Question 114. Asked on :24 May 2022:03:29:21 PM

Which of the following equation has 2 as a root:

(a) x2+4=0

(b) x2-4

(c) x2+3x-12=0

(d) 3x2-6x-2=0


-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

  3x2-6x-2=0 has 2 as a root.

-Answered by Shruti Srivastva On 24 May 2022:04:28:13 PM


Question 115. Asked on :24 May 2022:03:16:32 PM

Which of the following is not a quadratic equation:

(a) 2(x-1)2 = 4x2-2x+1

(b) 3x-x= x2+6 

(c) (√3x+√2) = 2x2-5x

(d) (x2+2x)2 = x4+3+4x2

-Added by Shruti Srivastva Mathematics » Quadratic Equations

Answer:

Shruti Srivastva
(d) (x2+2x)= x4+3+4x2

-Answered by Shruti Srivastva On 24 May 2022:04:28:51 PM


Question 116. Asked on :23 May 2022:05:06:50 PM

 Find the sum of all natural numbers that are less than 100 and divisible by 4?

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

 1200.

-Answered by Shruti Srivastva On 23 May 2022:05:11:32 PM


Question 117. Asked on :23 May 2022:05:03:13 PM

 How many irrational numbers lie between √2 and √3? 

-Added by Manisha Kumari Mathematics » Real Numbers

Answer:

Shruti Srivastva

uncountable

-Answered by Shruti Srivastva On 23 May 2022:05:05:58 PM


Question 118. Asked on :23 May 2022:05:00:44 PM

 Find the least positive integer which if diminished by 5 is exactly divisible by 36 and 54

-Added by Manisha Kumari Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

113.

-Answered by Shruti Srivastva On 23 May 2022:05:06:16 PM


Question 119. Asked on :23 May 2022:04:58:21 PM

 Find the 5th term from the end of the A.P. 10,7,4,......,-65.

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

-53.

-Answered by Shruti Srivastva On 23 May 2022:05:06:31 PM


Question 120. Asked on :23 May 2022:04:55:30 PM

 Find the sum of 20 terms of the A.P 1,6,11,16.....

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Shruti Srivastva

970.

-Answered by Shruti Srivastva On 23 May 2022:05:06:49 PM


Question 121. Asked on :23 May 2022:04:51:57 PM

 Solve: x2-8x+16=0.

-Added by Manisha Kumari Mathematics » Quadratic Equations

Answer:

Shruti Srivastva

4.

-Answered by Shruti Srivastva On 23 May 2022:05:07:03 PM


Question 122. Asked on :23 May 2022:04:48:49 PM

 if 'a' and 'b' are prime numbers, then their LCM is.

-Added by Manisha Kumari Mathematics » Real Numbers

Answer:

Shruti Srivastva

(axb)

-Answered by Shruti Srivastva On 23 May 2022:05:07:17 PM


Question 123. Asked on :23 May 2022:04:45:24 PM

 the distance of the point (6,-6) from origin is:

-Added by Manisha Kumari Mathematics » Co-ordiante Geometry

Answer:

Shruti Srivastva

6√2.

-Answered by Shruti Srivastva On 23 May 2022:05:07:32 PM


Question 124. Asked on :23 May 2022:04:40:05 PM

 For what value of k, the following system of equations will be inconsistent 

kx+3y = k-3

12x+ky=k

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 K=-6

-Answered by Manisha Kumari On 23 May 2022:04:43:52 PM


Question 125. Asked on :23 May 2022:04:38:44 PM

 The difference of two numbers is 66. If one number is four times the other , find the numbers.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 88,22.

-Answered by Manisha Kumari On 23 May 2022:04:41:51 PM


Question 126. Asked on :23 May 2022:04:35:32 PM

Ram is walking along the line joining (1,4) and (0,6)

Rahim is walking along the line joining (3,4) and (1,0)

Represent on graph and find the point where both of them cross each other.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 2,2.

-Answered by Manisha Kumari On 23 May 2022:04:42:23 PM


Question 127. Asked on :23 May 2022:04:32:38 PM

 Solve the pair of linear equations by substituting method x-7y+42=0 and x-3y-6=0

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 42,12.

-Answered by Manisha Kumari On 23 May 2022:04:41:07 PM


Question 128. Asked on :23 May 2022:04:27:19 PM

 In an A.P. if S21=1250,S20=1200,Find A21

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Manisha Kumari

 50

-Answered by Manisha Kumari On 23 May 2022:04:31:51 PM


Question 129. Asked on :23 May 2022:04:28:38 PM

 For what value of p the pair of linear equations (p+2)x-(2p+1)y=3(2p-1) and 2x-3y=7 has a unique solution.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

 p≠4

-Answered by Shruti Srivastva On 23 May 2022:04:31:11 PM


Question 130. Asked on :23 May 2022:04:21:18 PM

 For what value of p the pair of linear equations (p+2)x-(2p+1)y = 3(2p-1) and 2x-3y=7 has a unique solution.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 p≠4.

-Answered by Manisha Kumari On 23 May 2022:04:24:42 PM


Question 131. Asked on :23 May 2022:04:17:28 PM

 If we draw lines of x=2 and y=3 what kind of lines do we get?

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 intersecting lines.

-Answered by Manisha Kumari On 23 May 2022:04:21:20 PM


Question 132. Asked on :23 May 2022:04:16:00 PM

 What is the value of p, for which the pair of linear equations x+y=3 and 3x+py=9 is inconsistent.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 p=3.

-Answered by Manisha Kumari On 23 May 2022:04:21:45 PM


Question 133. Asked on :23 May 2022:04:11:39 PM

 If 2x+5y=4, write another linear equation, so that lines represented by the pair are coincident.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 4x + 10y=8

-Answered by Manisha Kumari On 23 May 2022:04:14:13 PM


Question 134. Asked on :23 May 2022:04:10:12 PM

Write the solution of y=x and y=-x.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

0,0. 

-Answered by Manisha Kumari On 23 May 2022:04:11:43 PM


Question 135. Asked on :23 May 2022:04:07:59 PM

 Find the value of k for which pair of linear equations 3x+2y=-5and x-ky=2 has a unique solution.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 k≠-2/3.

-Answered by Manisha Kumari On 23 May 2022:04:12:17 PM


Question 136. Asked on :23 May 2022:04:05:33 PM

 A motor cyclist is moving along the line x-y=2 and another motor cyclist is moving along the line x-y=4 find out their moving direction.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 Move parallel.

-Answered by Manisha Kumari On 23 May 2022:04:14:57 PM


Question 137. Asked on :23 May 2022:03:56:57 PM

 Find the number of natural numbers between 102 and 998 which are divisible by 2 and 5 both.

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Manisha Kumari

 89

-Answered by Manisha Kumari On 23 May 2022:04:04:20 PM


Question 138. Asked on :23 May 2022:04:02:57 PM

For what value of p, system of equation 2x+py=8 and x+y=6 have no solution.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 p=2.

-Answered by Manisha Kumari On 23 May 2022:04:15:24 PM


Question 139. Asked on :23 May 2022:04:01:34 PM

 What is the point of intersection of the line represented by 3x-2y=6 and the y-axis?

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 0,-3.

-Answered by Manisha Kumari On 23 May 2022:04:15:49 PM


Question 140. Asked on :23 May 2022:03:58:56 PM

 If x=3m-1 and y=4 is a solution of the equation x+y=6, then find the value of m.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 m=1.

-Answered by Manisha Kumari On 23 May 2022:04:16:45 PM


Question 141. Asked on :23 May 2022:03:54:09 PM

 In ΔABC, ∠C=3∠B, ∠C=2(∠A+∠B) then, ∠A,∠B,∠C are respectively.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

  20°, 40º,120º.

-Answered by Manisha Kumari On 24 May 2022:04:18:56 PM


Question 142. Asked on :23 May 2022:03:50:51 PM

 If ax+by=c and lx+my=n has unique solution then the relation between the coefficient will be:

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

am≠lb

-Answered by Shruti Srivastva On 23 May 2022:03:53:25 PM


Question 143. Asked on :23 May 2022:03:47:50 PM

 If HCF of 144 and 180 is expressed in the form 13m-16. find the value of m.

-Added by Manisha Kumari Mathematics » Real Numbers

Answer:

Shruti Srivastva

 4.

-Answered by Shruti Srivastva On 23 May 2022:03:53:17 PM


Question 144. Asked on :23 May 2022:03:49:22 PM

 One of the common solution of ax+by=c and y axis is

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

 (0, c/b)

-Answered by Shruti Srivastva On 23 May 2022:03:50:19 PM


Question 145. Asked on :23 May 2022:03:47:51 PM

 For 2x+3y=4, y can be written in terms of x as:

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

 y = 4-2x/3

-Answered by Shruti Srivastva On 23 May 2022:03:49:00 PM


Question 146. Asked on :23 May 2022:03:45:09 PM

 If the first term of an ap are b,c and 2b, then find the ratio of b and c

-Added by Manisha Kumari Mathematics » Arithmetic Progressions

Answer:

Manisha Kumari

 2:3

-Answered by Manisha Kumari On 23 May 2022:03:53:00 PM


Question 147. Asked on :23 May 2022:03:42:35 PM

 If a pair of linear equations in two variables is consistent, then the lines represented by two equations are: 

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 intersecting or coincident.

-Answered by Manisha Kumari On 23 May 2022:04:17:46 PM


Answer:

Shruti Srivastva

 6

-Answered by Shruti Srivastva On 23 May 2022:03:46:52 PM


Question 149. Asked on :23 May 2022:03:40:06 PM

 The value of k for which the system of equations 3x5y=0 and kx+10y=0 has a non-zero solution is

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 6.

-Answered by Manisha Kumari On 23 May 2022:03:44:11 PM


Question 150. Asked on :23 May 2022:03:36:23 PM

 The area of the triangle formed by the lines x=3, y=4 and x=y is

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

 1/2  sq. unit

-Answered by Shruti Srivastva On 23 May 2022:03:39:06 PM


Question 151. Asked on :23 May 2022:03:26:20 PM

 the distance of the point P(-3,-4) from the x-axis (in unit) is:

-Added by Manisha Kumari Mathematics » Co-ordiante Geometry

Answer:

Shruti Srivastva

 the unit is 4

-Answered by Shruti Srivastva On 23 May 2022:03:39:51 PM


Question 152. Asked on :23 May 2022:03:31:13 PM

 If x=a and y=b is the solution of the equation x-y=2 and x+y=4, then the values of a and b are respectively____.

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Manisha Kumari

 A=3,B=1.

-Answered by Manisha Kumari On 23 May 2022:03:38:03 PM


Question 153. Asked on :23 May 2022:03:19:02 PM

 If the lines given by 3x+2ky=2 and 2x +5y = 1 are parallel, then the value of k is:

-Added by Shruti Srivastva Mathematics » Pair Of Linear Equations In Two Variables

Answer:

Shruti Srivastva

 k = 15/4

-Answered by Shruti Srivastva On 23 May 2022:03:28:16 PM


Question 154. Asked on :23 May 2022:03:15:00 PM

 If triangle  ABC is right angled at C,then the value of the sec (A+B) is

-Added by Manisha Kumari Mathematics » Trigonometry

Answer:

Manisha Kumari

 Not defined

-Answered by Manisha Kumari On 23 May 2022:03:25:30 PM


Question 155. Asked on :20 May 2022:04:28:39 PM

If α and β are zeros of x2-x-2, find a polynomial whose zero are (2α+1) and (2β+1)

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 x2-4x-5

-Answered by Shruti Srivastva On 20 May 2022:04:31:01 PM


Question 156. Asked on :20 May 2022:04:25:30 PM

 If zeros of the polynomial ax2+bx-c, a≠0 are additive inverse of each other then what is the value of b?

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 B=0.

-Answered by Manisha Kumari On 20 May 2022:04:28:45 PM


Question 157. Asked on :20 May 2022:04:23:02 PM

 Find the value of k such that 3x2+2kx+x-k-5 has the sum of zeroes as half of their of product.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 1.

-Answered by Manisha Kumari On 20 May 2022:04:29:59 PM


Question 158. Asked on :20 May 2022:04:16:17 PM

 If x4+2x3+8x2+12x+18 is divided by (x2+5), remainder comes out to be (px+q), find values of k.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 P=2 , Q=3.

-Answered by Manisha Kumari On 20 May 2022:04:25:48 PM


Question 159. Asked on :20 May 2022:04:11:05 PM

 If (k+y) is a factor of each of the polynomial y2+2y-15 and y3+a, find the value of k and a.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 k=-3, 5 and a = -27, 125

-Answered by Shruti Srivastva On 20 May 2022:04:13:30 PM


Question 160. Asked on :20 May 2022:04:07:04 PM

What should be added to the polynomial x3-3x2+6x-15, so that it is completely divisible by x-3?

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 On dividing x3-3x2+6x-15 by x-3, remainder is +3, hence -3 must be added to x3-3x2+6x-15.

-Answered by Shruti Srivastva On 20 May 2022:04:09:30 PM


Question 161. Asked on :20 May 2022:04:05:19 PM

 If the sum of squares of zeros of the polynomial x2-8x+k is 40, find the value of k.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 12.

-Answered by Manisha Kumari On 20 May 2022:04:08:14 PM


Question 162. Asked on :20 May 2022:04:01:58 PM

 If α and β are the zeros of the polynomial x2-5x+m such that α - β = 1, find m.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 6.

-Answered by Manisha Kumari On 20 May 2022:04:07:47 PM


Question 163. Asked on :20 May 2022:03:59:50 PM

 If one zero of the quadratic polynomial (k2+k)x2+68k+6k is reciprocal of the other, find k.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 5.

-Answered by Manisha Kumari On 20 May 2022:04:08:36 PM


Question 164. Asked on :20 May 2022:03:58:14 PM

 If zeroes of x2-Kx+6 are in the ratio 3:2, find K.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 -5 ,5

-Answered by Manisha Kumari On 20 May 2022:04:08:55 PM


Question 165. Asked on :19 May 2022:05:17:04 PM

 If the product of zeroes of ax2-6x-6 is 4, find the value of a. Hence find the sum of its zeroes.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 a = -3/2, sum of zeroes = -4

-Answered by Shruti Srivastva On 19 May 2022:05:19:13 PM


Question 166. Asked on :19 May 2022:05:12:08 PM

 For what value of K, x2-4x+K touches x-axis.

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 4.

-Answered by Manisha Kumari On 20 May 2022:04:09:42 PM


Question 167. Asked on :19 May 2022:05:02:33 PM

  What will be the number of zeroes of a linear polynomial p(x) if its graph doesnot intersect or touch x-axis at any point?

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 have 0 zero

-Answered by Shruti Srivastva On 19 May 2022:05:03:54 PM


Question 168. Asked on :19 May 2022:04:59:58 PM

 What will be the number of zeroes of a linear polynomial p(x) if its graph passes through the origin?

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 Have only 1 zero.

-Answered by Manisha Kumari On 20 May 2022:04:10:37 PM


Question 169. Asked on :19 May 2022:04:56:39 PM

 If p(x) = x3-2x2-x+2 = (x+1)(x-2)(x-d) then what is the value of d?

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 1.

-Answered by Manisha Kumari On 20 May 2022:04:12:24 PM


Question 170. Asked on :19 May 2022:04:53:47 PM

 If a quadratic polynomial f(x) is a square of a linear polynomial, then its two zeroes are coincident. (True/False)

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Manisha Kumari

 True.

