**Master Purushottam**

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 Master Purushottam* On 22 August 2019:09:17:36 PM

**Question 1.** **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:**

Theorem 6.8 :

*-Answered by Master Purushottam* On 22 August 2019:09:17:36 PM

**Question 2.** **Asked on :**21 August 2019:09:31:44 AM

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.

*-Added by Prince Rawat* **Mathematics** » **Triangle **

**Answer:**

.

*-Answered by Master Purushottam* On 22 August 2019:09:18:51 PM

**Question 3.** **Asked on :**19 August 2019:09:49:02 AM

Who discovered the zero?

*-Added by Akki chauhan* **Mathematics** » **Number**

**Answer:**

Aryabhatta discovered zero.

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

**Question 4.** **Asked on :**18 August 2019:06:31:17 PM

X-2=7

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

**Answer:**

X-2=7

X=7+2

X=9

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

**Question 5.** **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:**

Let the quadratic polynomial be ax^{2}+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 **x ^{2}+3x+2.**

*-Answered by Himanshi Verma* On 18 August 2019:11:00:35 AM

**Question 6.** **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:**

By **Thales theorem **or basic propositionality Theorem

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 7.** **Asked on :**17 August 2019:09:38:34 AM

What is mean , mode and Median?

*-Added by Akki chauhan* **Mathematics** » **Stastics**

**Answer:**

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 8.** **Asked on :**17 August 2019:09:27:38 AM

What is the form of Arithmetic Progressions?

*-Added by Akki chauhan* **Mathematics** » **Arithmetic Progressions **

**Answer:**

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 9.** **Asked on :**17 August 2019:09:24:51 AM

*-Added by Akki chauhan* **Mathematics** » **G.**

**Answer:**

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 10.** **Asked on :**17 August 2019:09:22:47 AM

Prove that √2 is irrational?

*-Added by Akki chauhan* **Mathematics** » **Real Numbers**

**Answer:**

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 11.** **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 **

**Answer:**

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

**Question 12.** **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:**

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

**Question 13.** **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:**

Given: a_{1} = 6, S_{6 }= 66

using Formula: S_{n} = n2 (*a +* *l*)

**Step by Step Explanation:**

S_{6} = 62 ( 6 + a_{6})

66 = 3(6 + 6^{th} term)

(6 + 6^{th} term) = 663 = 22

6^{th} term = 22 - 6

6^{th} term = 16 **Answer**

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

**Question 14.** **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:**

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 15.** **Asked on :**09 July 2019:07:05:00 PM

If the sum of n^{th} terms of an A.P. is given by 4n^{2} - 7n. Find

(i) Sum of 23 terms

(ii) 15^{th} term

(iii) n^{th} term

*-Added by ATP Admin* **Mathematics** » **Arithmetic Progressions **

**Answer:**

**Given**:S_{n} = 4n^{2} - 7n

**Step by step** explanation:

**(i) Sum of 23 terms **

S_{n} = 4n^{2} - 7n ............. (**i**)

Replace n by 23 we have,

S_{23} = 4(23)^{2} - 7(23)

= 4 × 529 - 161

= 2116 - 161

= 1955 **Answer**

**(ii) 15 ^{th} term**

a_{15} = S_{15} - S_{14}

S_{15} = 4(15)^{2} - 7(15) = 4 × 225 - 105 = 900 - 105 = 795

S_{14} = 4(14)^{2} - 7(14) = 4 × 196 - 98 = 784 - 98 = 686

Now, a_{15} = S_{15} - S_{14}

= 795 - 686

= 109 **Answer**

(iii) n^{th} term

a_{n} = S_{n} - S_{n-1}

Given, S_{n} = 4n^{2} - 7n

Replace n by n-1 we have

S_{n-1} = 4(n-1)^{2} - 7(n-1)

= 4(n^{2} - 2n + 1) - 7n + 7

= 4n^{2} - 8n + 4 - 7n + 7

= 4n^{2} - 15n + 11 ............. (ii)

Now Applying equation (i) and (ii) in formula a_{n} = S_{n} - S_{n-1}

a_{n} = (4n^{2} - 7n) - (4n^{2} - 15n + 11)

= 4n^{2} - 7n - 4n^{2} + 15n - 11

= 8n - 11

Therefore, a_{n} = 8n - 11 **Answer**

*******************************

*-Answered by Master Mind* On 11 July 2019:09:42:19 PM

**Question 16.** **Asked on :**09 July 2019:06:56:05 PM

Prove the identity:

*-Added by ATP Admin* **Mathematics** » **Trigonometry **

**Question 17.** **Asked on :**09 July 2019:06:53:37 PM

Find the nature of quadratic equation x^{2} + 3x + 7.

