Wellcome!

Question 1. Asked on :29 June 2021:11:08:46 AM

#### Prove that √5 is an irrational number.

-Added by Master Purushottam Mathematics » Real Numbers

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 2. 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

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 3. 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

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 4. 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

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 5. 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 6. Asked on :05 August 2020:05:56:50 PM

#### Write the identity 8?

-Added by Shruti Srivastva Mathematics » Algebric Expression

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 7. Asked on :05 August 2020:05:55:01 PM

#### Write the identity 7?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Shruti Srivastva

(x-y)3 = x- y3 - 3xy(x-y)

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

Question 8. Asked on :05 August 2020:05:53:30 PM

#### Write the identity 6?

-Added by Shruti Srivastva Mathematics » Algebric Expression

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

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

Question 9. Asked on :05 August 2020:05:51:20 PM

#### Write the identity 5?

-Added by Shruti Srivastva Mathematics » Current Electricity

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 10. Asked on :05 August 2020:05:50:02 PM

#### Write the identity 4?

-Added by Shruti Srivastva Mathematics » Algebric Expression

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

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

Question 11. Asked on :05 August 2020:05:49:05 PM

#### Write the identity 3?

-Added by Shruti Srivastva Mathematics » Current Electricity

Shruti Srivastva

(a+b)(a-b) = a2-b2

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

Question 12. Asked on :05 August 2020:05:47:49 PM

#### Write the identity 2?

-Added by Shruti Srivastva Mathematics » Algebric Expression

Shruti Srivastva

(a-b)2 = a2 - 2ab + b2

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

Question 13. Asked on :05 August 2020:05:43:22 PM

#### Proof the identity 1?

-Added by Shruti Srivastva Mathematics » Algebric Expression

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 14. Asked on :05 August 2020:05:40:52 PM

#### Write the identity 1?

-Added by Shruti Srivastva Mathematics » Algebric Expression

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

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

Question 15. 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

Shruti Srivastva

50

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

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 17. 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

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 18. 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 19. Asked on :23 March 2020:07:27:04 AM

#### Divide (x*x*x)+1 by x+1

-Added by Aman Senapati Mathematics » POLYNOMIALS

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

Question 22. 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

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 23. 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

priyanshu kumar

52 cm square.

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

Question 24. 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

Rohit Rajput

lunar calender.

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

Question 25. 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

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 26. Asked on :10 October 2019:07:06:18 PM

#### Who is father of trignometry ?

-Added by Aarohi Chauhan Mathematics » Introduction To Trignometry

priyanshu kumar
Hipparchus.

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

Question 27. 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

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 28. 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

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 29. 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

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 30. 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

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 31. 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

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 32. Asked on :07 October 2019:11:23:47 AM

#### Prove CosA1+sinA+1+sinAcosA=2secA

-Added by Himanshi Verma Mathematics » Introduction To Trignometry

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 33. 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

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 34. Asked on :01 October 2019:06:14:01 PM

#### what is formula of distance?

-Added by Shivang Gupta Mathematics » Coodinate Geomertry

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 35. Asked on :30 September 2019:10:14:41 AM

#### Perimeter of square is.......

-Added by Akki chauhan Mathematics » Formula

Nishant Verma

4xsquare

-Answered by Nishant Verma On 08 October 2019:09:25:52 AM

Question 36. Asked on :30 September 2019:10:13:16 AM

#### What is circumference of Circle?

-Added by Akki chauhan Mathematics » Gk

priyanshu kumar
πrh

-Answered by priyanshu kumar On 30 September 2019:10:42:01 AM

Question 37. Asked on :30 September 2019:10:12:51 AM

#### What is perimeter of Square?

-Added by Akki chauhan Mathematics » Formula

Nishant Verma
4*side.

-Answered by Nishant Verma On 08 October 2019:09:26:35 AM

Question 38. Asked on :30 September 2019:10:12:25 AM

#### WHat is area of Square?

-Added by Akki chauhan Mathematics » Formula

Nishant Verma
side * side

-Answered by Nishant Verma On 08 October 2019:09:26:46 AM

Question 39. Asked on :30 September 2019:10:11:22 AM

#### What is formula of Total surface area of Hemisphere?

-Added by Akki chauhan Mathematics » Formula

Nishant Verma
(3 r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:26:57 AM

Question 40. Asked on :30 September 2019:10:10:34 AM

#### What is curved surface area of Hemisphere?

-Added by Akki chauhan Mathematics » Formula

Nishant Verma
(2 r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:27:07 AM

Question 41. Asked on :30 September 2019:10:09:29 AM

#### What is surface area of Sphere?

-Added by Akki chauhan Mathematics » Formula

Nishant Verma
(4 r2) sq. units.

