**Master Mind**

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

**Question 1.** **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 2.** **Asked on :**23 March 2020:07:27:04 AM

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

*-Added by Aman Senapati* **Mathematics** » **POLYNOMIALS**

**Question 3.** **Asked on :**20 February 2020:08:15:19 PM

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

*-Added by Master Mind* **Mathematics** » **Triangles**

**Question 4.** **Asked on :**19 February 2020:11:24:57 AM

If a,b and c are the sides of a right angled triangle where c is the hypotenuse ,then prove that the radius r or the circle which touches the sides of the triangle is given by

r = a + b - c2

*-Added by Master Mind* **Mathematics** » **Circle**

**Answer:**

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

**Question 5.** **Asked on :**16 February 2020:03:00:47 PM

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

*-Added by Khushi Chauhan* **Mathematics** » **Probablity**

**Answer:**

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 6.** **Asked on :**25 December 2019:10:06:08 PM

*-Added by Dhrumil Sheth* **Mathematics** » **Ch 12**

**Answer:**

52 cm square.

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

**Question 7.** **Asked on :**14 December 2019:08:13:05 PM

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

*-Added by Aman Senapati* **Mathematics** » **Star And Solar System**

**Answer:**

lunar calender.

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

**Question 8.** **Asked on :**16 October 2019:08:07:00 PM

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

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

**Answer:**

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 9.** **Asked on :**10 October 2019:07:06:18 PM

Who is father of trignometry ?

*-Added by Aarohi Chauhan* **Mathematics** » **Introduction To Trignometry**

**Answer:**

Hipparchus.

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

**Question 10.** **Asked on :**07 October 2019:05:01:00 PM

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

*-Added by Master Mind* **Mathematics** » **Comparing Quantities**

**Answer:**

**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 11.** **Asked on :**07 October 2019:11:36:04 AM

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

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

**Answer:**

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 12.** **Asked on :**07 October 2019:11:34:52 AM

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

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

**Answer:**

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 13.** **Asked on :**07 October 2019:11:32:08 AM

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

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

**Answer:**

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 14.** **Asked on :**07 October 2019:11:29:31 AM

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

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

**Answer:**

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 15.** **Asked on :**07 October 2019:11:23:47 AM

*-Added by Himanshi Verma* **Mathematics** » **Introduction To Trignometry**

**Answer:**

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 16.** **Asked on :**07 October 2019:11:16:08 AM

Find the value of (sin°45- cos°45)

*-Added by Himanshi Verma* **Mathematics** » **Introduction To Trignometry**

**Answer:**

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 17.** **Asked on :**01 October 2019:06:14:01 PM

what is formula of distance?

*-Added by Shivang Gupta* **Mathematics** » **Coodinate Geomertry**

**Answer:**

Pythagorean theorem as d=√((x_2-x_1)²+(y_2-y_1)²) to

*-Answered by priyanshu kumar* On 05 October 2019:03:52:57 PM

**Question 18.** **Asked on :**30 September 2019:10:14:41 AM

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

**Answer:**

4xsquare

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

**Question 19.** **Asked on :**30 September 2019:10:13:16 AM

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

**Answer:**

πrh

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

**Question 20.** **Asked on :**30 September 2019:10:12:51 AM

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

**Answer:**

4*side.

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

**Question 21.** **Asked on :**30 September 2019:10:12:25 AM

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

**Answer:**

side * side

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

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

What is formula of Total surface area of Hemisphere?