*-Added by ATP Admin* **Mathematics** » **Quadratic Equations**

**Answer:**

x^{2}+ 3x+7

This equation is of the form of ax^{2}+bx+c=0

so, a=1, b=3, c=7

b^{2}+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 18.** **Asked on :**08 July 2019:10:36:51 PM

x and y are connected parametrically by the equation x = 2at^{2}, y = at^{4} without eleminating the parameter.

Find dydx .

*-Added by ATP Admin* **Mathematics** » **Continuity And Differentiability **

**Answer:**

*-Answered by Master Purushottam* On 08 July 2019:10:58:57 PM

**Question 19.** **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:**

*-Answered by ATP Admin* On 08 July 2019:10:45:29 PM

**Question 20.** **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:**

This is an AP a=6,d=6, and n=40

Using formula,

S_{n} = n2 [2a+(n-1)d]

S_{40}= 402 [2*6+(40-1)6]

S_{40}=20(12+234)

S_{40}=20*246

S_{40}=4920

*-Answered by Akki chauhan* On 18 July 2019:10:26:06 AM

**Question 21.** **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:**

**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 22.** **Asked on :**13 May 2019:10:29:43 AM

*-Added by ravi varma* **Mathematics** » **Maths**

**Answer:**

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 23.** **Asked on :**08 May 2019:10:19:35 AM

*-Added by ravi varma* **Mathematics** » **Maths**

**Answer:**

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 24.** **Asked on :**08 May 2019:10:14:22 AM

क्या शुन्य परिमेय संख्या है ?

*-Added by Hitesh kumar* **Mathematics** » **Mathematics**

**Answer:**

yes zero is a rational number.

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

**Answer:**

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 26.** **Asked on :**08 May 2019:09:55:15 AM

*-Added by Hitesh kumar* **Mathematics** » **Math**

**Answer:**

The rational number are 16, 17.

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

**Question 27.** **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:**

**Density** is **important** because it affects whether objects will float or sink. It is an**important** 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 28.** **Asked on :**21 April 2019:10:53:53 AM

What is activity series ?

*-Added by Nitish kumar* **Mathematics** » **Types Of Chemical Reactions **

**Answer:**

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 29.** **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:**

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 30.** **Asked on :**21 April 2019:10:45:16 AM

what is oxidation?

*-Added by Nitish kumar* **Mathematics** » **Types Of Chemical Reactions **

**Answer:**

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 31.** **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:**

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 32.** **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**

**Question 33.** **Asked on :**19 April 2019:08:21:00 AM

*-Added by Prince Rawat* **Mathematics** » **Real Number**

**Answer:**

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 34.** **Asked on :**19 April 2019:08:18:18 AM

Check whether 6^{n} can end digit 0 for any nature number n.

*-Added by Prince Rawat* **Mathematics** » **Real Number**

**Answer:**

prime factors of 6^{n}

= (2*3)^{n}

= 2^{n}*3^{n}

While the number ending with zero have prime factor as 2^{n}*5^{n}

Hence, 6^{n} is not end with zero.

*-Answered by Akki chauhan* On 28 June 2019:09:30:20 AM

**Question 35.** **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:**

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

**Question 36.** **Asked on :**31 March 2019:01:14:39 PM

If the side of the square is increased by 50% the ratio of the area of the resulting square is the area of the resulting square to the area of the given square is:

*-Added by Master Purushottam* **Mathematics** » **Mensuration**

**Answer:**

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 37.** **Asked on :**31 March 2019:01:06:03 PM

*-Added by Master Purushottam* **Mathematics** » **Mensuration**

**Answer:**

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

**Question 38.** **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:**

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 39.** **Asked on :**31 March 2019:12:53:32 PM

The length of diagonal of the square whose area is 16900m^{2} is:

*-Added by Master Purushottam* **Mathematics** » **Mensuration**

**Answer:**

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 40.** **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:**

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 41.** **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:**

In the figure, ABCD is a rectangular field.

AC is the diagonal.

Triangle ABC,

=

= 12 m.

The breadth of the field is 12 m.

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

**Question 42.** **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:**

(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 43.** **Asked on :**09 March 2019:01:54:23 PM

कैल्सीफिरोल किस विटामिन का रासायनिक नाम है ?