-Answered by Nishant Verma On 08 October 2019:09:27:28 AM

Question 42. Asked on :30 September 2019:10:06:39 AM

#### What is curved surface are of cone?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar
( rl) sq. units.

-Answered by priyanshu kumar On 30 September 2019:10:45:03 AM

Question 43. Asked on :30 September 2019:10:06:06 AM

#### What is volume of Cone?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar   r2h cubic units.

-Answered by priyanshu kumar On 30 September 2019:10:45:24 AM

Question 44. Asked on :30 September 2019:10:03:38 AM

#### What is Diagonal of cube?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar
Diagonal = 3a units

-Answered by priyanshu kumar On 30 September 2019:10:46:56 AM

Question 45. Asked on :30 September 2019:10:03:01 AM

#### What is Surface Area of Cube?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar
6a2 sq. units.

-Answered by priyanshu kumar On 30 September 2019:10:47:09 AM

Question 46. Asked on :30 September 2019:10:02:26 AM

#### What is volume of Cube?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar
a3 cubic units.

-Answered by priyanshu kumar On 30 September 2019:10:47:49 AM

Question 47. Asked on :30 September 2019:10:00:06 AM

#### What is Volume of Cuboid?

-Added by Akki chauhan Mathematics » Formula

priyanshu kumar
(l x b x h) cubic units

-Answered by priyanshu kumar On 30 September 2019:10:48:32 AM

Question 48. Asked on :30 September 2019:09:57:29 AM

#### What is Mode?

-Added by Akki chauhan Mathematics » Gk

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 49. Asked on :30 September 2019:09:57:06 AM

#### What is MEdian?

-Added by Akki chauhan Mathematics » STATISTICS

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 50. Asked on :30 September 2019:09:56:38 AM

#### What is Mean?

-Added by Akki chauhan Mathematics » STATISTICS

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 51. Asked on :28 September 2019:07:17:58 AM

#### How it is possible?999+888+777 = 999

-Added by Rohit Rajput Mathematics » Brain Teaser

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 52. Asked on :25 September 2019:03:05:35 PM

#### If 60% 1200 then the value of x

-Added by Sohail alam Mathematics » All Question

Shivang Gupta

85%

-Answered by Shivang Gupta On 05 October 2019:03:14:19 PM

Question 53. 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

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)2 = (x – 3)2 + (y – 2)2 (x + 1)2 = (x – 3)2x 2 + 2x + 1 = x 2 – 6x + 92x + 6x = 9 – 18x = 8x = 1In 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)22[(x + 1)2 + (y – 2)2] = (4)2 + (0)22[(1 + 1)2 + (y – 2)2] = 16  ( x = 1)2[ 4 + (y – 2)2] = 168 + 2 (y – 2)2 = 162 (y – 2)2 = 16 – 8 = 8(y – 2)2 = 4y – 2 = ± 2y – 2 = 2 or y – 2 = –2y = 4 or y = 0Thus, 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 54. 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

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

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 56. 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

priyanshu kumar

-Answered by priyanshu kumar On 03 October 2019:01:59:58 PM

Question 57. Asked on :07 September 2019:08:51:52 AM

#### What is full form of HCF

-Added by Sohail alam Mathematics » Maths

Akki chauhan
Highest common factor.

-Answered by Akki chauhan On 13 September 2019:09:38:11 AM

Question 58. 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

Shruti Srivastva
8100 cm sq.

-Answered by Shruti Srivastva On 02 September 2019:03:06:18 PM

Question 59. Asked on :01 September 2019:12:21:47 PM

#### Who discovered bacterial transformation?

-Added by Akki chauhan Mathematics » Arithmetic Progressions

Nishant Verma
Frederick Griffith.

-Answered by Nishant Verma On 02 September 2019:11:45:39 AM

Question 60. 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

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 61. Asked on :30 August 2019:03:52:44 PM

#### write the formula of C.I.?

-Added by Suman Kumari Mathematics » Maths

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

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

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 64. 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

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

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

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 67. 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

Akki chauhan

(i) Distance between the two points is given by -Answered by Akki chauhan On 26 August 2019:07:58:00 PM

Question 68. 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

priyanshu kumar

336.

