32581 + Interview Questions in Mathematics

1.	A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60∘ with the level of the ground. Determine the height of the wall.
Answer» A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of $60^{\circ}$ with the level of the ground. Determine the height of the wall.

Discussion

2.	Find the area of a parallelogram ABCD if three of its vertices are A (2, 4), B (2+√3,5) and C (2, 6).
Answer» Find the area of a parallelogram ABCD if three of its vertices are A (2, 4), B $(2 + \sqrt{3}, 5)$ and C (2, 6).

Discussion

3.	Which one of the following is solution for p(x)= (x-1) (x+6) ?
Answer» Which one of the following is solution for p(x)= (x-1) (x+6) ?

Discussion

4.	At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.
Answer» At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Discussion

5.	If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?
Answer» If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?

Discussion

6.	A contractor plans to install two slides for the children to play in a park. She prefers to have a slide whose top is at a height of √3m and is inclined at an angle of 60∘ to the ground. What should be the length of the slide?
Answer» A contractor plans to install two slides for the children to play in a park. She prefers to have a slide whose top is at a height of √3m and is inclined at an angle of $60^{\circ}$ to the ground. What should be the length of the slide?

Discussion

7.	Find the number of values of x satisfying 3x−3≤7x+5 and 5−x≥(x4)−(54),where x ϵ N.
Answer» Find the number of values of x satisfying $3 x - 3 \leq 7 x + 5 a n d 5 - x \geq (\frac{x}{4}) - (\frac{5}{4}), w h e r e x ϵ N .$

7.

Find the number of values of x satisfying 3x−3≤7x+5 and 5−x≥(x4)−(54),where x ϵ N.

Answer»

Find the number of values of x satisfying

$3 x - 3 \leq 7 x + 5 a n d 5 - x \geq (\frac{x}{4}) - (\frac{5}{4}), w h e r e x ϵ N .$

Discussion

8.	What is the probability of getting a 7 when a die is rolled once?
Answer» What is the probability of getting a 7 when a die is rolled once?

Discussion

9.	Find the equation of a straight line passing through the intersection of 2x+5y-4=0 with X axis and perpendicular to the line 3x-7y+8=0
Answer» Find the equation of a straight line passing through the intersection of 2x+5y-4=0 with X axis and perpendicular to the line 3x-7y+8=0

Discussion

10.	Question 112 (i) Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1 The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?
Answer» Question 112 (i) Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1 The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?

10.

Question 112 (i) Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1 The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?

Answer»

Question 112 (i)

Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1

The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?

Discussion

11.	If n ' is a rational number and √y is irrational then prove that x+√y is rational?
Answer» If n ' is a rational number and √y is irrational then prove that x+√y is rational?

Discussion

12.	If x=a,and y=b is the solution of the equation 2x+y=3 and x-y=3. Find the values of a and b.
Answer» If x=a,and y=b is the solution of the equation 2x+y=3 and x-y=3. Find the values of a and b.

Discussion

13.	If a,b belongs to C are the distinct roots of the equation x^2-x+1=0 then find a^101+b^107 is
Answer» If a,b belongs to C are the distinct roots of the equation x^2-x+1=0 then find a^101+b^107 is

Discussion

14.	Construct a circle in a regular hexagon of side 3 cm. [3 MARKS]
Answer» Construct a circle in a regular hexagon of side 3 cm. [3 MARKS]

Discussion

15.	Hello Please help me with the following Is interest charged on a current account? Regards Nikita
Answer» Hello Please help me with the following Is interest charged on a current account? Regards Nikita

15.

Hello Please help me with the following Is interest charged on a current account? Regards Nikita

Answer»

Hello

Please help me with the following

Is interest charged on a current account?

Regards

Nikita

Discussion

16.	When a polynomial f(x) is divided by (x-1) the remainder is 5 and when it is divided by (x-2),the remainder is 7.Find the remainder when it is divided by (x-1)(x-2).
Answer» When a polynomial f(x) is divided by (x-1) the remainder is 5 and when it is divided by (x-2),the remainder is 7.Find the remainder when it is divided by (x-1)(x-2).