-Answered by Manisha Kumari On 20 May 2022:04:14:05 PM


Question 171. Asked on :19 May 2022:04:51:21 PM

 If a quadratic polynomial f(x) is not factorizable into linear factors, thenit has no real zero. (True/False)

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 True

-Answered by Shruti Srivastva On 19 May 2022:04:53:34 PM


Question 172. Asked on :19 May 2022:04:49:14 PM

 What should be added to the polynomial x2 - 5x + 4,so that 3 is the zero of the resulting polynomial

-Added by Shruti Srivastva Mathematics » Polynomial

Answer:

Shruti Srivastva

 2

-Answered by Shruti Srivastva On 19 May 2022:04:51:02 PM


Question 173. Asked on :19 May 2022:04:47:14 PM

 If the zero of the quadratic polynomial x2 + (a+1)x + b are 2 and -3, then

-Added by Shruti Srivastva Mathematics » Polynomials

Answer:

Shruti Srivastva

 a=0, b=-6

-Answered by Shruti Srivastva On 19 May 2022:04:48:50 PM


Question 174. Asked on :19 May 2022:04:37:40 PM

 If one zero of the polynomial p(x) = 5x2 + 13x + K is reciprocal of the other, then value of K is 

-Added by Shruti Srivastva Mathematics » Polynomials

Answer:

Shruti Srivastva

 5

-Answered by Shruti Srivastva On 19 May 2022:04:44:54 PM


Question 175. Asked on :19 May 2022:04:34:02 PM

 The LCM of two numbers is 14 times their HCF. The sum of LCM and HCF is 600. If one of the number is 280. Find the other number.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 HCF = 40, LCM = 560

other no. = 80

-Answered by Shruti Srivastva On 19 May 2022:04:35:46 PM


Question 176. Asked on :19 May 2022:04:32:12 PM

 If the HCF of 1032 and 408 is expressble in the form 1032 p - 408 x 5, find p.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Manisha Kumari

 P=2.

-Answered by Manisha Kumari On 20 May 2022:04:28:08 PM


Question 177. Asked on :19 May 2022:04:26:08 PM

 Find the samllest number which when increased by 20 is exactly divisible by 90 and 144. If we express the smallest number, the LCM, a multiple of 144?

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

[The LCM of 90 and 144 - 20] = Required No.

=> Required No. = 700

If 720 = 144m + 90n then m = 5, n = 0, Yes

-Answered by Shruti Srivastva On 19 May 2022:04:30:12 PM


Question 178. Asked on :19 May 2022:04:22:54 PM

 Find the number nearest to 110000 but greater than 1 lakh, which is exactly divisible by 8,15,21.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 109200

-Answered by Shruti Srivastva On 19 May 2022:04:25:52 PM


Question 179. Asked on :19 May 2022:04:15:50 PM

 Find the smallest number, which when increasedby17, is exactly devisible by both 520 and 468.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 4663 

LCM of 468 and 520 = 4680

Required no. = 4680 - 17 = 4663

-Answered by Shruti Srivastva On 19 May 2022:04:19:45 PM


Question 180. Asked on :19 May 2022:04:14:12 PM

 Find the HCF of 56, 96, 324.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 4

-Answered by Shruti Srivastva On 19 May 2022:04:15:41 PM


Question 181. Asked on :19 May 2022:04:10:12 PM

 Find HCF and LCM of 404 and 96 and verify that HCF x LCM = Product of two given number.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 HCF of 404 and 96 = 4


LCM of 404 and 96 = 9696


HCF x LCM = 38, 784


Also,       404 x 96 = 38,784

-Answered by Shruti Srivastva On 19 May 2022:04:12:09 PM


Question 182. Asked on :19 May 2022:04:08:01 PM

 Find the HCF of 180, 252, and 324.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 36

-Answered by Shruti Srivastva On 19 May 2022:04:10:02 PM


Answer:

Shruti Srivastva

 LCM of 9,12,15 is 180

so, after 180 minutes the bell ring together.

-Answered by Shruti Srivastva On 19 May 2022:04:07:11 PM


Question 184. Asked on :19 May 2022:03:56:01 PM

 Using Euclid's division algorith, find the largest number that divides 1251, 9377 and 15628 leaving reaminder 1,2 and 3 respectively.

-Added by Shruti Srivastva Mathematics » Real Number

Answer:

Shruti Srivastva

 1251-1 = 1250, 9377-2 = 9375, 15628-3 = 15625

HCF of 15625 and 9375 = 3125

HCF of 3125 and 1250 + 625


=> HCF of 1250, 9375, 15625 = 625

-Answered by Shruti Srivastva On 19 May 2022:03:58:43 PM


Question 185. Asked on :19 May 2022:03:49:56 PM

 The HCF of 65 and 117 is expressible in the form 65m - 117. Find the value of m. Also find the LCM of 65and 117 using prime factorisation method.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 Hcf od 117 and 56 by Euclid divisionalgorith

117= 65x1+52

65= 52x1= 52

52= 13x4 + 0


HCF of 117 and 52 = 13

Given that 65m - 117 = 13 => 65m = 130 => m=2.

LCM of 65 and 117 is 13x32x5 = 585 

-Answered by Shruti Srivastva On 19 May 2022:03:52:18 PM


Question 186. Asked on :19 May 2022:03:43:08 PM

Find the largest number that divides 31 and 99 leaving reaminder 5 and 8 respectively.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 given number 31 and 99

31-5=26

99-8=91

prime factor of 26 = 2x13

prime factor of 91 = 7x13 


HCF of 26 and 91 is 13


13 is the largest number which divides 31 and 99 leaving reaminder 5 and 8 respectively.


-Answered by Shruti Srivastva On 19 May 2022:03:46:36 PM


Question 187. Asked on :19 May 2022:03:41:24 PM

 What can you say about the product of a non-zero rational and irrational?

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Manisha Kumari

 irrational.

-Answered by Manisha Kumari On 20 May 2022:04:15:22 PM


Question 188. Asked on :19 May 2022:03:39:35 PM

 What would be the value of n for which n2-1 is divisible by 8.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 An odd integer

-Answered by Shruti Srivastva On 19 May 2022:03:41:01 PM


Question 189. Asked on :19 May 2022:03:37:51 PM

 Write the form in which every odd integer can be written taking t as variable:

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 2t+1

-Answered by Shruti Srivastva On 19 May 2022:03:39:20 PM


Question 190. Asked on :19 May 2022:03:35:45 PM

 Write the prime factor of 2x7x11x13x17+21

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 7

-Answered by Shruti Srivastva On 19 May 2022:03:37:14 PM


Question 191. Asked on :19 May 2022:03:32:00 PM

 If n is a natural number, then 252n-92n is alwaya divisible by:

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 16 or 34

-Answered by Shruti Srivastva On 19 May 2022:03:35:04 PM


Question 192. Asked on :19 May 2022:03:29:10 PM

 HCF of 33x54 and 34x5is.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Manisha Kumari

33 , 52.

-Answered by Manisha Kumari On 20 May 2022:04:30:44 PM


Question 193. Asked on :19 May 2022:03:25:36 PM

 A number N when divided by 16 gives the remainder 5 ______ is the remainder when thesame number isdivided by 8.

-Added by Shruti Srivastva Mathematics » Real Numbers

Answer:

Shruti Srivastva

 5

-Answered by Shruti Srivastva On 19 May 2022:03:28:55 PM


Answer:

Master Mind

Explaination, 

S.I and C.I for 1st year will be same

Compound Interest for 2 years = ₹110 (given)

S.I for 2 years = ₹100 (given)

S.I for 1st year = ₹50 

C.I for 1st year = ₹50  

C.I for 2nd year = ₹110 - ₹50 = ₹60 

∴ S.I for 2nd year = ₹60 - ₹50 = ₹10 

It means he paid ₹10 as interest on ₹50 

S.I = ₹10, P = ₹50, t = 1 year R = ? 

R = S.I x 100p x t 

   = 10 x 10050 x 1 

   = 20 %

Now, calculating the principle for 2 years

S.I = ₹100, R = 20%, t = 2 yaers 

P = S.I x 100R x t 

   = 100 x 10020 x 2 

   = 5 x 50 

   = ₹250 

So, Sum amount = ₹250 and rate = 20% 

-Answered by Master Mind On 24 December 2021:09:34:47 PM


Question 195. Asked on :29 June 2021:11:08:46 AM

Prove that √5 is an irrational number.

-Added by Master Purushottam Mathematics » Real Numbers

Answer:

Master Purushottam

Let us assume that √5 is a rational number. 

 we can write it as √5 = pq 

Now we can reduce p and q and we get reduced value of p and q as a and b which are co-prime have no common factor other than 1. 

So we have √5 = ab 

⇒ √5b = a  

⇒ 5b2 = a2   [squaring both sides]  ............ (i) 

⇒ b2 = a25 

5 divides a2 so a is also divisible by 5   (theorem 1.3) ..... (ii) 

so 5 is a factor of a.

Now taking a = 5c for some integer c 

⇒ 5b2 = (5c)2  

⇒ 5b2 = 25 c2 

⇒ b2 = 5 c2 

⇒ c2 = b25 

5 divides b2 so b is also divisible by 5 (theorem 1.3)  ...... (iii) 

from (ii) and (iii) we get that 

a and b are divisible by 5 this implies that 5 is common factor of a and b, while we assume that a and b are co-prime having no common factor other than 1. 

This contradiction has risen due to our wrong assumption so √5 cann't be 

expressed as pq, Hence √5 is an irrational number. 

-Answered by Master Purushottam On 29 June 2021:11:10:35 AM


Question 196. Asked on :24 June 2021:06:26:16 PM

Show that any odd positive integer is of the form 4q + 1 or 4q + 3, where q is some integer.

-Added by Master Mind Mathematics » Real Numbers

Answer:

Master Mind

Let the a is the any odd positive interger

To Show that: a = 4q + 1 or 4q + 3 

Using Euclid's division algorithem 

a = bq + r  

∴ b = 4 

so, possible remainder will be 0, 1, 2, 3 ( 0 ≤ r < b) 

Hence, a is an odd positive integer therefore remainder will be also odd.

∴ r = 1 or 3 

Now expressing a in the form of bq + r 

a = 4q + 1 or 4q + 3 

Hence proved 

-Answered by Master Mind On 24 June 2021:06:28:42 PM


Question 197. Asked on :24 June 2021:06:10:31 PM

If the HCF of 210 and 55 is expressible in the form 210 × 5 + 55y then find y.

-Added by Master Mind Mathematics » Real Numbers

Answer:

Master Mind
HCF of 210 and 55 using Euclid's division algorithem

210 = 55 × 3 + 45

  55 = 45 × 1 + 10 

  45 = 10 × 4 + 5

  10 = 5 × 2 + 0 

∴ HCF = 5 

Now 210 × 5 + 55y = 5 

       1050 + 55y = 5 

                   55y = 5 - 1050 

                   55y = - 1045       

                      y = - 104555 = - 19 

y = - 19 


-Answered by Master Mind On 24 June 2021:06:15:15 PM


Question 198. Asked on :05 March 2021:01:06:35 PM

 To buy a house, Ashok paid Rs. 75,750 every month for 12 years. How much money did he pay in all?

-Added by Palak Khazanchi Mathematics » Ways To Multiply And Divide

Answer:

Master Mind

Ashok Paid Rs. = 75,750 Every month
Months in 12 years = 12 × 12 

                             = 144 months 

Total amount paid by Ashok = 75,750 × 144 

                                         = 10,908,000

Therefore, Ashok paid in 12 years Rs. 10,908,000 


-Answered by Master Mind On 09 April 2021:04:48:55 PM


Question 199. Asked on :04 January 2021:08:57:20 PM

 If p = 2 - a, then prove that a3 + 6ap + p3 - 8 = 0 

-Added by Master Mind Mathematics » Algebra


Question 200. Asked on :05 August 2020:05:56:50 PM

Write the identity 8?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva
x3 + y3 +z3 - 3xyz = (x + y + z)(x2 + y2 + z2 - xy - yz- zx)

-Answered by Shruti Srivastva On 05 August 2020:05:57:19 PM


Question 201. Asked on :05 August 2020:05:55:01 PM

Write the identity 7?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva

(x-y)3 = x- y3 - 3xy(x-y) 

-Answered by Shruti Srivastva On 05 August 2020:05:55:27 PM


Question 202. Asked on :05 August 2020:05:53:30 PM

Write the identity 6?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva
(x+y)3 = x3 + y3 + 3xy(x+y)

-Answered by Shruti Srivastva On 05 August 2020:05:54:00 PM


Question 203. Asked on :05 August 2020:05:51:20 PM

Write the identity 5?

-Added by Shruti Srivastva Mathematics » Current Electricity

Answer:

Shruti Srivastva
(x+y+z)2 = x2 + y2 + z2 + 2xy+2yz+2xz

-Answered by Shruti Srivastva On 05 August 2020:05:51:46 PM


Question 204. Asked on :05 August 2020:05:50:02 PM

Write the identity 4?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva
(x+a)(x+b) = x2 (a+b)x + ab

-Answered by Shruti Srivastva On 05 August 2020:05:50:31 PM


Question 205. Asked on :05 August 2020:05:49:05 PM

Write the identity 3?

-Added by Shruti Srivastva Mathematics » Current Electricity

Answer:

Shruti Srivastva

 (a+b)(a-b) = a2-b2

-Answered by Shruti Srivastva On 05 August 2020:05:49:30 PM


Question 206. Asked on :05 August 2020:05:47:49 PM

Write the identity 2?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva

 (a-b)2 = a2 - 2ab + b2

-Answered by Shruti Srivastva On 05 August 2020:05:48:29 PM


Question 207. Asked on :05 August 2020:05:43:22 PM

Proof the identity 1?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva

 (a+b)2=   (a+b)(a+b)

           = a(a+b) + b(a+b)

           = a2 + ab + ba + b2

              = a2 + 2ab + b2

-Answered by Shruti Srivastva On 05 August 2020:05:43:50 PM


Question 208. Asked on :05 August 2020:05:40:52 PM

Write the identity 1?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Answer:

Shruti Srivastva
(a+b)2 = a2 + 2ab + b2

-Answered by Shruti Srivastva On 05 August 2020:05:42:16 PM


Question 209. Asked on :02 June 2020:02:04:49 AM

 The next term in the series 2,5,10,17,26,37,? is

-Added by Master Purushottam Mathematics » Series

Answer:

Shruti Srivastva

 50

-Answered by Shruti Srivastva On 03 June 2020:12:24:19 PM


Answer:

Aman Senapati

Given,

  1. Area of trapezium ABCE = 475 sq.cm
  2. Height = 19 cm.
  3. one side is 4 cm greater than the other.

Area of trapezium = 1/2 ( sum of // sides ) * H

let the // sides of trapezium are x and x + 4.

475 sq.cm = 1/2 ( x + x + 4) * 19cm.

475/19  = 2x + 42 

25 * 2  = 2x + 4

50 - 4 = 2x

46 cm = 2x

46/2 = x

23=x 

x + 4 = 23 + 4 = 27.

∴ // sides of trapezium are 23 cm and 27 cm.