*-Added by Rohit rajput* **Mathematics** » **G.k **

**Answer:**

Vitamin D.

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

**Question 44.** **Asked on :**01 March 2019:04:06:17 PM

Find the value of k for which one root of the quadratic equation kx^{2}-14x+8=0 is 2.

*-Added by Harshita Rathore* **Mathematics** » **G.k **

**Answer:**

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 45.** **Asked on :**01 March 2019:03:26:35 PM

How to prove Pythagorus theorem .

*-Added by Akki chauhan* **Mathematics** » **Maths**

**Answer:**

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

**Question 46.** **Asked on :**01 March 2019:03:15:18 PM

*-Added by Akki chauhan* **Mathematics** » **Algebra**

**Answer:**

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

**Question 48.** **Asked on :**13 February 2019:10:06:57 AM

** Find the value of X**

*-Added by Akki chauhan* **Mathematics** » **Circles**

**Question 49.** **Asked on :**09 February 2019:04:37:21 PM

In the following figure, D and E are two points on BC such that BD = DE = EC. Show that ar (ABD) = ar (ADE) = ar (AEC). Can you answer the question that you have left in the ’Introduction’ of this chapter, whether the field of Budhia has been actually divided into three parts of equal area?

*-Added by Harshita Rathore* **Mathematics** » **Areas Of Pallelograms And Triangles**

**Answer:**

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 50.** **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:**

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

**Question 51.** **Asked on :**09 February 2019:04:27:51 PM

Water is placed in a cylindrical vessel of 14cm radius. If a spherical ball of radius 7cm is dropped in the vessel completely. How much water will rise to the height of the cylindrical vessel?

*-Added by Himanshi Verma* **Mathematics** » **Volume**

**Answer:**

बेलन के पानी का आयतन = गोले का आयतन

πr^{2}h = 4/3 πr^{3}

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 52.** **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**

**Question 53.** **Asked on :**07 February 2019:09:36:04 AM

*-Added by SURAJ KUMAR* **Mathematics** » **Trignometry **

**Question 54.** **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 1470cm^{2 }, AB =35cm and AD=49 *cm ,find the length of BM and DL.*

*-Added by Himanshi Verma* **Mathematics** » **Chapter 11 Perimeter And Area**

**Answer:**

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 55.** **Asked on :**05 February 2019:05:27:35 PM

*-Added by Himanshi Verma* **Mathematics** » **G.k **

**Answer:**

8 8 8

8 8

8

8

+ 8

= 1000

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

**Question 56.** **Asked on :**05 February 2019:05:12:59 PM

If x = , what is the value of

*-Added by Harshita Rathore* **Mathematics** » **Number System **

**Question 57.** **Asked on :**05 February 2019:05:11:52 PM

*-Added by Himanshi Verma* **Mathematics** » **Perimeter And Area**

**Answer:**

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 58.** **Asked on :**05 February 2019:09:14:22 AM

Which is the largest chord in circle.

*-Added by Akki chauhan* **Mathematics** » **Circles**

**Answer:**

Diameter is the greatest chord of circle.

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

**Question 59.** **Asked on :**03 February 2019:05:07:16 PM

Prove that :- 777+888+999=999

*-Added by Himanshi Verma* **Mathematics** » **Addition**

**Answer:**

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 60.** **Asked on :**03 February 2019:05:02:10 PM

Prove that :- 777+888+999=999

*-Added by Shalu Shukla* **Mathematics** » **Addition**

**Answer:**

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 61.** **Asked on :**30 January 2019:02:19:19 PM

Why is the area of circle is πr^{2}?

*-Added by Himanshi Verma* **Mathematics** » **Circle**

**Answer:**

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 62.** **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:**

(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 64.** **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:**

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 65.** **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:**

A=6400m^{2}

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

**Question 66.** **Asked on :**27 January 2019:11:08:39 AM

(4-k)x^{2}+(2k+4)x+(8k+1)=0.

k=?

एक पुर्ण वर्ग है ?