-Answered by priyanshu kumar On 20 October 2019:04:14:05 PM

Question 69. 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

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

Akki chauhan  -Answered by Akki chauhan On 27 August 2019:09:27:23 AM

Question 71. 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

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

Hence the sum of first 25 multiple of 7 is 2275.

-Answered by Master Mind On 24 August 2019:11:38:04 PM

Question 72. 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

Akki chauhan

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 73. 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

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 74. 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

Master Purushottam

2268

-Answered by Master Purushottam On 24 August 2019:09:29:41 PM

Question 75. 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

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

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

. -Answered by Suraj Kumar On 11 December 2019:08:33:46 AM

Question 77. Asked on :19 August 2019:09:49:02 AM

#### Who discovered the zero?

-Added by Akki chauhan Mathematics » Number

Akki chauhan

Aryabhatta discovered zero.

-Answered by Akki chauhan On 19 August 2019:09:50:45 AM

Question 78. Asked on :18 August 2019:06:31:17 PM

#### X-2=7

-Added by Master Purushottam Mathematics » One Variable In Linear Equation

Akki chauhan

X-2=7

X=7+2

X=9

-Answered by Akki chauhan On 18 August 2019:08:35:07 PM

Question 79. 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

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 80. 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

Himanshi Verma

By Thales theorem or basic propositionality Theorem

IN∆ABC
LM||BC so by B.P.T
AL/AC=AM/AB-----------(1)
from equation 1 &2 L.H.S is same so R.H.S will also same.
so

-Answered by Himanshi Verma On 18 August 2019:10:58:35 AM

Question 81. Asked on :17 August 2019:09:38:34 AM

#### What is mean , mode and Median?

-Added by Akki chauhan Mathematics » Stastics

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 82. Asked on :17 August 2019:09:27:38 AM

#### What is the form of Arithmetic Progressions?

-Added by Akki chauhan Mathematics » Arithmetic Progressions

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 83. Asked on :17 August 2019:09:24:51 AM

#### What is Arithmetic Progressions?

-Added by Akki chauhan Mathematics » G.

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 84. Asked on :17 August 2019:09:22:47 AM

#### Prove that √2 is irrational?

-Added by Akki chauhan Mathematics » Real Numbers

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 85. 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 ΔRPQ∼ΔRTS.

-Added by Himanshi Verma Mathematics » Traingles

Himanshi Verma -Answered by Himanshi Verma On 23 July 2019:07:52:25 PM

Question 86. 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

Himanshi Verma -Answered by Himanshi Verma On 18 July 2019:09:05:33 PM

Question 87. 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.

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

-Answered by Master Mind On 11 July 2019:09:08:06 PM

Question 88. Asked on :09 July 2019:11:51:22 PM

#### Solve the equation 6(7b - 4) = 60 for b.

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

Question 89. 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

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

(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

(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

Harshita Rathore

Cos

-Answered by Harshita Rathore On 24 August 2019:02:57:10 PM

Question 91. Asked on :09 July 2019:06:53:37 PM

#### Find the nature of quadratic equation x2 + 3x + 7.

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 92. 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 .

Master Purushottam -Answered by Master Purushottam On 08 July 2019:10:58:57 PM Question 94. 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

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 95. 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.

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.

Question 96. Asked on :13 May 2019:10:29:43 AM

##### 7 और  9 के बीच 10 परिमेय संख्या लिखे ?

-Added by ravi varma Mathematics » Maths

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 97. Asked on :08 May 2019:10:19:35 AM

#### x का मान  ज्ञात कीजिए  2x-1=14-x?

-Added by ravi varma Mathematics » Maths

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 98. Asked on :08 May 2019:10:14:22 AM

#### क्या शुन्य परिमेय संख्या है ?

-Added by Hitesh kumar Mathematics » Mathematics

Himanshi Verma

yes zero is a rational number.

-Answered by Himanshi Verma On 14 May 2019:11:23:16 AM

Question 99. Asked on :08 May 2019:10:15:06 AM

#### 4z+3=6+2z

-Added by ravi varma Mathematics » Maths

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 100. Asked on :08 May 2019:09:55:15 AM

#### 5 और 6 के बीच दो  परिमेय संख्या लिखो ?

-Added by Hitesh kumar Mathematics » Math

Himanshi Verma

The rational number are 16, 17.