-Answered by Aman Senapati On 25 May 2020:10:02:27 AM


Question 211. Asked on :25 May 2020:08:00:22 AM

 Q-1)Find the area of trapezium PQRS with height PQ where SP=12cm,SR=13cm,QR=7cm?

-Added by Aman Senapati Mathematics » Herons Formula

Answer:

Aman Senapati

Given,

  • PS=12m
  • SR=13m
  • QR=7m

PQRS is a trapezium.

let SUR is a triangle and PQUR is a rectangle.

then SU=PS-QR

       SU=12m-7m

       SU=5m.

By Pythagorous theorm:-

(H sq.)=(P sq.) + (B sq.)

(13m sq.)=(P sq.) + (5m sq.)

169 sq. m=(P sq.) + 25 sq.m

169-25=(P sq.)

144=(P sq.)

√144=P

√12*12=P

12m=P


UR = 12m


According to the property of rectangle ( Opposite side's are equal )

UR=PQ

∴ PQ=12m.

-Answered by Aman Senapati On 25 May 2020:08:46:56 AM


Question 212. Asked on :23 March 2020:07:33:34 AM

 Find the remainder when x*x*x+3x*x+3x+1 is divided by x+1?

-Added by Aman Senapati Mathematics » POLYNOMIALS


Question 213. Asked on :23 March 2020:07:27:04 AM

 Divide (x*x*x)+1 by x+1

-Added by Aman Senapati Mathematics » POLYNOMIALS


Question 214. Asked on :20 February 2020:08:15:19 PM

In the given figure, we have AB || CD || EF. If AB = 6 cm, CD = x cm, EF = 10 cm, BD = 4 cm and DE = y cm, Calculate the values of x and y.

-Added by Master Mind Mathematics » Triangles


Answer:

Master Mind

-Answered by Master Mind On 19 February 2020:04:27:15 PM


Question 216. Asked on :16 February 2020:03:00:47 PM

 If S is the sample space of random experiment then p (S).

-Added by Khushi Chauhan Mathematics » Probablity

Answer:

A??k Pal
After the experiment, the result of the random experiment is known. An outcome is a result of a random experiment. The set of all possible outcomes is called the sample space. Thus in the context of a random experiment, the sample space is our universal set.

-Answered by A??k Pal On 17 February 2020:03:01:06 PM


Question 217. Asked on :25 December 2019:10:06:08 PM

If the perimeter of a sector of a circle of radius 6.5 cm is 29 cm,then it's area is______cmsquare

-Added by Dhrumil Sheth Mathematics » Ch 12

Answer:

priyanshu kumar

 52 cm square.


-Answered by priyanshu kumar On 15 January 2020:11:22:33 AM


Question 218. Asked on :14 December 2019:08:13:05 PM

 What is the name of the calender which is based on moon?

-Added by Aman Senapati Mathematics » Star And Solar System

Answer:

Rohit Rajput

 lunar calender.


-Answered by Rohit Rajput On 29 December 2019:10:23:39 AM


Question 219. Asked on :16 October 2019:08:07:00 PM

 Which is the smallest number which is divisible by 1to10 and remainder is 0?

-Added by Himanshi Verma Mathematics » G.K

Answer:

Nishant Verma

 2520 is the smallest number which is divisible by 1to 10 and remainder is 0.


-Answered by Nishant Verma On 17 October 2019:02:30:51 PM


Question 220. Asked on :10 October 2019:07:06:18 PM

 Who is father of trignometry ?

-Added by Aarohi Chauhan Mathematics » Introduction To Trignometry

Answer:

priyanshu kumar
Hipparchus.

-Answered by priyanshu kumar On 12 October 2019:04:12:31 PM


Question 221. Asked on :07 October 2019:05:01:00 PM

The price of sugar gets decreased by 25% by how much percent can the consumption of sugar be increased in the same expenditures.  

-Added by Master Mind Mathematics » Comparing Quantities

Answer:

Rohit Rajput

Step-by-step explanation:

Let the price of rs. 100

and the consumption be 100x

If it's price decreased by 25 %

then new price = 100-(25/100×100)

= 100-25

=75

then at same price ,it's consumption will be 75x

Original consumption = 100x

Net percent increase = 100-75

= 25x

Now , percent increase

=net increase /100×(new consumption)

= 25/100×75

= 18.75 %

-Answered by Rohit Rajput On 24 October 2019:10:15:03 AM


Question 222. Asked on :07 October 2019:11:36:04 AM

 Find the value of “x” in the equation 2a2 + 2xa + 5x + 10 if (a + x) is one of its factors.

-Added by Himanshi Verma Mathematics » POLYNOMIALS

Answer:

Master Purushottam

 Let f(a) = 2a2 + 2xa + 5x + 10

As (a + x) is a factor of 2a2 + 2xa + 5x + 10, f(-x) = 0

So, f(-x) = 2x2 – 2x2 – 5x + 10 = 0

Or, -5x + 10 = 0

Thus, x = 2


-Answered by Master Purushottam On 07 October 2019:09:09:32 PM


Question 223. Asked on :07 October 2019:11:34:52 AM

 How many zeros does the polynomial (x – 3)2 – 4 can have? Also, find its zeroes.

-Added by Himanshi Verma Mathematics » Polynomials

Answer:

Himanshi Verma

Given equation is (x – 3)2 – 4

Now, expand this equation.

=> x2 + 9 – 6x – 4

= x2 – 6x + 5

As the equation has a degree of 2, the number of zeroes it will have is 2.

Now, solve x2 – 6x + 5 = 0 to get the roots.

So, x2 – x – 5x + 5 = 0

=> x(x-1) -5(x-1) = 0

=> (x-1)(x-5)

So, the roots are 1 and 5.


-Answered by Himanshi Verma On 07 October 2019:11:36:47 AM


Question 224. Asked on :07 October 2019:11:32:08 AM

  Find the quadratic polynomial if its zeroes are 0, √5.

-Added by Himanshi Verma Mathematics » Polynomials

Answer:

Himanshi Verma

 A quadratic polynomial can be written using the sum and product of its zeroes as:

x2 +(α + β)x + αβ = 0

Where α and β are the roots of the equation.

Here, α = 0 and β = √5

So, the equation will be:

x2 +(0 + √5)x + 0(√5) = 0

Or, x2 + √5x = 0

-Answered by Himanshi Verma On 07 October 2019:11:34:36 AM


Question 225. Asked on :07 October 2019:11:29:31 AM

  Find the value of “p” from the equation x2 + 3x + p, if one of the zeroes of the polynomial is 2.

-Added by Himanshi Verma Mathematics » Polynomials

Answer:

Himanshi Verma

As 2 is the zero of the polynomial,

x2 + 3x + p, for x = 2

Now, put x = 2

22 + 3(2) + p = 0

=> 4 + 6 + p = 0

Or, p = -10

-Answered by Himanshi Verma On 07 October 2019:11:30:47 AM


Question 226. Asked on :07 October 2019:11:23:47 AM

Prove CosA1+sinA+1+sinAcosA=2secA

-Added by Himanshi Verma Mathematics » Introduction To Trignometry

Answer:

Himanshi Verma
LHS =cosA/(1+sinA) +(1+sinA)/cosA
={cos²A +(1+sinA)²}/cosA.(1+sinA)
={cos²A+1+sin²A+2sinA}/cosA.(1+sinA)
use sin²∅ +cos²∅ =1
=(1+1+2sinA)/cosA(1+sinA)
=2(1+sinA)/cosA(1+sinA)
=2/cosA
=2secA = RHS

-Answered by Himanshi Verma On 07 October 2019:11:28:21 AM


Question 227. Asked on :07 October 2019:11:16:08 AM

  Find the value of (sin°45- cos°45)

-Added by Himanshi Verma Mathematics » Introduction To Trignometry

Answer:

Master Purushottam
Sin 45°=1/√2
cos 45°=1/√2

Sin 45 + cos 45=
1/√2+1/√2=
2/√2=
2√2/2=
√2

-Answered by Master Purushottam On 07 October 2019:08:49:05 PM


Question 228. Asked on :01 October 2019:06:14:01 PM

 what is formula of distance?

-Added by Shivang Gupta Mathematics » Coodinate Geomertry

Answer:

priyanshu kumar
Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to find the distance between any two points.

-Answered by priyanshu kumar On 05 October 2019:03:52:57 PM


Question 229. Asked on :30 September 2019:10:14:41 AM

Perimeter of square is.......

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma

 4xsquare


-Answered by Nishant Verma On 08 October 2019:09:25:52 AM


Question 230. Asked on :30 September 2019:10:13:16 AM

What is circumference of Circle?

-Added by Akki chauhan Mathematics » Gk

Answer:

priyanshu kumar
πrh

-Answered by priyanshu kumar On 30 September 2019:10:42:01 AM


Question 231. Asked on :30 September 2019:10:12:51 AM

What is perimeter of Square?

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma
4*side.

-Answered by Nishant Verma On 08 October 2019:09:26:35 AM


Question 232. Asked on :30 September 2019:10:12:25 AM

WHat is area of Square?

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma
side * side

-Answered by Nishant Verma On 08 October 2019:09:26:46 AM


Question 233. Asked on :30 September 2019:10:11:22 AM

What is formula of Total surface area of Hemisphere?

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma
(3r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:26:57 AM


Question 234. Asked on :30 September 2019:10:10:34 AM

What is curved surface area of Hemisphere?

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma
 (2r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:27:07 AM


Question 235. Asked on :30 September 2019:10:09:29 AM

What is surface area of Sphere?

-Added by Akki chauhan Mathematics » Formula

Answer:

Nishant Verma
(4r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:27:28 AM


Question 236. Asked on :30 September 2019:10:06:39 AM

What is curved surface are of cone?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
(rl) sq. units.

-Answered by priyanshu kumar On 30 September 2019:10:45:03 AM


Question 237. Asked on :30 September 2019:10:06:06 AM

What is volume of Cone?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
 r2h cubic units.

-Answered by priyanshu kumar On 30 September 2019:10:45:24 AM


Question 238. Asked on :30 September 2019:10:03:38 AM

What is Diagonal of cube?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
 Diagonal = 3a units

-Answered by priyanshu kumar On 30 September 2019:10:46:56 AM


Question 239. Asked on :30 September 2019:10:03:01 AM

What is Surface Area of Cube?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
 6a2 sq. units.

-Answered by priyanshu kumar On 30 September 2019:10:47:09 AM


Question 240. Asked on :30 September 2019:10:02:26 AM

What is volume of Cube?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
a3 cubic units.

-Answered by priyanshu kumar On 30 September 2019:10:47:49 AM


Question 241. Asked on :30 September 2019:10:00:06 AM

What is Volume of Cuboid?

-Added by Akki chauhan Mathematics » Formula

Answer:

priyanshu kumar
(l x b x h) cubic units

-Answered by priyanshu kumar On 30 September 2019:10:48:32 AM


Question 242. Asked on :30 September 2019:09:57:29 AM

What is Mode?

-Added by Akki chauhan Mathematics » Gk

Answer:

priyanshu kumar
Mode - The mode is the number that appears the most. There are a few tricks to remember about mode:

-Answered by priyanshu kumar On 30 September 2019:10:49:12 AM


Question 243. Asked on :30 September 2019:09:57:06 AM

What is MEdian?

-Added by Akki chauhan Mathematics » STATISTICS

Answer:

priyanshu kumar
Median - The median is the middle number of the data set. It is exactly like it sounds. To figure out the median you put all the numbers in order (highest to lowest or lowest to highest) and then pick the middle number. If there is an odd number of data points, then you will have just one middle number. If there is an even number of data points, then you need to pick the two middle numbers, add them together, and divide by two. That number will be your median.

-Answered by priyanshu kumar On 30 September 2019:10:49:27 AM


Question 244. Asked on :30 September 2019:09:56:38 AM

What is Mean?

-Added by Akki chauhan Mathematics » STATISTICS

Answer:

priyanshu kumar
Mean - When people say "average" they usually are talking about the mean. You can figure out the mean by adding up all the numbers in the data and then dividing by the number of numbers. For example, if you have 12 numbers, you add them up and divide by 12. This would give you the mean of the data.

-Answered by priyanshu kumar On 30 September 2019:10:50:00 AM


Question 245. Asked on :28 September 2019:07:17:58 AM

 How it is possible?

999+888+777 = 999

-Added by Rohit Rajput Mathematics » Brain Teaser

Answer:

priyanshu kumar

7+7+8+9+9+9 = 49

8+7+4 = 19.        (4 carry)

8+1  = 9.              (1 carry)

So, 999+888+777 =999

-Answered by priyanshu kumar On 30 September 2019:11:53:24 AM


Question 246. Asked on :25 September 2019:03:05:35 PM

 If 60% 1200 then the value of x

-Added by Sohail alam Mathematics » All Question

Answer:

Shivang Gupta

 85%

-Answered by Shivang Gupta On 05 October 2019:03:14:19 PM


Question 247. Asked on :23 September 2019:09:47:39 AM

The two opposite vertices of a square are (-1,2)and (3,2).find the coordinate of the two other vertices.

-Added by Rohit Rajput Mathematics » Cooridinate Triangle

Answer:

Suraj Kumar

Let ABCD be a square and A (–1, 2) and C (3, 2) be the given vertices. Let the coordinates of vertex B be (x, y).

AB = BC  (As ABCD is a square)

AB2 = BC2

[x – (–1)] 2 + (y – 2)= (x – 3)2 + (y – 2)

(x + 1)2 = (x – 3)2

2 + 2x + 1 = x – 6x + 9

2x + 6x = 9 – 1

8x = 8

x = 1

In ΔABC, we have:

AB2 + BC2 = AC2  (Pythagoras theorem)

2AB2 = AC2  (Since, AB = BC)

2[(x – (–1))2 + (y – 2)2] = (3 – (–1))2 + (2 – 2)2

2[(x + 1)2 + (y – 2)2] = (4)2 + (0)2

2[(1 + 1)2 + (y – 2)2] = 16  ( x = 1)

2[ 4 + (y – 2)2] = 16

8 + 2 (y – 2)2 = 16

2 (y – 2)2 = 16 – 8 = 8

(y – 2)2 = 4

y – 2 = ± 2

y – 2 = 2 or y – 2 = –2

y = 4 or y = 0

Thus, the other two vertices of the square ABCD are (1, 4) and (1, 0).

-Answered by Suraj Kumar On 07 November 2019:08:37:47 AM


Question 248. Asked on :23 September 2019:09:44:14 AM

 find the center of circle passing though the points (6,-6),(3,-7)and (3,3).

-Added by Rohit Rajput Mathematics » Cooridinate Triangle

Answer:

priyanshu kumar

let O (x, y) is the point of circle

if three given points A (3,-7) B (3,3) and C (6,-6)

we know distance between circumference and center is always same. i.e radius .
now,
OA^2=OB^2=OC^2

OA^2=OB^2
=>(x-3)^2+(y+7)^2=(x-3)^2+(y-3)^2

=>(x-3)^2-(x-3)^2=(y-3)^2-(y+7)^2

=> 0=(2y+4)(3)

=> y= -2
now again ,
OB^2=OC^2
(x-3)^2+(y-3)^2=(x-6)^2+(y+6)^2
put y=-2

=>(x-3)^2+(-2-3)^2=(x-6)^2+(-2+6)^2

=>(x-3)^2-(x-6)^2=16-25

=>(2x-9)(3)=-9

=> 2x= -3+9=6

=> x=3

hence center co-ordinate is (3,-2)

-Answered by priyanshu kumar On 02 October 2019:12:31:07 PM


Answer:

priyanshu kumar

Let A(0,-1) , B(2,1) ,C(0,3) are vertices of the


Triangle.