*-Added by SURAJ KUMAR* **Mathematics** » **POLYNOMIALS**

**Answer:**

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 67.** **Asked on :**27 January 2019:10:59:13 AM

abx^{2}_{+(b}^{2}_{ac)x-bc=0.सरल करे|}

_{}

*-Added by SURAJ KUMAR* **Mathematics** » **POLYNOMIALS**

**Answer:**

Consider, abx +(b-ac)x-bc = 0

⇒ abx + bx – 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 68.** **Asked on :**27 January 2019:10:54:59 AM

ax^{2}_{+4ax+(a}^{2}_{-b}^{2}_{)=0}

*-Added by SURAJ KUMAR* **Mathematics** » **POLYNOMIALS**

**Question 69.** **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:**

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 71.** **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**

**Question 72.** **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:**

: (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 73.** **Asked on :**20 January 2019:10:13:42 AM

cotΦ-1/sinΦ=1

*-Added by Rohit Rajput* **Mathematics** » **Maths**

**Answer:**

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 74.** **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:**

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 75.** **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:**

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 76.** **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:**

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 77.** **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:**

Total surface area= 2πr(r+h) -πr^{2}

curved surface area = 2πrh+πr^{2}

*-Answered by Master Purushottam* On 24 August 2019:12:15:48 AM

**Question 78.** **Asked on :**17 January 2019:05:34:31 PM

ग्राफ में आमने सामने की भुजाओ को समान्तर बताने के लिए सूत्र लिखो?

*-Added by Sumitra Mahajan* **Mathematics** » **G.k **

**Answer:**

vb

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

**Question 79.** **Asked on :**17 January 2019:08:47:48 AM

path 1m wide built along the border and inside a square garden of side 30m. find ;

[i] The area of the path.

[ii] the cost of planting grass in the remaining portion of the garden at the rate of Rs.40 per m^{2}

*-Added by Nitish kumar* **Mathematics** » **Perimeter And Area **

**Answer:**

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 80.** **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:**

An integer that is divisible by 2 is called Even Number.

*-Answered by Master Purushottam* On 24 August 2019:12:15:00 AM

**Question 81.** **Asked on :**16 January 2019:06:14:35 PM

Counting number are kept under _______ number.

*-Added by Himanshi Verma* **Mathematics** » **G.k **

**Answer:**

*-Answered by Master Purushottam* On 24 August 2019:12:15:06 AM

**Question 82.** **Asked on :**16 January 2019:05:34:22 PM

(a^{2}-b^{2})^{3}+(b^{2}-c^{2})^{3}+(c^{2}-a^{2})^{3}(a-b)^{3}+(b-c)^{3}+(c-a)^{3}Simplify this Equation:

*-Added by Shalu Shukla* **Mathematics** » **Ch-2**

**Answer:**

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 83.** **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:**

2

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

**Question 84.** **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:**

The Hindu-Arabic numerals are the

*-Answered by Master Purushottam* On 24 August 2019:12:11:22 AM

**Question 85.** **Asked on :**15 January 2019:09:48:55 AM

The lateral surface area of a cube is 256cm^{2}. Find its volume.

*-Added by Prince Rawat* **Mathematics** » **SURFACE AREAS AND VOLUMES**

**Answer:**

Lateral Surface Area of cube=256 cm²

4(side)² =256side²=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 86.** **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. 7.50perm^{2}.

*-Added by Prince Rawat* **Mathematics** » **SURFACE AREAS AND VOLUMES**

**Answer:**

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

= 114m^{2}

The cost of white washing the wall and the ceiling of the room = 7.50 per m^{2}

The cost of 114m^{2} 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 87.** **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:**

The total surface area of sphere= 4πr

The total surface area of hemisphere= 3πr^{2}

The ratio of total surface area of sphere and hemisphere= 4πr^{2}/3πr^{2}

= 4:3

*-Answered by Master Purushottam* On 24 August 2019:12:04:08 AM

**Question 88.** **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:**

Total surface area of cube is 150sq. cm

Total surface area of cube : 6a^{2}

^{To find perimeter of its one faces : ?}

Total surface area of cube =150sq.cm^{}

6a^{2 }=150sq.cm

= 1506

= 25cm

=a^{2} = √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 89.** **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:**

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(8x^{2}+2x^{2}+4x^{2}) =1372

=2(14x^{2})= 1372

=28x^{2}=1372

= x^{2}=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 90.** **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:**

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 91.** **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:**

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 92.** **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 93.** **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:**

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

**Question 94.** **Asked on :**13 January 2019:12:42:04 PM

Fill in the blanks :

(i) The probability of an impossible event is .............

(ii) The probability of happening of a possible event is always lies between ........... and...........

(iii) On tossing a coin, We get a total of ............. outcomes.

*-Added by Akki chauhan* **Mathematics** » **Probability**

**Answer:**

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 95.** **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**

**Question 96.** **Asked on :**13 January 2019:11:53:09 AM

A bag contain slips bearing from 1-89. A slip is drawn at random from the bag. Find the probability that the slip drawn has:

(a) A number written on it such that sum of its digit is 11.