-Answered by Himanshi Verma On 14 May 2019:11:16:10 AM

Question 101. 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

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 102. Asked on :21 April 2019:10:53:53 AM

#### What is activity series ?

-Added by Nitish kumar Mathematics » Types Of Chemical Reactions

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 103. 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

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 104. Asked on :21 April 2019:10:45:16 AM

#### what is oxidation?

-Added by Nitish kumar Mathematics » Types Of Chemical Reactions

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 105. 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

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

Akki chauhan

what is the polynomials.

-Answered by Akki chauhan On 24 August 2019:03:13:10 PM

Question 107. Asked on :19 April 2019:08:21:00 AM

#### Prove that√5 is irrational.

-Added by Prince Rawat Mathematics » Real Number

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 108. 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

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 109. 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

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

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 111. 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

Himanshi Verma -Answered by Himanshi Verma On 06 April 2019:06:46:28 PM

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 113. 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

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

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
480 = 2(5x + 3x)
480 = 16x
x=30
length = 5x=5*30 = 150
breadth = 3x = 3*30 =90
Area = 150 * 90
Area = 13500 sq. m

-Answered by Himanshi Verma On 06 April 2019:06:53:50 PM

Question 115. 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

Himanshi Verma In the figure, ABCD is a rectangular field.
AC is the diagonal.
Triangle ABC,
$A{C}^{2}=A{B}^{2}+B{C}^{2}$
${20}^{2}={16}^{2}+B{C}^{2}$
$B{C}^{2}={20}^{2}-{16}^{2}$
=$\left(20+16\right)\left(20-16\right)=36×4$
$BC=6×2$ = 12 m.
The breadth of the field is 12 m.

-Answered by Himanshi Verma On 06 April 2019:06:43:16 PM

Question 116. 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

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

Himanshi Verma

Vitamin D.

-Answered by Himanshi Verma On 23 March 2019:05:59:38 PM

Question 118. 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

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 119. Asked on :01 March 2019:03:26:35 PM

#### How to prove Pythagorus theorem .

-Added by Akki chauhan Mathematics » Maths

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

Shalu Shukla -Answered by Shalu Shukla On 01 March 2019:03:47:38 PM

Question 121. Asked on :27 February 2019:07:34:58 AM

-Added by praful kumar Mathematics » P

Akki chauhan

-Answered by Akki chauhan On 27 August 2019:09:42:31 AM

Akki chauhan
(i) 550

-Answered by Akki chauhan On 15 September 2019:11:03:28 AM

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 124. 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

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

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 126. 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

Akki chauhan

-Answered by Akki chauhan On 27 August 2019:09:43:11 AM

Question 127. Asked on :07 February 2019:09:36:04 AM

#### tanA-conA /sinAcosA =tan2A-cot2A

-Added by SURAJ KUMAR Mathematics » Trignometry

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

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

Himanshi Verma

8 8 8

8 8

8

8

+      8

= 1000

-Answered by Himanshi Verma On 05 February 2019:05:36:22 PM

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 132. Asked on :05 February 2019:09:14:22 AM

#### Which is the largest chord in circle.

-Added by Akki chauhan Mathematics » Circles

Himanshi Verma

Diameter is the greatest chord of circle.

-Answered by Himanshi Verma On 05 February 2019:04:58:06 PM

Question 133. Asked on :03 February 2019:05:07:16 PM

#### Prove that :- 777+888+999=999

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 134. Asked on :03 February 2019:05:02:10 PM

#### Prove that :- 777+888+999=999

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 135. Asked on :30 January 2019:02:19:19 PM

#### Why is the area of circle is πr2?

-Added by Himanshi Verma Mathematics » Circle

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 136. 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

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 137. Asked on :28 January 2019:11:31:30 AM

-Added by SURAJ KUMAR Mathematics » Trigmometpy

Akki chauhan

-Answered by Akki chauhan On 30 August 2019:08:52:40 PM

Question 138. 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

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 139. 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

Himanshi Verma

A=6400m2

-Answered by Himanshi Verma On 03 February 2019:04:19:42 PM

Question 140. 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

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 141. Asked on :27 January 2019:10:59:13 AM

#### abx2+(b2ac)x-bc=0.सरल करे|

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

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 142. Asked on :27 January 2019:10:54:59 AM

#### ax2+4ax+(a2-b2)=0

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

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 143. 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