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

**Answer:**

(3

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

**Question 23.** **Asked on :**30 September 2019:10:10:34 AM

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

**Answer:**

(2

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

**Question 24.** **Asked on :**30 September 2019:10:09:29 AM

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

**Answer:**

(4

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

**Question 25.** **Asked on :**30 September 2019:10:06:39 AM

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

**Answer:**

(

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

**Question 26.** **Asked on :**30 September 2019:10:06:06 AM

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

**Answer:**

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

**Question 27.** **Asked on :**30 September 2019:10:03:38 AM

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

**Answer:**

Diagonal = √3

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

**Question 28.** **Asked on :**30 September 2019:10:03:01 AM

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

**Answer:**

6

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

**Question 29.** **Asked on :**30 September 2019:10:02:26 AM

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

**Answer:**

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

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

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

**Answer:**

(

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

**Question 31.** **Asked on :**30 September 2019:09:57:29 AM

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

**Answer:**

*-Answered by priyanshu kumar* On 30 September 2019:10:49:12 AM

**Question 32.** **Asked on :**30 September 2019:09:57:06 AM

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

**Answer:**

*-Answered by priyanshu kumar* On 30 September 2019:10:49:27 AM

**Question 33.** **Asked on :**30 September 2019:09:56:38 AM

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

**Answer:**

*-Answered by priyanshu kumar* On 30 September 2019:10:50:00 AM

**Question 34.** **Asked on :**28 September 2019:07:17:58 AM

How it is possible?

999+888+777 = 999

*-Added by Rohit Rajput* **Mathematics** » **Brain Teaser**

**Answer:**

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

If 60% 1200 then the value of x

*-Added by Sohail alam* **Mathematics** » **All Question**

**Answer:**

85%

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

**Question 36.** **Asked on :**23 September 2019:09:47:39 AM

The two opposite vertices of a square are (-1,2)and (3,2).find the coordinate of the two other vertices.

*-Added by Rohit Rajput* **Mathematics** » **Cooridinate Triangle**

**Answer:**

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)

AB^{2} = BC^{2}

[x – (–1)] ^{2} + (y – 2)^{2 }= (x – 3)^{2} + (y – 2)^{2 }

(x + 1)^{2} = (x – 3)^{2}

x ^{2} + 2x + 1 = x ^{2 }– 6x + 9

2x + 6x = 9 – 1

8x = 8

x = 1

In ΔABC, we have:

AB^{2} + BC^{2} = AC^{2} (Pythagoras theorem)

2AB^{2} = AC^{2} (Since, AB = BC)

2[(x – (–1))^{2} + (y – 2)^{2}]^{ }= (3 – (–1))^{2} + (2 – 2)^{2}

2[(x + 1)^{2} + (y – 2)^{2}] = (4)^{2} + (0)^{2}

2[(1 + 1)^{2} + (y – 2)^{2}] = 16 ( x = 1)

2[ 4 + (y – 2)^{2}] = 16

8 + 2 (y – 2)^{2} = 16

2 (y – 2)^{2} = 16 – 8 = 8

(y – 2)^{2} = 4

y – 2 = ± 2

y – 2 = 2 or y – 2 = –2

y = 4 or y = 0

Thus, the other two vertices of the square ABCD are (1, 4) and (1, 0).

*-Answered by Suraj Kumar* On 07 November 2019:08:37:47 AM

**Question 37.** **Asked on :**23 September 2019:09:44:14 AM

find the center of circle passing though the points (6,-6),(3,-7)and (3,3).

*-Added by Rohit Rajput* **Mathematics** » **Cooridinate Triangle**

**Answer:**

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

**Question 38.** **Asked on :**23 September 2019:09:33:49 AM

find the area of triangle formed by joining the midpoint of the sides of the triangle whose vertices are (0,-1),(0,3)and (0,3). find the ratio of this area of the given triangle.

*-Added by Rohit Rajput* **Mathematics** » **Cooredinate Geometry **

**Answer:**

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 39.** **Asked on :**07 September 2019:05:10:32 PM

*-Added by Reddy cbse* **Mathematics** » **NCERT Solutions For Class 10 Maths**

**Answer:**

What is your question

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

**Question 40.** **Asked on :**07 September 2019:08:51:52 AM

What is full form of HCF

*-Added by Sohail alam* **Mathematics** » **Maths**

**Answer:**

Highest common factor.