(b) A number greater than 63 written on it.

*-Added by Akki chauhan* **Mathematics** » **Probability**

**Answer:**

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

**Question 97.** **Asked on :**13 January 2019:11:49:45 AM

In a class test, the mean marks of boys and girls are respectively 42 and 45. If the mean marks of boys and girls are 44, Find the ratio of the number of boys to the number of girls.

*-Added by Akki chauhan* **Mathematics** » **Statistics**

**Answer:**

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 98.** **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:**

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 99.** **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:**

r= 32

Volume of hemisphere= 23 πr^{3}

^{}

= 23 ×22/7×3/2×3/2×3/2

= 7.071

*-Answered by Master Purushottam* On 23 August 2019:11:33:27 PM

**Question 100.** **Asked on :**13 January 2019:11:15:32 AM

Define concentric circles.

*-Added by Akki chauhan* **Mathematics** » **Circles**

**Answer:**

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 101.** **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:**

√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 102.** **Asked on :**12 January 2019:05:54:25 PM

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

*-Added by Himanshi Verma* **Mathematics** » **Number System **

**Question 103.** **Asked on :**12 January 2019:05:52:26 PM

prove that the cyclic parallelogram is rectangle.

*-Added by khushi chauhan* **Mathematics** » **Circles**

**Answer:**

∠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 104.** **Asked on :**12 January 2019:10:52:27 AM

Find the zero of 2x-5.

*-Added by Akki chauhan* **Mathematics** » **Number System**

**Answer:**

2x-5=0

2x=5

x= 5/2

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

**Question 105.** **Asked on :**12 January 2019:10:49:51 AM

Factorise:

x^{3}-23x^{2}+142x-120

*-Added by Akki chauhan* **Mathematics** » **Polynomials**

**Answer:**

x^{3 }-23x^{2}+142x-120

=x^{3}-x^{2}-22x^{2}+22x+120-120

=x^{2}(x-1)-22x(x-1)+120(x-1)

=(x-1)(x^{2}-22x+120)

=(x-1)(x^{2}-12x-10x+120)

=(x-1)[x(x-12)-10(x-12)]

=(x-1)(x-10)(x-12)

*-Answered by Master Purushottam* On 22 August 2019:09:12:12 PM

**Question 106.** **Asked on :**12 January 2019:10:45:37 AM

If the polynomials ax^{3}+3x^{2}-13 and 2x^{3}-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:**

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 Master Purushottam* On 22 August 2019:09:12:19 PM

**Question 107.** **Asked on :**12 January 2019:10:38:50 AM

If a = 9-4√5, then find the value of

a^{2} + 1a^{2}

*-Added by Akki chauhan* **Mathematics** » **Polynomials**

**Answer:**

(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 Master Purushottam* On 22 August 2019:09:08:56 PM

**Question 108.** **Asked on :**11 January 2019:02:55:18 PM

Find the median of first 10 prime numbers.

*-Added by Prince Rawat* **Mathematics** » **STATISTICS**

**Answer:**

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 Master Purushottam* On 22 August 2019:09:04:22 PM

**Question 109.** **Asked on :**11 January 2019:10:18:43 AM

Define frequency of the observation.

*-Added by Prince Rawat* **Mathematics** » **STATISTICS**

**Answer:**

The number of times an observation occurs in the given data is called frequency of the observation.

*-Answered by Master Purushottam* On 22 August 2019:09:04:32 PM

**Question 110.** **Asked on :**11 January 2019:10:10:33 AM

The volume of sphere is 310.4 cm^{3}. Find its radius.

*-Added by Prince Rawat* **Mathematics** » **SURFACE AREAS AND VOLUMES**

**Answer:**

volume of the sphere = 43 πr^{3}= 310.4cm^{3}

4/3×22/7×r^{3}=310.4

88/21×r^{3}= 310.4

r^{3}= 310.4×21/88

= 6518.4/88

r^{3} = 74.0727272cm

*-Answered by Master Purushottam* On 22 August 2019:09:04:44 PM

**Question 111.** **Asked on :**11 January 2019:10:04:29 AM

What is Degree of the Polynomials?

*-Added by Prince Rawat* **Mathematics** » **POLYNOMIALS**

**Answer:**

Highest power of x in the algebraic expression is called the degree of the polynomials.