D , E , F are midpoints of BC , CA and AB.

*************************************************

The midpoint of the line segment joining

the points (x1,y1) and (x2 , y2 ) is P( x , y ).

x = ( x1 + x2 )/2 ;

y = ( y1 + y2 )/2

*************************************************

Now ,

i ) mid point of B(2,1) , C(0,3) is D( x , y )

x = ( 2 + 0 )/2 = 1

y = ( 1 + 3 )/2 = 2

D = ( 1 , 2 )

Similarly ,

ii ) mid point of C( 0,3) , A(0,-1) = E( 0,1)

iii ) mid point of A(0,-1), B(2,1) = F(1,0)

*************************************************
The area of the triangle formed by the

vertices ( x1,y1 ), ( x2, y2 ) , ( x3 , y3 ) is

1/2|x1 ( y2 - y3 )+x2( y3 - y1 ) +x3( y2 - y1) |

*********************************************

iv ) Area of the triangle A( 0, -1), B( 2 , 1 )

C( 0 ,3 ) is

1/2|0( 1 - 3 ) + 2( 3 + 1 ) + 0 ( -1-1 ) |

= 1/2 | 8 |

= 4 sq units

v ) Area of the triangle D( 1,2 ) , E( 0 , 1 ),

and F( 1 , 0 ) is

1/2 | 1( 1 - 0 ) + 0( 0 - 2 ) + 1( 2 - 1 ) |

= 1/2 | 2 |

= 1 sq units

vi )

ratio = ( area ∆ABC )/( area ∆DEF )

= 4/1

= 4 : 1

-Answered by priyanshu kumar On 02 October 2019:12:32:50 PM


Question 250. Asked on :07 September 2019:05:10:32 PM

NCERT solutions for class 10 maths solved by subject experts from latest editions books and as per NCERT(CBSE) Guidelines

-Added by Reddy cbse Mathematics » NCERT Solutions For Class 10 Maths

Answer:

priyanshu kumar
What is your question

-Answered by priyanshu kumar On 03 October 2019:01:59:58 PM


Question 251. Asked on :07 September 2019:08:51:52 AM

 What is full form of HCF

-Added by Sohail alam Mathematics » Maths

Answer:

Akki chauhan
Highest common factor.

-Answered by Akki chauhan On 13 September 2019:09:38:11 AM


Question 252. Asked on :02 September 2019:03:04:03 PM

 Q what is the area of square when side is 90cm?

-Added by Shruti Srivastva Mathematics » Maths

Answer:

Shruti Srivastva
8100 cm sq.

-Answered by Shruti Srivastva On 02 September 2019:03:06:18 PM


Question 253. Asked on :01 September 2019:12:21:47 PM

 Who discovered bacterial transformation?

-Added by Akki chauhan Mathematics » Arithmetic Progressions

Answer:

Nishant Verma
Frederick Griffith.

-Answered by Nishant Verma On 02 September 2019:11:45:39 AM


Question 254. Asked on :01 September 2019:12:20:02 PM

Which term is 78 of A.P 3,8,13,18...................

-Added by Akki chauhan Mathematics » Arithmetic Progressions

Answer:

Nishant Verma
78 is the 16th term of the given A.P. 16th term of A.P : 3,8,13,18,is 78.

-Answered by Nishant Verma On 02 September 2019:10:23:45 AM


Question 255. Asked on :30 August 2019:03:52:44 PM

 write the formula of C.I.?

-Added by Suman Kumari Mathematics » Maths

Answer:

Nishant Verma
CI formula
P = the principal amount. r = the annual interest rate (decimal) n = the number of times that interest is compounded per unit t. t = the time the money is invested or borrowed for.

-Answered by Nishant Verma On 30 August 2019:03:54:16 PM


Question 256. Asked on :30 August 2019:03:12:53 PM

Pythagoras Theorem: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

-Added by Prince Rawat Mathematics » Triangle

Answer:

Nishant Verma
Pythagorean Theorem. In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

-Answered by Nishant Verma On 30 August 2019:03:56:50 PM


Answer:

Nishant Verma
If in two trianglessides of one triangle are proportional to the sides of the other trianglethen their corresponding angles are equal and hence the two triangles are similar. This is also called SSS (Side-Side-Sidecriterion.

-Answered by Nishant Verma On 30 August 2019:03:57:22 PM


Question 258. Asked on :30 August 2019:03:11:19 PM

If a line divides any of the two sides of a triangle in the same ratio, then that line is parallel to the third side.

-Added by Prince Rawat Mathematics » Triangle

Answer:

Nishant Verma
If a line divides any two sides of a triangle in the same ratio,then the line is parallel to the third side.

-Answered by Nishant Verma On 30 August 2019:03:57:52 PM


Answer:

Akki chauhan

Let a ΔABC in which a line DE parallel to SC intersects AB at D and AC at E.To prove DE divides the two sides in the same ratio. 

-Answered by Akki chauhan On 30 August 2019:08:51:32 PM


Question 260. Asked on :28 August 2019:09:45:10 AM

Find the ratio in which the line segment joining A(1,-5) B(6,-8) is divided by the X-Axis. Also find the coordinates of the point of division.

-Added by Akki chauhan Mathematics » Coordinate Geometry

Answer:

Akki chauhan

If the ratio in which P divides AB is k:1 , then the co-ordinates of the point P will be


 

 

-Answered by Akki chauhan On 28 August 2019:09:47:46 AM


Question 261. Asked on :26 August 2019:07:47:56 PM

Find the distance between the following pairs of points:

(i) (2,3),(4,1)

-Added by Akki chauhan Mathematics » Coordinate Geometry

Answer:

Akki chauhan

(i) Distance between the two points is given by

-Answered by Akki chauhan On 26 August 2019:07:58:00 PM


Question 262. Asked on :25 August 2019:03:25:31 PM

 Find the next  number in the sequence 6,24,60,120.......

-Added by Akki chauhan Mathematics » Maths

Answer:

priyanshu kumar

336.


-Answered by priyanshu kumar On 20 October 2019:04:14:05 PM


Question 263. Asked on :25 August 2019:03:23:16 PM

 Find the next number in the sequence 0,2,24,252......

Please give right answer other wise dont touch this question.

-Added by Akki chauhan Mathematics » Maths

Answer:

Shivang Gupta

0,2,24,252 Adding 1,2,3,4 n 5 respectively, 0+1=1 2+2=4 24+3=27 252+4=256 We get, 1,4,27,256 Now, 1=1^1 4=2^2 27=3^3 256=4^4 So, next no. = 5^5 - 5= 3120 :)

-Answered by Shivang Gupta On 25 August 2019:03:38:16 PM



Question 265. Asked on :24 August 2019:09:16:21 PM

 Find the sum of the first 25 multiples of 7.

-Added by Prince Rawat Mathematics » Arithmetic Progressions

Answer:

Master Mind

The A.P. : 7, 14, 21, .............. 

Now We have to find 7 + 14 + 21 + ........... 25 terms

∴ a = 7, d = 7 n = 25 

Sn = n2 {2a + (n - 1)d}

S25 = 252 {2 × 7 + (25 - 1)7}

      = 252 {14 + (24)7}

      = 252 (14 + 168)

      = 252 × 182

      = 25 × 91 

      = 2275 Answer

Hence the sum of first 25 multiple of 7 is 2275.

-Answered by Master Mind On 24 August 2019:11:38:04 PM


Question 266. Asked on :24 August 2019:09:15:05 PM

 Find the sum of n terms of A.P. 2+4+6+...... .

-Added by Prince Rawat Mathematics » Arithmetic Progressions

Answer:

Akki chauhan
Answer:30,240

Step-by-step explanation:

Let a be the first term and d the common difference

          A=2

        D=4-2=2

       So, 15th term=a+(15-1)*d

       =2+(14*2)

       2+28

       =30

Sum of first 15 term=

n/2(a+an),where n=number

of terms. 

=15/2(2+30)

=15/2(32)

=15*16

=240


-Answered by Akki chauhan On 24 August 2019:09:27:13 PM


Question 267. Asked on :24 August 2019:09:11:37 PM

Find the sum of the A.p.1+3+5+7+.....+199.

-Added by Prince Rawat Mathematics » Arithmetic Progressions

Answer:

Akki chauhan
an = a+ (n-1)d
199 = 1 + (n-1)2
198 = (n-1)2
198/2 = n - 1
99 = n - 1
n = 100

No: of terms = n = 100
Sum is 100.
Sum = Sn

Sn = n/2 [a + an]
     = 100/2 [ 1 + 199]
     = 50 [ 200]
     = 10000

-Answered by Akki chauhan On 27 August 2019:09:29:28 AM


Question 268. Asked on :24 August 2019:08:27:55 PM

 Find the sum of the first 27 multiples of 6 ?

-Added by Gunnaj sheikh Mathematics » Ch 5

Answer:

Master Purushottam

 2268

-Answered by Master Purushottam On 24 August 2019:09:29:41 PM


Question 269. Asked on :21 August 2019:09:36:36 AM

 In a right triangle the square of the hypotenuse is equal to the sum of the squares of the other two sides.

-Added by Prince Rawat Mathematics » Triangle

Answer:

Suraj Kumar
Theorem 6.8 : In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

-Answered by Suraj Kumar On 11 December 2019:08:33:38 AM


Answer:

Suraj Kumar
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points ,then theother two sides are divided in the same ratio

.Image result for If a line is drawn parallel to one side of a triangle to intersect the other two sides in point, the other two sides are divided in the same ratio.

-Answered by Suraj Kumar On 11 December 2019:08:33:46 AM


Question 271. Asked on :19 August 2019:09:49:02 AM

 Who discovered the zero?

-Added by Akki chauhan Mathematics » Number

Answer:

Akki chauhan

 Aryabhatta discovered zero.

-Answered by Akki chauhan On 19 August 2019:09:50:45 AM


Question 272. Asked on :18 August 2019:06:31:17 PM

X-2=7


-Added by Master Purushottam Mathematics » One Variable In Linear Equation

Answer:

Akki chauhan

 X-2=7

 X=7+2

 X=9

-Answered by Akki chauhan On 18 August 2019:08:35:07 PM


Question 273. Asked on :17 August 2019:05:57:38 PM

 Find a quadratic polynomial , The sum and product of whose zeroes are -3 and 2 respectively.

-Added by Khushi Chauhan Mathematics » POLYNOMIALS

Answer:

Himanshi Verma

 Let the quadratic polynomial be ax2+bx+c=0 and its zeroes be α and β.

sum of zeroes     α+β = -3 = -b/a 

product of zeroes      αβ = 2= c/a

If a=1   then b=3,  c=2

So, the quadratic polynomial is x2+3x+2.

-Answered by Himanshi Verma On 18 August 2019:11:00:35 AM


Question 274. Asked on :17 August 2019:05:50:41 PM

 If LM||CB and LN||CD prove that AM/AB =AN/AD.

-Added by Khushi Chauhan Mathematics » Chapter 6

Answer:

Himanshi Verma

 By Thales theorem or basic propositionality Theorem

IN∆ABC
LM||BC so by B.P.T
AL/AC=AM/AB-----------(1)
IN∆ADC
AL/LC=AN/AD------(2)
from equation 1 &2 L.H.S is same so R.H.S will also same.
so
AM/AB=AN/AD

-Answered by Himanshi Verma On 18 August 2019:10:58:35 AM


Question 275. Asked on :17 August 2019:09:38:34 AM

 What is mean , mode and Median?

-Added by Akki chauhan Mathematics » Stastics

Answer:

Himanshi Verma

 Mean, Mode, Median are the measurment of central tendency.  mean and mode cann't be shown on graph but median can be shown on the graph.

-Answered by Himanshi Verma On 17 August 2019:10:34:55 AM


Question 276. Asked on :17 August 2019:09:27:38 AM

 What is the form of Arithmetic Progressions? 

-Added by Akki chauhan Mathematics » Arithmetic Progressions

Answer:

Himanshi Verma

 The general form of an Arithmetic progression is a, a+1, a+2, a+3.....

-Answered by Himanshi Verma On 17 August 2019:10:41:29 AM


Question 277. Asked on :17 August 2019:09:24:51 AM

What is Arithmetic Progressions?

-Added by Akki chauhan Mathematics » G.

Answer:

Himanshi Verma
A sequence of numbers in which each differs from the preceding one by a constant quantity.examples are 1,2,3,4 etc.

-Answered by Himanshi Verma On 18 August 2019:10:41:56 AM


Question 278. Asked on :17 August 2019:09:22:47 AM

 Prove that √2 is irrational?

-Added by Akki chauhan Mathematics » Real Numbers

Answer:

Himanshi Verma
Let √2 be a rational number 

Therefore, √2= p/q  [ p and q are in their least terms i.e., HCF of (p,q)=1 and q ≠ 0

On squaring both sides, we get 
                   p²= 2q²           ...(1)
Clearly, 2 is a factor of 2q²
⇒ 2 is a factor of p²          [since, 2q²=p²]
⇒ 2 is a factor of p

 Let p =2 m for all m ( where  m is a positive integer)

Squaring both sides, we get 
            p²= 4 m²          ...(2)
From (1) and (2), we get 
           2q² = 4m²      ⇒      q²= 2m²
Clearly, 2 is a factor of 2m²
⇒       2 is a factor of q²          [since, q² = 2m²]
⇒       2 is a factor of q 

Thus, we see that both p and q have common factor 2 which is a contradiction that H.C.F. of (p,q)= 1

 Therefore, Our supposition is wrong

Hence √2 is not a rational number i.e., irrational number.

-Answered by Himanshi Verma On 18 August 2019:11:09:55 AM


Question 279. Asked on :22 July 2019:07:46:58 PM

 S and T are points on sides PR and QR of ΔPQR such that ∠P= ∠RTS. Show that ΔRPQΔRTS.

-Added by Himanshi Verma Mathematics » Traingles

Answer:

Himanshi Verma

-Answered by Himanshi Verma On 23 July 2019:07:52:25 PM


Question 280. Asked on :18 July 2019:07:27:12 PM

 If a line intersects sides AB and AC of a ΔABC at D and E respectively and is a parallel to BC, prove that AD/AB= AE/AC.

-Added by Himanshi Verma Mathematics » Triangles

Answer:

Himanshi Verma

-Answered by Himanshi Verma On 18 July 2019:09:05:33 PM


Question 281. Asked on :10 July 2019:11:49:11 PM

The first term of an A.P. is 6. The sum of first 6 terms is 66. Find it's 6th term.

-Added by ATP Admin Mathematics » Arithmetic Progressions

Answer:

Master Mind

Given: a1 = 6, S= 66 

using Formula: Sn = n2 (a + l

Step by Step Explanation: 

S6 = 62 ( 6 + a6)

66 = 3(6 + 6th term) 

(6 + 6th term) = 663 = 22

6th term = 22 - 6 

6th term = 16 Answer 

-Answered by Master Mind On 11 July 2019:09:08:06 PM


Question 282. Asked on :09 July 2019:11:51:22 PM

Solve the equation 6(7b - 4) = 60 for b. 