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

**Question 41.** **Asked on :**02 September 2019:03:04:03 PM

Q what is the area of square when side is 90cm?

*-Added by Shruti Srivastva * **Mathematics** » **Maths**

**Answer:**

8100 cm sq.

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

**Question 42.** **Asked on :**01 September 2019:12:21:47 PM

Who discovered bacterial transformation?

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

**Answer:**

Frederick Griffith.

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

**Question 43.** **Asked on :**01 September 2019:12:20:02 PM

Which term is 78 of A.P 3,8,13,18...................

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

**Answer:**

∴

*-Answered by Nishant Verma* On 02 September 2019:10:23:45 AM

**Question 44.** **Asked on :**30 August 2019:03:52:44 PM

write the formula of C.I.?

*-Added by Suman Kumari* **Mathematics** » **Maths**

**Answer:**

CI formula

*-Answered by Nishant Verma* On 30 August 2019:03:54:16 PM

**Question 45.** **Asked on :**30 August 2019:03:12:53 PM

Pythagoras Theorem: In a right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

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

**Answer:**

*-Answered by Nishant Verma* On 30 August 2019:03:56:50 PM

**Question 46.** **Asked on :**30 August 2019:03:12:00 PM

In two triangles, If the sides of one triangle are proportional to the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar, also called SSS (side-side-side) criterion.

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

**Answer:**

*-Answered by Nishant Verma* On 30 August 2019:03:57:22 PM

**Question 47.** **Asked on :**30 August 2019:03:11:19 PM

If a line divides any of the two sides of a triangle in the same ratio, then that line is parallel to the third side.

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

**Answer:**

*-Answered by Nishant Verma* On 30 August 2019:03:57:52 PM

**Question 48.** **Asked on :**30 August 2019:03:09:49 PM

To Prove that, If a line is drawn parallel to one side of a Triangle and intersects the other two sides, then the other two sides are divided in the same ratio.

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

**Answer:**

Let a ΔABC in which a line DE parallel to SC intersects AB at D and AC at E.To prove DE divides the two sides in the same ratio.

*-Answered by Akki chauhan* On 30 August 2019:08:51:32 PM

**Question 49.** **Asked on :**28 August 2019:09:45:10 AM

Find the ratio in which the line segment joining A(1,-5) B(6,-8) is divided by the X-Axis. Also find the coordinates of the point of division.

*-Added by Akki chauhan* **Mathematics** » **Coordinate Geometry**

**Answer:**

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 50.** **Asked on :**26 August 2019:07:47:56 PM

Find the distance between the following pairs of points:

(i) (2,3),(4,1)

*-Added by Akki chauhan* **Mathematics** » **Coordinate Geometry**

**Answer:**

(i) Distance between the two points is given by

*-Answered by Akki chauhan* On 26 August 2019:07:58:00 PM

**Question 51.** **Asked on :**25 August 2019:03:25:31 PM

Find the next number in the sequence 6,24,60,120.......

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

**Answer:**

336.

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

**Question 52.** **Asked on :**25 August 2019:03:23:16 PM

Find the next number in the sequence 0,2,24,252......

Please give right answer other wise dont touch this question.

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

**Answer:**

0,2,24,252 Adding 1,2,3,4 n 5 respectively, 0+1=1 2+2=4 24+3=27 252+4=256 We get, 1,4,27,256 Now, 1=1^1 4=2^2 27=3^3 256=4^4 So, next no. = 5^5 - 5= 3120 :).

*-Answered by Shivang Gupta* On 25 August 2019:03:38:16 PM

**Question 53.** **Asked on :**25 August 2019:10:39:42 AM

(i) A king of a red colour (ii) A face card

(iii) A red face card (iv) The queen of diamonds.

*-Added by Harshita Rathore* **Mathematics** » **Probability**

**Answer:**

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

**Question 54.** **Asked on :**24 August 2019:09:16:21 PM

Find the sum of the first 25 multiples of 7.