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 144. Asked on :27 January 2019:10:46:14 AM

-Added by SURAJ KUMAR Mathematics » POLYNOMIALS

Akki chauhan

-Answered by Akki chauhan On 30 August 2019:08:53:43 PM

Question 145. 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

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 146. 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

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 147. Asked on :20 January 2019:10:13:42 AM

#### cotΦ-1/sinΦ=1

-Added by Rohit Rajput Mathematics » Maths

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 148. 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

Master Purushottam

Total no. of times tossing a coin= 1000

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 149. 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

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 150. 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

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 151. Asked on :18 January 2019:05:21:24 PM

#### Write the formula of cylinder open from the top ?

-Added by khushi chauhan Mathematics » Maths

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

Master Purushottam

vb

-Answered by Master Purushottam On 24 August 2019:12:14:15 AM

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 154. 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

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 155. Asked on :16 January 2019:06:14:35 PM

#### Counting number are kept under _______ number.

-Added by Himanshi Verma Mathematics » G.k

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 156. 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

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 157. 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

Master Purushottam

2

-Answered by Master Purushottam On 24 August 2019:12:11:09 AM

Question 158. 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

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 159. 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

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

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 161. 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

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 162. 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

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

-Answered by Master Purushottam On 24 August 2019:12:01:30 AM

Question 163. 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

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 164. 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

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 165. 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

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 166. 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 167. 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

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

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 169. 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

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

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

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 172. 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.

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 173. 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.

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 174. Asked on :13 January 2019:11:15:32 AM

#### Define concentric circles.

-Added by Akki chauhan Mathematics » Circles

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 175. Asked on :12 January 2019:05:55:36 PM

#### add √125 + 2√27 and -5√5 - √3

-Added by khushi chauhan Mathematics » Number System

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 176. Asked on :12 January 2019:05:54:25 PM

#### Rationalise the denominator = 1√3+√5+√7

-Added by Himanshi Verma Mathematics » Number System

priyanshu kumar -Answered by priyanshu kumar On 17 February 2020:02:57:05 PM

Question 177. Asked on :12 January 2019:05:52:26 PM

#### prove that the cyclic parallelogram is rectangle.

-Added by khushi chauhan Mathematics » Circles

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 178. Asked on :12 January 2019:10:52:27 AM

#### Find the zero of 2x-5.

-Added by Akki chauhan Mathematics » Number System

Master Purushottam

2x-5=0

2x=5

x= 5/2

-Answered by Master Purushottam On 22 August 2019:09:11:57 PM

Question 179. Asked on :12 January 2019:10:49:51 AM

#### Factorise:x3-23x2+142x-120

-Added by Akki chauhan Mathematics » Polynomials

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

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 181. Asked on :12 January 2019:10:38:50 AM

#### If a = 9-4√5, then find the value ofa2 + 1a2

-Added by Akki chauhan Mathematics » Polynomials

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 182. Asked on :11 January 2019:02:55:18 PM

#### Find the median of first 10 prime numbers.

-Added by Prince Rawat Mathematics » STATISTICS

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

-Answered by Shivang Gupta On 25 August 2019:03:29:06 PM

Question 183. Asked on :11 January 2019:10:18:43 AM

#### Define frequency of the observation.

-Added by Prince Rawat Mathematics » STATISTICS

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 184. 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

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 185. Asked on :11 January 2019:10:04:29 AM

#### What is Degree of the Polynomials?

-Added by Prince Rawat Mathematics » POLYNOMIALS

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 186. 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

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 187. Asked on :09 January 2019:09:37:10 AM

#### Ques.1. prove that 2+2= 5

-Added by Master Purushottam Mathematics » Number System

Nishant Verma

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 188. Asked on :09 January 2019:09:36:20 AM

#### What is Euclid's division algorithm.

-Added by Master Purushottam Mathematics » Number System

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 189. 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

Nishant Verma

21b - 32 + 7b - 20b

=(21b+7b -20b) - 32

-Answered by Nishant Verma On 17 October 2019:02:37:18 PM

Question 190. 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

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 191. 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

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 192. 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

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 193. 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

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 194. 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

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 195. 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

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 196. Asked on :07 January 2019:12:03:07 PM

#### What is mean?

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 197. Asked on :31 December 2018:02:20:01 PM

#### factorise x2 + 2x + 1

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 198. 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.

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 199. 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.

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 200. 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?

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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