-Added by ATP Admin Mathematics » Algebra

Answer:

ATP Admin

Given equation is 6(7b - 4) = 60  Step by Step explanation

7b - 4 = 606 

7b - 4 = 10 

7b = 10 + 4 

7b = 14 

b = 147 = 2 Answer

-Answered by ATP Admin On 09 July 2019:11:53:03 PM


Question 283. Asked on :09 July 2019:07:05:00 PM

If the sum of nth terms of an A.P. is given by 4n2 - 7n. Find 

(i) Sum of 23 terms 

(ii) 15th term

(iii) nth term

-Added by ATP Admin Mathematics » Arithmetic Progressions

Answer:

Master Mind

Given:Sn = 4n2 - 7n 

Step by step explanation: 

(i) Sum of 23 terms 

Sn = 4n2 - 7n ............. (i

Replace n by 23 we have,

S23 = 4(23)2 - 7(23) 

= 4 × 529 - 161

= 2116 - 161 

= 1955 Answer

(ii) 15th term 

a15 = S15 - S14 

S15 = 4(15)2 - 7(15) = 4 × 225 - 105 = 900 - 105 = 795 

S14 = 4(14)2 - 7(14) = 4 × 196 - 98 = 784 - 98 = 686

Now, a15 = S15 - S14 

              = 795 - 686 

              = 109 Answer

(iii) nth term 

an = Sn - Sn-1

Given, Sn = 4n2 - 7n 

Replace n by n-1 we have 

Sn-1 = 4(n-1)2 - 7(n-1) 

       = 4(n2 - 2n + 1) - 7n + 7

       = 4n2 - 8n + 4 - 7n + 7 

       = 4n2 - 15n + 11 ............. (ii) 

Now Applying equation (i) and (ii) in formula an = Sn - Sn-1 

an = (4n2 - 7n) - (4n2 - 15n + 11) 

    = 4n2 - 7n - 4n2 + 15n - 11

    = 8n - 11 

Therefore, an = 8n - 11 Answer  

*******************************

-Answered by Master Mind On 11 July 2019:09:42:19 PM


Question 284. Asked on :09 July 2019:06:56:05 PM

Prove the identity: 


-Added by ATP Admin Mathematics » Trigonometry

Answer:

Harshita Rathore

 Cos

-Answered by Harshita Rathore On 24 August 2019:02:57:10 PM


Question 285. Asked on :09 July 2019:06:53:37 PM

Find the nature of quadratic equation x2 + 3x + 7.  

-Added by ATP Admin Mathematics » Quadratic Equations

Answer:

Himanshi Verma

 x2+ 3x+7 

This equation is of the form of ax2+bx+c=0

so, a=1,     b=3,    c=7

b2+4ac = 3×3 - 4×1×5

           = 9 - 28 

            = 19 

∴  19 > 0

So, the given equation has two real roots.

-Answered by Himanshi Verma On 18 July 2019:07:35:08 PM


Question 286. Asked on :08 July 2019:10:36:51 PM

x and y are connected parametrically by the equation x = 2at2, y = at4 without eleminating the parameter.  

Find dydx .

-Added by ATP Admin Mathematics » Continuity And Differentiability

Answer:

Master Purushottam

 

-Answered by Master Purushottam On 08 July 2019:10:58:57 PM


Question 287. Asked on :08 July 2019:09:55:52 PM

In the Given fig. DE ‖ AC and DF ‖AE.  

BFFE = BEEC .


-Added by ATP Admin Mathematics » Triangles

Answer:

ATP Admin

-Answered by ATP Admin On 08 July 2019:10:45:29 PM


Question 288. Asked on :08 July 2019:04:56:29 PM

 Find the sum of the first 40 positive integer divisible by 6.

-Added by Himanshi Verma Mathematics » A.p

Answer:

Akki chauhan

 This is an AP a=6,d=6, and n=40

Using formula,  

Sn = n2 [2a+(n-1)d]


S40= 402 [2*6+(40-1)6]

S40=20(12+234)

S40=20*246

S40=4920

-Answered by Akki chauhan On 18 July 2019:10:26:06 AM


Question 289. Asked on :17 June 2019:11:25:45 PM

Show that one and only one out of n, n+2 or n+4 is divisible by 3, where n is any positive integer. 

-Added by ATP Admin Mathematics » Real Numbers

Answer:

ATP Admin

Solution: Using Euclid's division lemma any positive integer can be written in the form of a = bq + r where r = 0, 1, 2 ...... and q is quotients. 

Let the number which is divisible by 3 be 3q + 0 or 3q + 1 or 3q + 2 where [0 <= r < b] 

Now n = 3q or n = 3q + 1 or n = 3q + 2 

Case I, 

When n = 3q  .......... (i) 

⇒ n = 3(q) where n is divisible by 3

Adding 2 both sides in equ. (i) 

We have,

    n + 2 = 3q + 2 Where n + 2 is not divisible by 3 

Now adding 4 both side in equ. (i) 

We have,

    n + 4 = 3q + 4 Where n + 4 is not divisible by 3 


Case II  

  Taking n = 3q + 1 ........ (ii) where n is not divisible by 3

Adding 2 both sides in equ. (ii) 

We have, 

n + 2 = 3q + 1 + 2 = 3q + 3 

n + 2 = 3(q + 1) where n + 2 is divisible by 3 

Now adding 4 both sides in equ. (ii) 

n + 4 = 3q + 1 + 4 = 3q + 5 where n + 4 is not divisible by 3 


Case III  

taking n = 3q + 2 .... (iii) where n is not divisible by 3 

Adding 2 both sides in equ. (iii) 

We have,

n + 2 = 3q + 2 + 2 = 3q + 4 where n + 2 is not divisible by 3

Now adding 4 both sides in equ. (iii) 

We have, 

n + 4 = 3q + 2 + 4 = 3q +6 

n + 4 = 3(q + 2) where n + 4 is divisible by 3 

Hence in all these three cases we have seen that either one and only one n or n + 2 or n + 4 is divisible by 3. 

 

 



-Answered by ATP Admin On 17 June 2019:11:28:43 PM


Question 290. Asked on :13 May 2019:10:29:43 AM

 7 और  9 के बीच 10 परिमेय संख्या लिखे ?


-Added by ravi varma Mathematics » Maths

Answer:

Himanshi Verma

 The rational numbers between 7 and 9 are 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 90. 

-Answered by Himanshi Verma On 14 May 2019:11:11:27 AM


Question 291. Asked on :08 May 2019:10:19:35 AM

x का मान  ज्ञात कीजिए  2x-1=14-x?

-Added by ravi varma Mathematics » Maths

Answer:

Jyoti Srivastva

 2x-1=14-x

2x+x=14+1

3x=15

x=15/3 

x=5

-Answered by Jyoti Srivastva On 07 July 2019:10:05:52 PM


Question 292. Asked on :08 May 2019:10:14:22 AM

 क्या शुन्य परिमेय संख्या है ? 

-Added by Hitesh kumar Mathematics » Mathematics

Answer:

Himanshi Verma

 yes zero is a rational number.

-Answered by Himanshi Verma On 14 May 2019:11:23:16 AM


Question 293. Asked on :08 May 2019:10:15:06 AM

4z+3=6+2z 

-Added by ravi varma Mathematics » Maths

Answer:

Jyoti Srivastva

 4z+3=6+2z

4z-2z=6-3

2z=3

z=3/2

-Answered by Jyoti Srivastva On 07 July 2019:10:11:51 PM


Question 294. Asked on :08 May 2019:09:55:15 AM

5 और 6 के बीच दो  परिमेय संख्या लिखो ?

-Added by Hitesh kumar Mathematics » Math

Answer:

Himanshi Verma

 The rational number are 16, 17.

-Answered by Himanshi Verma On 14 May 2019:11:16:10 AM


Question 295. Asked on :22 April 2019:09:43:52 AM

 Why study of density is important for a science student?

-Added by Nitish kumar Mathematics » ORGANISATION IN THE LIVING WORLD

Answer:

rocki kumar

 Density is important because it affects whether objects will float or sink. It is animportant property to consider when building things like ships and hot air balloons. ... He realized that the amount of water that spilled was equal in volume to the space that his body occupied.

-Answered by rocki kumar On 08 May 2019:08:23:43 AM


Question 296. Asked on :21 April 2019:10:53:53 AM

What is activity series ? 

-Added by Nitish kumar Mathematics » Types Of Chemical Reactions

Answer:

Himanshi Verma

 Arrangement of metals in order of decreasing reactivities in vertical column is called activity series.

-Answered by Himanshi Verma On 21 April 2019:10:58:07 AM


Question 297. Asked on :21 April 2019:10:51:49 AM

 what happens when Mg ribbon is burnt in oxygen?

-Added by Nitish kumar Mathematics » Types Of Chemical Reactions

Answer:

Himanshi Verma

 

When magnesium ribbon is burnt in oxygen it burns with a dazzling flame and gives a white magnesium oxide.


-Answered by Himanshi Verma On 21 April 2019:10:59:16 AM


Question 298. Asked on :21 April 2019:10:45:16 AM

 what is oxidation?

-Added by Nitish kumar Mathematics » Types Of Chemical Reactions

Answer:

Himanshi Verma

 The reaction in which addition of oxygen and removal of hydrogen is called oxidation.

-Answered by Himanshi Verma On 21 April 2019:11:03:26 AM


Question 299. Asked on :19 April 2019:08:34:46 AM

 Given that HCF (306,657) =9 find LCM (306,657).

-Added by Prince Rawat Mathematics » Real Number

Answer:

Himanshi Verma
Product of LCM and HCF= Product of two numbers

9×LCM = 306×657

9×LCM = 201042

LCM   = 22338

-Answered by Himanshi Verma On 21 April 2019:10:32:51 AM


Question 300. Asked on :19 April 2019:08:23:46 AM

 Check whether the first polynomials is a factors of the second polynomials by dividing the second polynomials by the first polynomials.

-Added by Prince Rawat Mathematics » POLYNOMIALS

Answer:

Akki chauhan

 what is the polynomials.

-Answered by Akki chauhan On 24 August 2019:03:13:10 PM


Question 301. Asked on :19 April 2019:08:21:00 AM

Prove that 5
 is irrational.

-Added by Prince Rawat Mathematics » Real Number

Answer:

Himanshi Verma

Let us assume that √5 is rational 

Then √5 =  

(a and b are co primes, with only 1 common factor and b≠0) 

⇒ √5 =  

(cross multiply) 

⇒ a = √5b 

⇒ a² = 5b² -------> α

⇒ 5/a² 

(by theorem if p divides q then p can also divide q²) 

⇒ 5/a ----> 1 

⇒ a = 5c 

(squaring on both sides) 

⇒ a² = 25c² ----> β 

From equations α and β 

⇒ 5b² = 25c²

⇒ b² = 5c² 

⇒ 5/b² 

(again by theorem) 

⇒ 5/b---> 2 


we know that a and b are co-primes having only 1 common factor but from 1 and 2 we can that it is wrong. 

This contradiction arises because we assumed that √5 is a rational number 

∴ our assumption is wrong 

∴ √5 is irrational number.

-Answered by Himanshi Verma On 21 April 2019:11:24:50 AM


Question 302. Asked on :19 April 2019:08:18:18 AM

 Check whether 6n can end digit 0 for any nature number n.

-Added by Prince Rawat Mathematics » Real Number

Answer:

Akki chauhan

 prime factors of 6n 

                = (2*3)n 

                = 2n*3n 

While the number ending with zero have prime factor as 2n*5n 

       Hence, 6n is not end with zero.

-Answered by Akki chauhan On 28 June 2019:09:30:20 AM


Question 303. Asked on :18 April 2019:08:18:35 AM

 Use euclid's division alogrithan to find the HCF of :

(i) 135 and 225 .

-Added by Nitish kumar Mathematics » Real Number

Answer:

Himanshi Verma

  Use Euclid division alogrithan 

 a=bq+r

225=135×1+90

135=90×1+45

90=45×2+0

HCF=45 .

-Answered by Himanshi Verma On 18 April 2019:04:26:31 PM


Answer:

Himanshi Verma

 Suppose, at first the side of the square was a

the area was a^2

now, the side of the square is (a+a★50/100)=a+a/2=3a/2

the area will be, 9a^2/4

so, 9a^2/4-a^2=5a^2/4

we now tell that, after increasing 50%of the side, the area will 5/4 times of the older(a^2).

-Answered by Himanshi Verma On 06 April 2019:06:44:55 PM


Question 305. Asked on :31 March 2019:01:06:03 PM

If the length of a rectangle is increased by 60% by what per cent would the width have to be decreased to maintain the same area?

-Added by Master Purushottam Mathematics » Mensuration

Answer:

Himanshi Verma




% Decrease

-Answered by Himanshi Verma On 06 April 2019:06:46:28 PM


Question 306. Asked on :31 March 2019:12:59:06 PM

 If the length and breadth of a rectangle plot are increased by 50% and 20% respectively, then the new area is how many times the original area

-Added by Master Purushottam Mathematics » Mensuration

Answer:

Hitesh kumar

  LET THE ORIGINAL LENGTH BE L

AND

ORIGINAL BREATH BE B.

ORIGINAL AREA = LB

LENGTH INCREASED BY 50% = 150 L / 100

BREATH INCREASED BY 20% = 120 B / 100

INCREASED AREA = 150 L X 120 B / 100 X 100

= 18000 LB / 10000

= 1.8 LB

NOW,

1.8 LB / LB = 1.8

CHANGING 1.8 INTO FRACTION.

1.8 = 18/10 = 9/5 

SO,

THE INCREASED AREA WILL BE 9/5 TIMES OF THE ORIGINAL AREA.

-Answered by Hitesh kumar On 13 April 2019:08:31:51 AM


Question 307. Asked on :31 March 2019:12:53:32 PM

The length of diagonal of the square whose area is 16900m2 is: 

-Added by Master Purushottam Mathematics » Mensuration

Answer:

Himanshi Verma

 so let us first consider a square with area x² unit²

so the side is of length √x² = x unit 

so square has angles of 90° so using Pythagoras we  get the length of the diagonal as  = 

√2x

so for this problem the area is 16900  m² so length of the side is √16900 = 130 m

so the length of the diagonal is √2 x 130 m = 130√2 m ≈ 183.82 m ANSWER

-Answered by Himanshi Verma On 06 April 2019:06:51:54 PM


Question 308. Asked on :31 March 2019:12:49:03 PM

 The perimeter of the rectangle field is 480m and the ratio between the length and breadth is 5 : 3. the area of the field  in square meters is :

-Added by Master Purushottam Mathematics » Mensuration

Answer:

Himanshi Verma

 The perimeter is given by twice the sum of length and breadth.

The length and  breadth are on ratio 5:3.Let the common ratio be x.
length = 5x
breadth = 3x
Perimeter = 2(length + breadth)
480 = 2(5x + 3x)
480 = 16x
x=30
length = 5x=5*30 = 150
breadth = 3x = 3*30 =90
Area = length * breadth
Area = 150 * 90
Area = 13500 sq. m 

-Answered by Himanshi Verma On 06 April 2019:06:53:50 PM


Question 309. Asked on :31 March 2019:12:34:26 PM

 A child walk 5m to cross a rectangular field  diagonally, if breadth of the field in 3m, its length is: 

-Added by Master Purushottam Mathematics » Mensuration

Answer:

Himanshi Verma



In the figure, ABCD is a rectangular field.
AC is the diagonal.
Triangle ABC, 
AC2=AB2+BC2
202=162+BC2
BC2=202162
=(20+16)(2016)=36×4
BC=6×2 = 12 m.
The breadth of the field is 12 m.