*-Added by Prince Rawat* **Mathematics** » **Arithmetic Progressions **

**Answer:**

The A.P. : 7, 14, 21, ..............

Now We have to find 7 + 14 + 21 + ........... 25 terms

∴ a = 7, d = 7 n = 25

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

S_{25} = 252 {2 × 7 + (25 - 1)7}

= 252 {14 + (24)7}

= 252 (14 + 168)

= 252 × 182

= 25 × 91

= 2275 **Answer**

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

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

**Question 55.** **Asked on :**24 August 2019:09:15:05 PM

Find the sum of n terms of A.P. 2+4+6+...... .

*-Added by Prince Rawat* **Mathematics** » **Arithmetic Progressions **

**Answer:**

Answer:30,240

Step-by-step explanation:

Let a be the first term and d the common difference

A=2

D=4-2=2

So, 15th term=a+(15-1)*d

=2+(14*2)

2+28

=30

Sum of first 15 term=

n/2(a+an),where n=number

of terms.

=15/2(2+30)

=15/2(32)

=15*16

=240

*-Answered by Akki chauhan* On 24 August 2019:09:27:13 PM

**Question 56.** **Asked on :**24 August 2019:09:11:37 PM

Find the sum of the A.p.1+3+5+7+.....+199.

*-Added by Prince Rawat* **Mathematics** » **Arithmetic Progressions **

**Answer:**

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 57.** **Asked on :**24 August 2019:08:27:55 PM

Find the sum of the first 27 multiples of 6 ?

*-Added by Gunnaj sheikh* **Mathematics** » **Ch 5**

**Answer:**

2268

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

**Question 58.** **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 Suraj Kumar* On 11 December 2019:08:33:38 AM

**Question 59.** **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 Suraj Kumar* On 11 December 2019:08:33:46 AM

**Question 60.** **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 61.** **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 62.** **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 63.** **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 64.** **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 65.** **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 66.** **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 67.** **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 68.** **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 69.** **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 70.** **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 71.** **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 72.** **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 73.** **Asked on :**09 July 2019:06:56:05 PM

Prove the identity:

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

**Answer:**

Cos

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

**Question 74.** **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 75.** **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 76.** **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 77.** **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 78.** **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 79.** **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 80.** **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 81.** **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 83.** **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 84.** **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 85.** **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 86.** **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 87.** **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 88.** **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 89.** **Asked on :**19 April 2019:08:23:46 AM

Check whether the first polynomials is a factors of the second polynomials by dividing the second polynomials by the first polynomials.

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

**Answer:**

what is the polynomials.

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

**Question 90.** **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 91.** **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 92.** **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 93.** **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 94.** **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 95.** **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 96.** **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 97.** **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 98.** **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 99.** **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 100.** **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 101.** **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 102.** **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 103.** **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

**Answer:**

Please give your question

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

**Question 105.** **Asked on :**13 February 2019:10:06:57 AM

** Find the value of X**

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

**Answer:**

(i) 55

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

**Question 106.** **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 107.** **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 108.** **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 109.** **Asked on :**09 February 2019:03:02:25 PM

In the following,find the area of the shaded portains:

*-Added by Himanshi Verma* **Mathematics** » **Chapter 11.4**

**Answer:**

What is shade portion

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

**Question 110.** **Asked on :**07 February 2019:09:36:04 AM

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

**Question 111.** **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 112.** **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 113.** **Asked on :**05 February 2019:05:12:59 PM

If x = , what is the value of

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

**Question 114.** **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 115.** **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 116.** **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 117.** **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 118.** **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 119.** **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

**Answer:**

Please give question

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

**Question 121.** **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 122.** **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 123.** **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 124.** **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 125.** **Asked on :**27 January 2019:10:54:59 AM

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

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

**Answer:**

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 126.** **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