*-Answered by Prince Rawat* On 11 January 2019:10:08:00 AM

**Question 112.** **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:**

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.t]

*-Answered by Master Purushottam* On 22 August 2019:08:59:15 PM

**Question 113.** **Asked on :**09 January 2019:09:37:10 AM

Ques.1. prove that 2+2= 5

*-Added by Master Purushottam* **Mathematics** » **Number System**

**Answer:**

Start with: -20 = -20

Which is the same as: 16-36 = 25-45Which 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 Master Purushottam* On 22 August 2019:09:00:11 PM

**Question 114.** **Asked on :**09 January 2019:09:36:20 AM

*-Added by Master Purushottam* **Mathematics** » **Number System**

**Answer:**

The basis of the Euclidean **division algorithm** is**Euclid'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 Master Purushottam* On 22 August 2019:09:00:20 PM

**Question 115.** **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:**

21b - 32 + 7b - 20b

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

=8b - 32 Answer

*-Answered by Master Purushottam* On 22 August 2019:09:00:32 PM

**Question 116.** **Asked on :**07 January 2019:02:26:38 PM

Find the sum : 3p^{2}q^{2} - 4pq + 5, - 10p^{2}q^{2}, 15 + 9pq + 7p^{2}q^{2}

*-Added by Master Purushottam* **Mathematics** » **Algebra Expreesion**

**Answer:**

3p^{2}q^{2} - 4pq + 5 + (-10p^{2}q^{2}) + 15 + 9pq + 7p^{2}q^{2}

= 3p^{2}q^{2} + 7p^{2}q^{2} - 10p^{2}q^{2} + 9pq - 4pq + 5 + 15

= 10p^{2}q^{2} - 10p^{2}q^{2} + 5pq + 20

= 5pq + 20

*-Answered by Master Purushottam* On 22 August 2019:09:00:43 PM

**Question 117.** **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:**

( 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 Himanshi Verma* On 22 March 2019:05:16:46 PM

**Question 118.** **Asked on :**07 January 2019:02:16:52 PM

If a = 2, b = -2, find the value of a^{2} + b^{2}.

*-Added by Master Purushottam* **Mathematics** » **Algebra Expreesion**

**Answer:**

The value of a

=4

The value of b^{2}= (-2^{2}) = 4

a^{2}+b^{2}= 4+4

= 8

*-Answered by Master Purushottam* On 22 August 2019:08:55:06 PM

**Question 119.** **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:**

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 Master Purushottam* On 22 August 2019:08:55:13 PM

**Question 120.** **Asked on :**07 January 2019:02:14:21 PM

simplify the expression and find its value when a = 5 and b = -3.

2(a^{2} + ab) + 3 - ab

*-Added by Master Purushottam* **Mathematics** » **Algebra Expreesion**

**Answer:**

a=5, b=-3

2(5^{2}+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 121.** **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:**

3a-2b-ab-(a-b+ab)+3ab+b-a

take same terms like this

3a-a-a=a

-2b+b+b=0

-ab-ab+3ab= -2ab+3ab=ab

=a+0+ab

*-Answered by Master Purushottam* On 22 August 2019:08:55:31 PM

**Question 122.** **Asked on :**07 January 2019:12:03:07 PM

What is mean?

*-Added by ATP Admin* **Mathematics** » **Mean**

**Answer:**

Mean is an average of some data which is calculated by dividing ∑Sum of data by total numbers of data.

*-Answered by Master Purushottam* On 22 August 2019:08:55:50 PM

**Question 123.** **Asked on :**31 December 2018:02:20:01 PM

factorise x^{2} + 2x + 1

*-Added by ATP Admin* **Mathematics** » **Factorisation**

**Answer:**

x^{2} + 2x + 1

= x^{2} + x + x + 1

= x(x + 1) + 1(x + 1)

= (x + 1) (x + 1)

*-Answered by Akki chauhan* On 10 January 2019:10:57:10 AM

**Question 124.** **Asked on :**31 December 2018:09:20:26 AM

*-Added by ATP Admin* **Mathematics** » **Mean Median**

**Answer:**

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 Master Purushottam* On 22 August 2019:08:53:15 PM

**Question 125.** **Asked on :**29 December 2018:01:00:20 AM

*-Added by ATP Admin* **Mathematics** » **Arithmetic Progressions**

**Answer:**

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 Master Purushottam* On 22 August 2019:08:54:07 PM

**Question 126.** **Asked on :**28 December 2018:11:00:50 PM

*-Added by ATP Admin* **Mathematics** » **Arithmetic Progressions **

**Answer:**

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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