-Answered by Himanshi Verma On 06 April 2019:06:43:16 PM


Question 310. Asked on :29 March 2019:04:53:40 PM

 Use Euclid’s division algorithm to find the HCF of :

(i) 135 and 225 (ii) 196 and 38220 (iii) 867 and 255

-Added by Rohit rajput Mathematics » Real Numbers

Answer:

Himanshi Verma

 (i)135 and 225

  a = 225, b = 135               {Greatest number is ‘a’ and smallest number is ‘b’}

 Using Euclid’s division algorithm

  a = bq + r (then)

  225 = 135 ×1 + 90

 135 = 90 ×1 + 45

 90 = 45 × 2 + 0                  {when we get r=0, our computing get stopped}

 b = 45 {b is HCF}

Hence:  HCF = 45

 (ii)196 and 38220

 a = 38220, b = 196          {Greatest number is ‘a’ and smallest number is ‘b’}

 Using Euclid’s division algorithm

 a = bq + r (then)

 38220= 196 ×195 + 0 {when we get r=0, our computing get stopped}

 b = 196 {b is HCF}

Hence:  HCF = 196

(iii)867 and 255

a = 867, b = 255               {Greatest number is ‘a’ and smallest number is ‘b’}

Using Euclid’s division algorithm

a = bq + r (then)

38220= 196 ×195 + 0 {when we get r=0, our computing get stopped}

b = 196 {b is HCF}

Hence:  HCF = 196


-Answered by Himanshi Verma On 29 March 2019:04:55:16 PM


Question 311. Asked on :09 March 2019:01:54:23 PM

कैल्सीफिरोल किस विटामिन का रासायनिक नाम है ?

-Added by Rohit rajput Mathematics » G.k

Answer:

Himanshi Verma

 Vitamin D.

-Answered by Himanshi Verma On 23 March 2019:05:59:38 PM


Question 312. Asked on :01 March 2019:04:06:17 PM

 Find the value of k for which one root of the quadratic equation kx2-14x+8=0 is 2.

-Added by Harshita Rathore Mathematics » G.k

Answer:

Himanshi Verma

 Since 2 is one root of the quadratic equation,

We substitute X=2


k(2)^2 - 14(2) +8= 0

4k-28+8=0

4k-20=0

4k=20

k=5

-Answered by Himanshi Verma On 10 March 2019:04:48:03 PM


Question 313. Asked on :01 March 2019:03:26:35 PM

 How to prove Pythagorus theorem .

-Added by Akki chauhan Mathematics » Maths

Answer:

Himanshi Verma

 ABC is a right angle triangle at B and BD is a perpendicular from B on to AC, the diagonal.


Triangles ABC and BDC are similar, as:

     . angle DBC = 90 - angle C = angle A

     . angle ABC = angle BDC = 90


Ratios of corresponding sides are equal.

     AB / BD = BC / DC = AC / BC

    So we get  BC² = AC * DC     --- (1)


Triangle ABC amd ADB are similar, as:

    . angle DBA = 90 - (90 - C) = angle C

    . angle ABC = 90 = angle ADB


so ratios of corresponding sides are equal

         AB / AD = BC / BD = AC / AB 

       So we get  AB² = AD * AC  --- (2)


  Add (1) and (2) to get:

       AB² + BC² = AC * ( AD + DC) = AC * AC = AC²


So the theorem is proved.

-Answered by Himanshi Verma On 01 March 2019:03:38:26 PM


Answer:

Shalu Shukla


-Answered by Shalu Shukla On 01 March 2019:03:47:38 PM


Question 315. Asked on :27 February 2019:07:34:58 AM

 

-Added by praful kumar Mathematics » P

Answer:

Akki chauhan

Please give your question

-Answered by Akki chauhan On 27 August 2019:09:42:31 AM


Question 316. Asked on :13 February 2019:10:06:57 AM

   Find the value of X

-Added by Akki chauhan Mathematics » Circles

Answer:

Akki chauhan
(i) 550

-Answered by Akki chauhan On 15 September 2019:11:03:28 AM


Answer:

Himanshi Verma

 Let us draw a line segment AM ⊥ BC.

We know that,

Area of a triangle = 1/2 x Base x Altitude

It is given that DE = BD = EC.

⊥ Area (ΔADE) = Area (ΔABD) = Area (ΔAEC)

It can be observed that Budhia has divided her field into 3 equal parts.

-Answered by Himanshi Verma On 09 February 2019:04:40:18 PM


Question 318. Asked on :09 February 2019:04:31:17 PM

What is the range of the probability of an event. 

-Added by Harshita Rathore Mathematics » Probability

Answer:

Himanshi Verma

 If an event is impossible its probability is zero. Similarly, if an event is certain to occur, its probability is one. The probability of any event lies in between these values. It is called the range of probability and is denoted as 0 ≤ P (E) ≤ 1.

-Answered by Himanshi Verma On 09 February 2019:04:32:27 PM


Answer:

Shalu Shukla

 बेलन के पानी का आयतन = गोले का आयतन 

   πr2h   = 4/3 πr3

   14×14×h = 4\3×7×7×7

          h   = 4/3 × 343/196

          h  = 7/3cm

-Answered by Shalu Shukla On 11 February 2019:05:45:38 PM


Question 320. Asked on :09 February 2019:03:02:25 PM

In the following,find the area of the shaded portains: 

-Added by Himanshi Verma Mathematics » Chapter 11.4

Answer:

Akki chauhan

 What is shade portion

-Answered by Akki chauhan On 27 August 2019:09:43:11 AM


Question 321. Asked on :07 February 2019:09:36:04 AM

tanA-conA /sinAcosA =tan2A-cot2

-Added by SURAJ KUMAR Mathematics » Trignometry


Question 322. Asked on :06 February 2019:04:16:04 PM

DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD .If the area of parallelogram is 1470cm2 , AB =35cm and AD=49 cm ,find the length of BM and DL. 


-Added by Himanshi Verma Mathematics » Chapter 11 Perimeter And Area

Answer:

Himanshi Verma

 Considering AB = Base;


Area = Base x Height

⇒ 1470 cm2 = AB x DL

⇒ 1470 cm2 = 35cm x DL

Or, DL = 1470 ÷ 35 = 42 cm


Now considering AD = Base;


Area = Base x Height

⇒ 1470 cm2 = AD x BM

⇒ 1470 cm2 = 49 cm x BM

Or, BM = 1470 ÷ 49 = 30 cm


Hence, DL = 42 cm and BM = 30 cm

-Answered by Himanshi Verma On 09 February 2019:04:21:59 PM


Question 323. Asked on :05 February 2019:05:27:35 PM

सिद्ध कीजेये की 8 को आठ बार जमा (Plus+) करने पर 1000 आएगा |

-Added by Himanshi Verma Mathematics » G.k

Answer:

Himanshi Verma

  8 8 8

     8 8

        8

        8

+      8

= 1000 

-Answered by Himanshi Verma On 05 February 2019:05:36:22 PM


Question 324. Asked on :05 February 2019:05:12:59 PM

  

Rationalise & find value of cubic expression

If x = 1860, what is the value of 

-Added by Harshita Rathore Mathematics » Number System


Answer:

Himanshi Verma

 Given

Ratio of side =3:2

Perimeter =60cm

Altitude =5cm


So let take one side as 3x and other is 2x


Then perimeter of parallelogram 

=3x+2x+3x+2x

=10x 


According to question perimeter =60cm 


Then 

10x=60cm 

X=60/10=6cm


Then one side is =6 x 3=18


And other is =2x6=12


So base=18cm 


Area of parallelogram =bxh


=18x5=90cm²


Altitude corresponding to smaller side 


90=12xh


H=7.5cm 

-Answered by Himanshi Verma On 05 February 2019:05:26:39 PM


Question 326. Asked on :05 February 2019:09:14:22 AM

 Which is the largest chord in circle.

-Added by Akki chauhan Mathematics » Circles

Answer:

Himanshi Verma

 Diameter is the greatest chord of circle.

-Answered by Himanshi Verma On 05 February 2019:04:58:06 PM


Question 327. Asked on :03 February 2019:05:07:16 PM

 Prove that :- 777+888+999=999

-Added by Himanshi Verma Mathematics » Addition

Answer:

Nishant Verma

 9+8+8+7+7=39,

9+9+8+3=29,

7+2=9

We write last nine of the three solution so, we get 777+888+999=999 

Hence, proved.

-Answered by Nishant Verma On 03 February 2019:05:23:34 PM


Question 328. Asked on :03 February 2019:05:02:10 PM

 Prove that :- 777+888+999=999

-Added by Shalu Shukla Mathematics » Addition

Answer:

Himanshi Verma

 9+8+8+7+7=39,

9+9+8+3=29,

7+2=9

We write last nine of the three solution so, we get 777+888+999=999 

Hence, proved.

-Answered by Himanshi Verma On 05 February 2019:04:51:38 PM


Question 329. Asked on :30 January 2019:02:19:19 PM

 Why is the area of circle is πr2?

-Added by Himanshi Verma Mathematics » Circle

Answer:

Himanshi Verma

 The usual definition of pi is the ratio of the circumference of a circle to its diameter, so that the circumference of a circle is pi times the diameter, or 2 pi times the radius. ... This give a geometric justification that the area of a circle really is "pi r squared".

-Answered by Himanshi Verma On 02 February 2019:01:33:01 PM


Question 330. Asked on :28 January 2019:11:33:19 AM

 tanA+secA-1/tanA+secA+1=cosA/1-sinA .

Proove that.

-Added by SURAJ KUMAR Mathematics » Trignometry

Answer:

Himanshi Verma

 (secA+tanA-(sec^2 A - tan ^2A)) )/tanA-secA+1) as sec^2 A= 1 + tan ^2 A so 1= sec^2 A - tan ^2 A 

= (sec A + tan A - (sec A + tan A) ( sec A - tan A)) / ( tanA-secA+1) 

= ( sec A + tan A ) ( 1- (sec A - tan A)/ ( tanA-secA+1) 

= (sec A + tan A)/(+ tan A - sec A)/(tan A- sec A+ 1) 

= (sec A + tan A) 

= 1/cos A + sin A/ cos A 

= (1+ sin A)/ cos A 

= (1 + sin A )(1- sin A)/(cos A (1- sin A)) 

= (1- sin ^2 A/(cos A (1- sin A)) 

= cos ^2 A / (cos A (1- sin A)) 

= cos A /(1- sin A) 


proved

-Answered by Himanshi Verma On 02 February 2019:01:40:14 PM


Question 331. Asked on :28 January 2019:11:31:30 AM

 

-Added by SURAJ KUMAR Mathematics » Trigmometpy

Answer:

Akki chauhan

Please give question

-Answered by Akki chauhan On 30 August 2019:08:52:40 PM


Question 332. Asked on :28 January 2019:10:53:52 AM

 A garden is 90 m long and 75 m broad. A path 5 m wide is  to be built outside and around it. find the area of the garden in hectare. 

-Added by praful kumar Mathematics » Perimeter And Area

Answer:

Himanshi Verma

 Length (l) of garden = 90 m


Breadth (b) of garden = 75 m


Area of garden = l × b = 90 × 75 = 6750 m2


From the figure, it can be observed that the new length and breadth of the garden, when path is also included, are 100m and 85m respectively.


Area of the garden including the path = 100 × 85 = 8500 m2


Area of path = Area of the garden including the path − Area of garden


= 8500 − 6750 = 1750 m2


1 hectare = 10000 m2


Therefore, area of garden in hectare


=6750/10000


=0.675

-Answered by Himanshi Verma On 02 February 2019:01:49:33 PM


Question 333. Asked on :28 January 2019:10:49:14 AM

 Find the area of a square park whose perimeter is 320m. 

-Added by praful kumar Mathematics » Perimeter And Area

Answer:

Himanshi Verma

 A=6400m2

-Answered by Himanshi Verma On 03 February 2019:04:19:42 PM


Question 334. Asked on :27 January 2019:11:08:39 AM

 (4-k)x2+(2k+4)x+(8k+1)=0.

k=? 

एक पुर्ण वर्ग है ?

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Answer:

Himanshi Verma

 The given quadratic will be a perfect square if it has two real and equal roots. To have two real and equal roots the discriminant must be zero.

i.e., b²-4ac=0

or, (2k+4)²-4(4-k)(8k+1)=0

or, 4k²+16k+16-4(32k-8k²+4-k)=0

o², 4k²+16k+16-128k+32k²-16+4k=0

or, 36k²-108k=0

or, 36k(k-3)=0

either 36k=0

or, k=0

or, k-3=0

or, k=3

∴, k=0,3 Ans.

-Answered by Himanshi Verma On 02 February 2019:01:43:20 PM


Question 335. Asked on :27 January 2019:10:59:13 AM

 abx2+(b2ac)x-bc=0.सरल करे|


-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Answer:

Himanshi Verma

 Consider, abx2 +(b2-ac)x-bc = 0

⇒ abx2 + b2x – acx – bc = 0
⇒ bx (ax + b) – c(ax + b) = 0
⇒ (ax + b)(bx – c) = 0

-Answered by Himanshi Verma On 02 February 2019:01:44:13 PM


Question 336. Asked on :27 January 2019:10:54:59 AM

 ax2+4ax+(a2-b2)=0

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Answer:

priyanshu kumar
Jul 16, 2018 - 4x² +4bx -(a² -b²) = 0 4x² +4bx -a² + b² =0 (2x)² + 2.(2x).b + b² -a² =0 (2x + b)² -a² = 0 use formula, a²-b² = (a -b)(a + b) {2x + b -a}{2x + b +a} =0

-Answered by priyanshu kumar On 09 October 2019:11:29:56 AM


Question 337. Asked on :27 January 2019:10:51:05 AM

1/a+b+x=1/a+1/b+1/x,a+b not equal 0.सरल करे |  

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Answer:

Himanshi Verma

ON solving the above equation we have a quadratic equation  

(a+b)x^2+(a+b)^2x+ab(a+b)

on solving the above equation by formula -b+root over(b^2-4ac) and -b-root over(b^2-4ac)

we got -a and -b as roots.

According to me this is much easier then others when compared.

 

-Answered by Himanshi Verma On 10 March 2019:04:49:29 PM


Question 338. Asked on :27 January 2019:10:46:14 AM

 

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Answer:

Akki chauhan

what is your question

-Answered by Akki chauhan On 30 August 2019:08:53:43 PM


Question 339. Asked on :27 January 2019:10:19:50 AM

 1,2,3 ,...,33,34,35 में 7 का गुणज  आने

-Added by praful kumar Mathematics » Prayikta

Answer:

priyanshu kumar
हल : 35 का गुणनखण्ड = 1,5,7,35 ... 120 का गुणनखण्ड = 1,2,3,4,5,6,8,10,12,15,20,24,30,60,120 ... हल : 3 का गुणज = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, ... 3 और 4 का गुणज = 12, 24, 36, 48, 60, 72, 84, 96 ... 68 का गुणनखण्ड = 12, 4, 17, 34, 86.