**Answer:**

what is your question

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

**Question 128.** **Asked on :**27 January 2019:10:19:50 AM

1,2,3 ,...,33,34,35 में 7 का गुणज आने

*-Added by praful kumar* **Mathematics** » **Prayikta**

**Answer:**

हल : 35 का गुणनखण्ड = 1,5,7,35 ... 120 का गुणनखण्ड = 1,2,3,4,5,6,8,10,12,

*-Answered by priyanshu kumar* On 10 November 2019:03:37:25 PM

**Question 129.** **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 130.** **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 131.** **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 132.** **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 133.** **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 134.** **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 135.** **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 136.** **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 137.** **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 138.** **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 139.** **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 140.** **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 141.** **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 142.** **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 143.** **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 144.** **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 145.** **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 146.** **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 147.** **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 148.** **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 149.** **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 150.** **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 151.** **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 152.** **Asked on :**13 January 2019:12:13:10 PM

If the ratio of altitude and area of the parallelogrm is 2:1 then find the length of the base of parallelogram.

*-Added by Himanshi Verma* **Mathematics** » **Areas Of Parallelogram And Triangles**

**Answer:**

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

**Question 153.** **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 154.** **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 155.** **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 156.** **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 157.** **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 158.** **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 159.** **Asked on :**12 January 2019:05:54:25 PM

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

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

**Answer:**

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

**Question 160.** **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 161.** **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 162.** **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 Shivang Gupta* On 25 August 2019:05:08:24 PM

**Question 163.** **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 Shivang Gupta* On 25 August 2019:05:08:54 PM

**Question 164.** **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 Nishant Verma* On 17 October 2019:02:43:54 PM

**Question 165.** **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 Shivang Gupta* On 25 August 2019:03:29:06 PM

**Question 166.** **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 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 167.** **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 Shivang Gupta* On 25 August 2019:03:29:31 PM

**Question 168.** **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 algebraic expressions is called the degree of polynomial.

*-Answered by Nishant Verma* On 17 October 2019:02:42:40 PM

**Question 169.** **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

*-Answered by Rahul Kumar * On 13 October 2019:10:01:29 AM

**Question 170.** **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 Nishant Verma* On 13 October 2019:09:38:52 AM

**Question 171.** **Asked on :**09 January 2019:09:36:20 AM

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

**Answer:**

The basis of the Euclidean

*-Answered by Nishant Verma* On 17 October 2019:02:37:10 PM

**Question 172.** **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 Nishant Verma* On 17 October 2019:02:37:18 PM

**Question 173.** **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 Nishant Verma* On 17 October 2019:02:37:38 PM

**Question 174.** **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 Akki chauhan* On 05 September 2019:08:41:17 PM

**Question 175.** **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 Nishant Verma* On 17 October 2019:02:38:02 PM

**Question 176.** **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 Nishant Verma* On 17 October 2019:02:38:41 PM

**Question 177.** **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 178.** **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 Nishant Verma* On 17 October 2019:02:39:08 PM

**Question 179.** **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 Nishant Verma* On 17 October 2019:02:39:17 PM

**Question 180.** **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 Nishant Verma* On 17 October 2019:02:40:08 PM

**Question 181.** **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 priyanshu kumar* On 03 November 2019:03:15:43 PM

**Question 182.** **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 Harshita Rathore* On 26 August 2019:03:25:54 PM

**Question 183.** **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

You can see here all the solutions of this question by various user for **NCERT Solutions**. We hope this try will help you in your study and performance.

This Solution may be usefull for your practice and **CBSE Exams** or All label exams of **secondory examination**. These solutions or answers are user based solution which may be or not may be by expert but you have to use this at your own understanding of your **syllabus**.

Our Expert Team reply with answer soon.

Ask Your Question

* Now You can earn points on every asked question and Answer by you. This points make you a valuable user on this forum. This facility is only available for registered user and educators.

Next moment you answer is ready .... go ahead ...

User Earned Point: Select

Sponsers link