-Answered by priyanshu kumar On 10 November 2019:03:37:25 PM


Question 340. Asked on :21 January 2019:10:00:50 AM

 __+__+__=30 (use this number and solve question, you also  reapet this number )

         

        [1,3,5,7,9,11,13,15,] 

-Added by Akki chauhan Mathematics » G.k

Answer:

Himanshi Verma

 : (11 + 9) + (3) + (7) = 30

ANOTHER: (13 + 15) + (1) + (1) = 30

OR: (7 + 9) + (1) + (13) = 30

-Answered by Himanshi Verma On 21 January 2019:04:52:39 PM


Question 341. Asked on :20 January 2019:10:13:42 AM

 cotΦ-1/sinΦ=1

-Added by Rohit Rajput Mathematics » Maths

Answer:

Master Purushottam

 Cscϕ/secϕ = (1+cotϕ)/(1+tanϕ) 

LHS = (1+cotϕ)/(1+tanϕ) 

where cotϕ=cosϕ/sinϕ and tanϕ = sinϕ/cosϕ 

= (1+(cosϕ/sinϕ))/(1+(sinϕ/cosϕ)) 

= ((cosϕ+sinϕ)/sinϕ)/((cosϕ+sinϕ)/cosϕ) 

= cosϕ/sinϕ 


wkt cosϕ=1/secϕ 

and sinϕ=1/cosecϕ 

= cscϕ/secϕ 


LHS = RHS 

Hence Proved

-Answered by Master Purushottam On 24 August 2019:12:17:05 AM


Question 342. Asked on :19 January 2019:10:22:48 AM

 On tossing a coin 1000 times head comes 425 times find the probability of getting a tails in this event.

-Added by Prince Rawat Mathematics » STATISTICS

Answer:

Master Purushottam

 Total no. of times tossing a coin= 1000

no. of head comes= 425

no. of tail comes= 1000-425= 575

probability   p(e)= 575/1000 

-Answered by Master Purushottam On 24 August 2019:12:18:13 AM


Question 343. Asked on :19 January 2019:10:07:46 AM

 Three spheres having radii 2 cm ,3 cm and 5 cm are melted together to from a single find the radius of the new sphere.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

Let three spheres are S1, S2 & S3

having radii r₁ = 3cm, r₂ = 4cm & r₃ = 5cm respectively.

Let the radius of new Big sphere S is R.

A/Q,

Volume of new Sphere  S = Sum of volumes three Spheres S1, S2 & S3

⇒ 4/3πR³ = 4/3π(r₁)³ + 4/3π(r₂)³+4/3π(r₃)³

⇒ 4/3πR³ = 4(r₁³ +r₂³ + r₃³)/3π

⇒ R³ = r₁³ +r₂³ + r₃³

⇒  R³ = 3³ +4³ + 5³ = 27 + 64 + 125

⇒ R³ =  216

⇒ R = ∛216

⇒ R = 6cm

Therefore radius of new Sphere is 6 cm.

-Answered by Master Purushottam On 24 August 2019:12:18:19 AM


Question 344. Asked on :19 January 2019:10:05:05 AM

 The slant height of a cone is 10 cm and its base radius is 8 cm find total surface area of the cone.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

 slant height of cone is : 10 

Radius of the base is : 8 cm

Total surface area of cone is : πr(l+r)

227 ×8(10+8) 

227 ×144

= 452.57

-Answered by Master Purushottam On 24 August 2019:12:15:34 AM


Question 345. Asked on :18 January 2019:05:21:24 PM

Write the formula of cylinder open from the top ? 


-Added by khushi chauhan Mathematics » Maths

Answer:

Master Purushottam

 Total surface area= 2πr(r+h) -πr2

curved surface area = 2πrh+πr2

-Answered by Master Purushottam On 24 August 2019:12:15:48 AM


Answer:

Master Purushottam

 vb

-Answered by Master Purushottam On 24 August 2019:12:14:15 AM


Answer:

Master Purushottam

  Let ABCD, the square garden of side= 30 m.

PQRS is the region inside the garden.

so,

PQ = (30 -1-1 ) = 28 m

also

PS = ( 30 – 1 – 1 ) = 28 m 


(i) Area of the path = Area of ABCD – Area of PQRS 

= [( 30 x 30) – (28 x 28)]

= 900 – 784 

= 116 sq.m 


(ii) Area of the remaining portion in which the grass is planted = Area of square PQRS 

= 28 x 28 

= 784 sq.m 


cost of planting the grass in the region PQRS =  area x cost = 764 x 40

 =31,360

-Answered by Master Purushottam On 24 August 2019:12:14:42 AM


Question 348. Asked on :16 January 2019:06:13:49 PM

 An integer that is divisible by 2 is called ?

-Added by Shalu Shukla Mathematics » G.k

Answer:

Master Purushottam
 An integer that is divisible by 2 is called Even Number.

-Answered by Master Purushottam On 24 August 2019:12:15:00 AM


Question 349. Asked on :16 January 2019:06:14:35 PM

 Counting number are kept under _______ number.

-Added by Himanshi Verma Mathematics » G.k

Answer:

Master Purushottam
 Counting numbers are numbers you can use to count whole items. You can use the positive integers to count marbles, for example. Whether 0 is a counting number or not, that's a big debate you may or may not be interested in 

-Answered by Master Purushottam On 24 August 2019:12:15:06 AM


Question 350. Asked on :16 January 2019:05:34:22 PM

(a2-b2)3+(b2-c2)3+(c2-a2)3(a-b)3+(b-c)3+(c-a)3Simplify this Equation: 

-Added by Shalu Shukla Mathematics » Ch-2

Answer:

Master Purushottam

 We know,

---> if a + b + c = 0 ; a³ + b³ + c³ = 3abc


We observe,

( a² - b² ) + ( b² - c² ) + ( c² - a² ) = 0

=> ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ = 3( a² - b² )( b² - c² )( c² - a² )


Similarly, 

( a - b ) + ( b - c ) + ( c - a ) = 0

=> ( a - b )³ + ( b - c )³ + ( c - a )³ = 3( a - b )( b - c )( c - a )


Now, [ ( a² - b² )³ + ( b² - c² )³ + ( c² - a² )³ ] / [ ( a - b )³ + ( b - c )³ + ( c - a )³ ]

== 3( a² - b² )( b² - c² )( c² - a² ) / 3( a - b )( b - c )( c - a )

-Answered by Master Purushottam On 24 August 2019:12:09:53 AM


Question 351. Asked on :16 January 2019:05:39:35 PM

 Among the following which natural numbers had no Prodecessor?

-Added by Himanshi Verma Mathematics » G.k

Answer:

Master Purushottam

 2

-Answered by Master Purushottam On 24 August 2019:12:11:09 AM


Question 352. Asked on :16 January 2019:05:34:43 PM

 How many digits are there in Hindu Arabic System?

 

-Added by Himanshi Verma Mathematics » G.k

Answer:

Master Purushottam
 The Hindu-Arabic numerals are the ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9). They are descended from Indian numerals, and the Hindu-Arabic numeral system by which a sequence of digits such as "406" is read as a whole number was developed by Indian mathematicians.

-Answered by Master Purushottam On 24 August 2019:12:11:22 AM


Question 353. Asked on :15 January 2019:09:48:55 AM

 The lateral surface area of a cube is 256cm2. Find its volume.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

  Lateral Surface Area of cube=256 cm²

4(side)² =256
side²=256÷4
side²=64
side=√64=8 cm
Volume of the cube=(side)³=8×8×8=512 cm³.

-Answered by Master Purushottam On 24 August 2019:12:03:45 AM


Question 354. Asked on :15 January 2019:09:31:00 AM

 The length, breadth and height of room are 5m, 4m and 3m respectively. Find the cost of white washing the walls of the room and the ceiling at the rate of s. 7.50perm2

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

 l=5m    b=4m      h=3m 

The total area of cuboid = 2(lb+bh+hl)+l×b

                                  = 2(5×4+4×3+3×5)+5×4

                                  = 2(20+12+15)+20

                                  = 2(47) +20

                                  =    94+20

                                  =     114m2

The cost of white washing the wall and the ceiling of the room = 7.50 per m2

      The cost of 114m2 of the walls and ceiling of the room= (7.50×114)Rs

                                                                                   = 855.00Rs.

-Answered by Master Purushottam On 24 August 2019:12:04:01 AM


Question 355. Asked on :15 January 2019:09:27:40 AM

 Find the ratio of total surface area of sphere and a hemisphere of same radius.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam
The total surface area of sphere= 4πr2

The total surface area of hemisphere= 3πr2

The ratio of total surface area of sphere and hemisphere= 4πr2/3πr2

                                                                                = 4:3

-Answered by Master Purushottam On 24 August 2019:12:04:08 AM


Question 356. Asked on :15 January 2019:09:24:30 AM

 The total surface area of a cube is 150sq. cm. Find the perimeter of  any one of its faces. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

   Total surface area of cube is 150sq. cm

Total surface area of cube : 6a2

To find perimeter of its one faces :  ?

Total surface area of cube =150sq.cm

                           6a2  =150sq.cm

 = 1506 

= 25cm

=a2 = √25cm

=a = 5 cm

Perimeter of its one face is = 4 × a

                                        = 4 × 5 cm

                                        = 20 cm Answer

-Answered by Master Purushottam On 24 August 2019:12:01:30 AM


Question 357. Asked on :15 January 2019:09:20:19 AM

 The surface area of the cuboid is 1372 sq. cm. If its dimensions are in the ratio of 4:2:1. Then find length. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

The surface area of the cuboid= 1372 sq. cm 

  Let the dimensions =4x, 2x, 1x

     The total surface area of the cuboid = 2(lb+bh+hl)=1372

                                                        = 2(4x × 2x + 2x × 1x + 4x × 1x )=1372 

=2(8x2+2x2+4x2) =1372

=2(14x2)= 1372

=28x2=1372

= x2=1372/28

       = 49

x=7m

the dimensions are 4x=4×7=28m

                           2x=2×7=14m

                           1x=1×7=7m

-Answered by Master Purushottam On 24 August 2019:12:01:38 AM


Question 358. Asked on :14 January 2019:10:35:56 AM

 The ratio of height of two cylinder is 5:3 as well as the ratio of their radii is 2:3. find the ratio of the volume of the cylinder. 

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Master Purushottam

 Let the radii be 2x and 3x,

let the height be 5y and 3y.

so, ratio of volume =r²h/R²H =(2x)²×5y/(3x)²×3y =20x²y/27x²y =20/27,

The ratio is = 20:27

-Answered by Master Purushottam On 23 August 2019:11:57:01 PM


Question 359. Asked on :13 January 2019:05:13:09 PM

 show that if sum of the two angles of a triangles is equal to the third angle is right triangle.


-Added by khushi chauhan Mathematics » Lines And Angles

Answer:

Master Purushottam

 Let the first and second angle be a and b respectively 


Third angle = a+b


By angle sum property of triangle 

a +b + a+b = 180

=> 2a +2b = 180

=> 2(a+b) = 180

=> a+b = 90°

Third angle = 90°

-Answered by Master Purushottam On 23 August 2019:11:41:59 PM


Question 360. Asked on :13 January 2019:04:58:17 PM

 In a ΔABC, ∠A+∠B=125º And ∠B+∠C=150º. Find all the angles of ΔABC.


-Added by Himanshi Verma Mathematics » Lines And Angles


Question 361. Asked on :13 January 2019:01:13:28 PM

 Find the median of11,12,2x+2,3x,21,23 where x is the mean of 5,10,3.

-Added by Akki chauhan Mathematics » Probability

Answer:

Master Purushottam

 We know, 

if the number of observation (n) is even 

then, 

1. first of all find the value at the position 

2. and find the value at the position 

3. now find the average of two value to get the median .

e.g., 


Given, 11, 12, 14, 18, (x + 2), (x + 4) , 30, 32 , 35 , 41 are in ascending order .

number of terms = 10 {even} 


so, median = {(n/2)th + (n/2 + 1) th }/2 

24 = (5th + 6th)/2 

24 = {(x + 2) + (x + 4)}/2 

24 = (x + 3) 

x = 21 


hence, x = 21

-Answered by Master Purushottam On 23 August 2019:11:36:15 PM


Answer:

Master Purushottam

  Ans 1. Zero(0)

Ans 2. 0 and 1

Ans 3. 2

-Answered by Master Purushottam On 23 August 2019:11:36:37 PM


Question 363. Asked on :13 January 2019:12:13:10 PM

 If the ratio of altitude and area of the parallelogrm is 2:1 then find the length of the base of parallelogram.  

-Added by Himanshi Verma Mathematics » Areas Of Parallelogram And Triangles

Answer:

Akki chauhan

 The area of a parallelogram is the "base" times the "height." Each base has its own height, but the area will be the same whichever base you choose.


If the altitude (height) of 88 cm goes with the side 55 cm, then the area is 4040 square cm and the altitude on the side 1010 cm is 44 cm.

If the altitude (height) of 88 cm goes with the side 1010 cm, then the area is 8080square cm and the altitude on the side 55cm is 1616 cm. However, we cannot have an altitude of 88 cm if the other side is only 55 cm (we would have a right triangle with leg 88 and hypotenuse 55), so this choice is not possible.

-Answered by Akki chauhan On 30 August 2019:08:55:18 PM


Answer:

Master Purushottam

Let 'x' be the number of boys and 'y' be the number of girls.


To find the total marks


The total marks of boys = 42x


The total marks of girls = 45y


Total number of boys and girls = x + y


To find the ratio


The total marks of boys and girls = 44(x + y)


Then we can write


44(x + y) = 42x + 45y


44x + 44y = 42x + 45y


2x = y


x/y = 1/2


Therefore the ratio of the number of boys to the number of girls is 1:2


-Answered by Master Purushottam On 23 August 2019:11:37:23 PM


Answer:

Master Purushottam

 Let 'x' be the number of boys and 'y' be the number of girls.


To find the total marks


The total marks of boys = 42x


The total marks of girls = 45y


Total number of boys and girls = x + y


To find the ratio


The total marks of boys and girls = 44(x + y)


Then we can write


44(x + y) = 42x + 45y


44x + 44y = 42x + 45y


2x = y


x/y = 1/2


Therefore the ratio of the number of boys to the number of girls is 1:2


-Answered by Master Purushottam On 23 August 2019:11:37:42 PM


Question 366. Asked on :13 January 2019:11:44:06 AM

 THe slant height of cone is 10 cm and its base radius is 8 cm. Find the total surface area of cone. 

-Added by Akki chauhan Mathematics » Surface Ares And Volumes.

Answer:

Master Purushottam

   l=10cm r=8cm

The total surface area of cone=πr(l+r)

                                          =22/7×8(10+8)

                                          =22/7×8(18)

                                          =22/7×144

                                          =3168/7cm

-Answered by Master Purushottam On 23 August 2019:11:37:53 PM


Question 367. Asked on :13 January 2019:11:37:50 AM

 Find the volume of hemisphere whose radius is 

32 cm.

-Added by Akki chauhan Mathematics » Surface Ares And Volumes.

Answer:

Master Purushottam

r= 32


Volume of hemisphere= 23 πr3


                                = 23 ×22/7×3/2×3/2×3/2

                                 = 7.071

-Answered by Master Purushottam On 23 August 2019:11:33:27 PM


Question 368. Asked on :13 January 2019:11:15:32 AM

 Define concentric circles.

-Added by Akki chauhan Mathematics » Circles

Answer:

Master Purushottam
 The concentric circle are the circles with a common center the region between two concentric circle of different radii is called an annulus. 

-Answered by Master Purushottam On 23 August 2019:11:34:12 PM


Question 369. Asked on :12 January 2019:05:55:36 PM

 add √125 + 2√27 and -5√5 - √3



-Added by khushi chauhan Mathematics » Number System

Answer:

Akki chauhan

 √125 +2√27 +(-5√5 -√3)

=√5×5×5 +2√3×3×3 -5√5 -√3 

=5√5 +6√3 -5√5 -√3

=5√3

-Answered by Akki chauhan On 15 January 2019:09:05:29 AM


Question 370. Asked on :12 January 2019:05:54:25 PM

Rationalise the denominator = 1√3+√5+√7
 

-Added by Himanshi Verma Mathematics » Number System

Answer:

priyanshu kumar
Image result for Rationalise the denominator = 1√3+√5+√7

-Answered by priyanshu kumar On 17 February 2020:02:57:05 PM


Question 371. Asked on :12 January 2019:05:52:26 PM

prove that the cyclic parallelogram is rectangle. 

-Added by khushi chauhan Mathematics » Circles

Answer:

Akki chauhan

  ∠A + ∠C = 180 ....1

But ∠A = ∠C

So ∠A = ∠C = 90

Again 

  ∠B + ∠D = 180 ....2

But ∠B = ∠D

So ∠B = ∠D = 90

Now each angle of parallelogram ABCD is 90.

Hense ABCD is a rectangle

-Answered by Akki chauhan On 15 January 2019:09:05:05 AM


Question 372. Asked on :12 January 2019:10:52:27 AM

 Find the zero of 2x-5.

-Added by Akki chauhan Mathematics » Number System

Answer:

Master Purushottam

2x-5=0

2x=5

x= 5/2

-Answered by Master Purushottam On 22 August 2019:09:11:57 PM


Question 373. Asked on :12 January 2019:10:49:51 AM

 Factorise:

x3-23x2+142x-120

-Added by Akki chauhan Mathematics » Polynomials

Answer:

Shivang Gupta

 x-23x2+142x-120 

=x3-x2-22x2+22x+120-120

=x2(x-1)-22x(x-1)+120(x-1)

=(x-1)(x2-22x+120)

=(x-1)(x2-12x-10x+120)

=(x-1)[x(x-12)-10(x-12)]

=(x-1)(x-10)(x-12)

-Answered by Shivang Gupta On 25 August 2019:05:08:24 PM


Question 374. Asked on :12 January 2019:10:45:37 AM

 If the polynomials ax3+3x2-13 and 2x3-5x+a , are divided by x+2 if the remainder in each case is the same, then find the value of 'a'

-Added by Akki chauhan Mathematics » Polynomials

Answer:

Shivang Gupta

When p(x) is divided by (x-2),


By remainder theorem,


Remainder= p(2)


p(2)=a*2^3 + 3*2^2 - 13


        =a*8+3*4-13


       =8a+12-13 = 8a-1



p(2) = 2*2^3-5*2+a


      =2*8-10+a


     =16-10+a = 6+a


Since the remainders of ax^3+3x^2-13 and 2x^3-5x+a are same when divided by x-2,


8a-1 = 6+a


8a-6+a=1


8a+8=1-6=-5


8a=-5-8 =-13


a=-13/8

-Answered by Shivang Gupta On 25 August 2019:05:08:54 PM


Question 375. Asked on :12 January 2019:10:38:50 AM

If a = 9-4√5, then find the value of

a21a2 

-Added by Akki chauhan Mathematics » Polynomials

Answer:

Nishant Verma

 (a+1/a)2=a2+1/a2+2

a2+1/a2=(a+1/a)2-2→ I

Now,

a=9-4root5

1/a=1/9-4root5

=(1/9-4root5)×9+4root5/9+4root5

=(9+4root5)

a+1/a=9-4root5+9+4root5

=81

Now,

a2+1/a2=(a+1/a)2-2 →(from I)

=(81)2-2

=6561-2

=6559

-Answered by Nishant Verma On 17 October 2019:02:43:54 PM


Question 376. Asked on :11 January 2019:02:55:18 PM

 Find the median of first 10 prime numbers.


-Added by Prince Rawat Mathematics » STATISTICS

Answer:

Shivang Gupta

The first 10 prime numbers are : 2,3,5,7,11,13,17,19,23 and 29.

n=10

Median if n is even numbers

n2 th term = 5th term = 11

n2 + 1 = 5 + 1 = 6th term = 13

Median = 5th term + 6th term2 

Median = 11 + 132 

 = 242 = 12 Answer

-Answered by Shivang Gupta On 25 August 2019:03:29:06 PM


Question 377. Asked on :11 January 2019:10:18:43 AM

 Define frequency of the observation.

-Added by Prince Rawat Mathematics » STATISTICS

Answer:

Nishant Verma
 The number of times of an observation occurs in the given data is called the frequency of the observation.

-Answered by Nishant Verma On 17 October 2019:02:42:20 PM


Question 378. Asked on :11 January 2019:10:10:33 AM

 The volume of sphere is 310.4 cm3. Find its radius.

-Added by Prince Rawat Mathematics » SURFACE AREAS AND VOLUMES

Answer:

Shivang Gupta

volume of the sphere = 43 πr3= 310.4cm3

                                4/3×22/7×r3=310.4

                                88/21×r3= 310.4

                                   r3=   310.4×21/88

                                      =   6518.4/88

                                   r3  = 74.0727272cm

-Answered by Shivang Gupta On 25 August 2019:03:29:31 PM


Question 379. Asked on :11 January 2019:10:04:29 AM

 What is Degree of the Polynomials?

-Added by Prince Rawat Mathematics » POLYNOMIALS

Answer:

Nishant Verma
Highest power of X in algebraic expressions is called the degree of polynomial.

-Answered by Nishant Verma On 17 October 2019:02:42:40 PM


Question 380. Asked on :09 January 2019:09:54:18 AM

Prove that if the chords are equal then the subtend angle at the center are equal?

-Added by Master Purushottam Mathematics » Circles

Answer:

Rahul Kumar

 Given : In a circle C(O,r) , ∠AOB = ∠COD 

To Prove : Chord AB = Chord CD .

Proof : In △AOB and △COD 

AO = CO [radii of same circle]

BO = DO [radii of same circle]

∠AOB = ∠COD  [given]

⇒  △AOB ≅  △COD [by SAS congruence axiom]

⇒   Chord AB = Chord CD [c.p.c

-Answered by Rahul Kumar On 13 October 2019:10:01:29 AM


Question 381. Asked on :09 January 2019:09:37:10 AM

 Ques.1. prove that 2+2= 5


-Added by Master Purushottam Mathematics » Number System

Answer:

Nishant Verma

Start with: -20 = -20

Which is the same as: 16-36 = 25-45
Which can also be expressed as: (2+2) 2 (9 X (2+2) = 52) 9 X 5
Add 81/4 to both sides: (2+2) 2 (9 X (2+2) + 81/4 = 52) 9 X 5 + 81/4
Rearrange the terms: ({2+2}) 9/2) 2 = (5-9/2) 2
Ergo: 2+2 - 9/2 = 5
Hence: 2 + 2 = 5

-Answered by Nishant Verma On 13 October 2019:09:38:52 AM


Question 382. Asked on :09 January 2019:09:36:20 AM

What is Euclid's division algorithm. 

-Added by Master Purushottam Mathematics » Number System

Answer:

Nishant Verma
The basis of the Euclidean division algorithm isEuclid's division lemma. To calculate the Highest Common Factor (HCF) of two positive integers a and b we use Euclid's division algorithm. HCF is the largest number which exactly divides two or more positive integers.

-Answered by Nishant Verma On 17 October 2019:02:37:10 PM


Question 383. Asked on :07 January 2019:02:34:53 PM

Q. simplify combining like terms

(1) 21b - 32 +7b - 20b

-Added by Master Purushottam Mathematics » Algebra Expression

Answer:

Nishant Verma

 21b - 32 + 7b - 20b

=(21b+7b -20b) - 32

=8b - 32 Answer

-Answered by Nishant Verma On 17 October 2019:02:37:18 PM


Question 384. Asked on :07 January 2019:02:26:38 PM

Find the sum : 3p2q2 - 4pq + 5, - 10p2q2, 15 + 9pq + 7p2q2

-Added by Master Purushottam Mathematics » Algebra Expreesion

Answer:

Nishant Verma

3p2q2 - 4pq + 5 + (-10p2q2) + 15 + 9pq + 7p2q2 

= 3p2q2 + 7p2q2 - 10p2q2 + 9pq - 4pq + 5 + 15 

= 10p2q2 - 10p2q2 + 5pq + 20 

= 5pq + 20

-Answered by Nishant Verma On 17 October 2019:02:37:38 PM


Question 385. Asked on :07 January 2019:02:17:56 PM

 Putting x = 2 (i) In x + 4, we get the value of x + 4, i.e., x + 4 = 2 + 4 = 6

-Added by Master Purushottam Mathematics » Algebra Expreesion

Answer:

Akki chauhan

( x + 1/x)² = x² + 1/x² + 2

=> 2² = x² + 1/x² + 2

=> x² + 1/x² = 4–2 = 2 . . . . . . . .(1)

(x - 1/x)² = x² + 1/x² -2

=> ( x-1/x)² = 2 - 2 = 0

=> (x-1/x) = 0 . . . . . . . . . .(2)

Now, x^4 - 1/x^4 = ( x² + 1/x²) ( x² - 1/x²)

= 2 ( x + 1/x) ( x-1/x)

= 2 * 2 * 0 ( by (1) & (2)

> x^4 - 1/x^4 = 0 

-Answered by Akki chauhan On 05 September 2019:08:41:17 PM


Question 386. Asked on :07 January 2019:02:16:52 PM

If a = 2, b = -2, find the value of a2 + b2.

-Added by Master Purushottam Mathematics » Algebra Expreesion

Answer:

Nishant Verma
The value of a2= 22

                   =4

The value of b2= (-22) = 4

 a2+b2= 4+4

         =  8

-Answered by Nishant Verma On 17 October 2019:02:38:02 PM


Question 387. Asked on :07 January 2019:02:15:12 PM

 . Simplify the expressions and find the value if x is equal to 2 

  (i) x + 7 + 4 (x – 5)

-Added by Master Purushottam Mathematics » Algebra Expreesion

Answer:

Nishant Verma

 x+7+4(x-5)=2

x+7+4x-20=2

5x-13=2

5x=2+13

5x=15 

x=3

So, The value of x is 3. 

-Answered by Nishant Verma On 17 October 2019:02:38:41 PM


Question 388. Asked on :07 January 2019:02:14:21 PM

 simplify the expression and find its value when a = 5 and b = -3.

2(a2 + ab) + 3 - ab

-Added by Master Purushottam Mathematics » Algebra Expreesion

Answer:

Master Purushottam

 a=5,      b=-3

2(52+5×(-3))+3-5×(-3)

2(25+(-15))+3+15

2(25-15)+18

2×10+18

20+18

38

-Answered by Master Purushottam On 22 August 2019:08:55:23 PM


Question 389. Asked on :07 January 2019:02:07:12 PM

 Q1. 3a - 2b - ab - (a-b+ab)+ 3ab +b - a

-Added by Master Purushottam Mathematics » Algebra

Answer:

Nishant Verma

 3a-2b-ab-(a-b+ab)+3ab+b-a


3a-2b-ab-a+b-ab+3ab+b-a
take same terms like this
3a-a-a -2b+b+b -ab-ab+3ab
3a-a-a=a
-2b+b+b=0
-ab-ab+3ab= -2ab+3ab=ab
=a+0+ab
=a+ab
=a(1+b)

-Answered by Nishant Verma On 17 October 2019:02:39:08 PM


Question 390. Asked on :07 January 2019:12:03:07 PM

 What is mean? 

  

-Added by ATP Admin Mathematics » Mean

Answer:

Nishant Verma
 Mean is an average of some data which is calculated by dividing ∑Sum of data by total numbers of data.

-Answered by Nishant Verma On 17 October 2019:02:39:17 PM


Question 391. Asked on :31 December 2018:02:20:01 PM

factorise x2 + 2x + 1 

-Added by ATP Admin Mathematics » Factorisation

Answer:

Nishant Verma

    x2 + 2x + 1 

= x2 + x + x + 1

= x(x + 1) + 1(x + 1) 

= (x + 1) (x + 1) 

-Answered by Nishant Verma On 17 October 2019:02:40:08 PM


Question 392. Asked on :31 December 2018:09:20:26 AM

Find the median of 11, 12, 2x + 2, 3x, 21, 23 where x is the mean of 5, 10, 3.

-Added by ATP Admin Mathematics » Mean Median

Answer:

priyanshu kumar

 For finding the value of x first we find mean of 5, 10, 3 

sum of observation = 5 + 10 + 3 = 18

mean = 18 / 3 = 6 

Therefore, x = 6 

Now we have data for median 11, 12, 14, 18, 21, 23 

n = 6 { n is an even number} 

n/2 th trem = 14 

and (n/2 + 1)th trem = 18 

Median = (14 + 18)/2 = 32/ 2 = 16 Answer

-Answered by priyanshu kumar On 03 November 2019:03:15:43 PM


Question 393. Asked on :29 December 2018:01:00:20 AM

If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first n terms.

-Added by ATP Admin Mathematics » Arithmetic Progressions

Answer:

Harshita Rathore

S7 = 7/2(2a + 6d) 

=> 49 = 7a + 21d

=> 7 = a + 3d   ------------ (i) 

S17 = 17/2 (2a + 16d) 

=> 289 = 17a + 136

=> 17 = a + 8d --------------  (ii) 

Substracting equation (i) from (ii) 

we have ... 

17 - 7 = a - a + 8d - 3d 

10 = 5d 

d = 10/5 

d = 2 

Putting the value in Equation (i) 

7 = a + 3d 

7 = a + 3 x 2 

a = 7 - 6 

a = 1 

Sum of first n terms = n/2 [2a + (n - 1) d]

= n/2 [2x 1 + (n - 1)2] 

= n/2 [2 + 2n - 2 ]

= n/2 (2n) 

= nxn = n2

-Answered by Harshita Rathore On 26 August 2019:03:25:54 PM


Question 394. Asked on :28 December 2018:11:00:50 PM

How many terms of the AP : 9, 17, 25, . . . must be taken to give a sum of 636?

-Added by ATP Admin Mathematics » Arithmetic Progressions

Answer:

Master Purushottam

 A.p= 9,17,25

a=9

d=17-9

=8

Sum of n terms=n÷2[2a+(n-1)d


636=n÷2[2(9)+(n-1)8]

636=n÷2[18+8n-8]

636=n÷2[10+8n]

1272=10n+8n^2

8n^2+10n-1272=0

2[4n^2+5n-636]=0

4n^2+5n-636=0

4n^2+53n-48n-636=0

n(4n+53)-12(4n+53)=0

(n-12)(4n+53)=0

n-12=0

n=12


12 terms must be given to sum of 636

-Answered by Master Purushottam On 22 August 2019:08:54:23 PM


 

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