Discussion

17.	30th term of the AP: 10,7,4,..., is
Answer» $30^{t h}$ term of the AP: 10,7,4,..., is

Discussion

18.	If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be
Answer» If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be

Discussion

19.	What is the remainder when 4x3 - 7x + 6 is divided by x – 1?
Answer» What is the remainder when $4 x^{3}$ - 7x + 6 is divided by x – 1?

Discussion

20.	Sin(45o – A) cos(45o - B) + cos(45o – A) sin(45o – B)
Answer» Sin(45^o – A) cos(45^o - B) + cos(45^o – A) sin(45^o – B)

Discussion

21.	The sum of three numbers in an A.P is 12 and the sum of their cubes is 288. Find the numbers.
Answer» The sum of three numbers in an A.P is 12 and the sum of their cubes is 288. Find the numbers.

Discussion

22.	If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A=
Answer» If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot²A=

Discussion

23.	Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. if the difference between the digits is 3. find the two digit number.
Answer» Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. if the difference between the digits is 3. find the two digit number.

Discussion

24.	The marked price of a bike is ₹ 46000 and is offered at a discount of 5%. If the sales tax is charged at a rate of 10%, find the selling price of the bike.
Answer» The marked price of a bike is ₹ 46000 and is offered at a discount of 5%. If the sales tax is charged at a rate of 10%, find the selling price of the bike.

Discussion

25.	In a circle, O is the centre and ∠COD is a right angle. AC=BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?
Answer» In a circle, O is the centre and $∠$ COD is a right angle. $A C = B D$ and $C D$ is the tangent at $P .$ Which of the following are true, if the radius of the circle is $1 m ?$

25.

In a circle, O is the centre and ∠COD is a right angle. AC=BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

Answer»

In a circle, O is the centre and $∠$ COD is a right angle. $A C = B D$ and $C D$ is the tangent at $P .$ Which of the following are true, if the radius of the circle is $1 m ?$

Discussion

26.	Let M be a 3×3 matrix satisying M⎡⎢⎣010⎤⎥⎦=⎡⎢⎣−123⎤⎥⎦,M⎡⎢⎣1−10⎤⎥⎦=⎡⎢⎣11−1⎤⎥⎦,and M⎡⎢⎣111⎤⎥⎦=⎡⎢⎣0012⎤⎥⎦. Then, the sum of the diagonal entries of M is ___
Answer» Let M be a $3 \times 3$ matrix satisying $M ⎡ ⎢ ⎣ \begin{matrix} 010 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} - 1 23 \end{matrix} ⎤ ⎥ ⎦, M ⎡ ⎢ ⎣ \begin{matrix} 1 - 1 0 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 11 - 1 \end{matrix} ⎤ ⎥ ⎦, a n d M ⎡ ⎢ ⎣ \begin{matrix} 111 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 0012 \end{matrix} ⎤ ⎥ ⎦ .$ Then, the sum of the diagonal entries of M is ___

Discussion

27.	In each of the following find the value of k for which the given value is a soluton of the given equation (i)7x2+kx−3=0,x=23(ii)x2−x(a+b)+k=0,x=a(iii)kx2+√2x−4=0,x=√2(iv)x23ax+k=0,x=−a
Answer» In each of the following find the value of k for which the given value is a soluton of the given equation $(i) 7 x^{2} + k x - 3 = 0, x = \frac{2}{3} (i i) x^{2} - x (a + b) + k = 0, x = a (i i i) k x^{2} + \sqrt{2 x} - 4 = 0, x = \sqrt{2} (i v) x^{2} 3 a x + k = 0, x = - a$

Discussion

28.	The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is
Answer» The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

Discussion

29.	Mean proportional of 10√m and 40√m is
Answer» Mean proportional of $10 \sqrt{m}$ and $40 \sqrt{m}$ is

Discussion

30.	Which of the following quadratic equation have equal roots?
Answer» Which of the following quadratic equation have equal roots?

Discussion

31.	All the three face cards of spade are removed from a well shuffled pack of 52 cards & card is drawn from the remaining pack. Find the probability of getting a black face card.
Answer» All the three face cards of spade are removed from a well shuffled pack of 52 cards & card is drawn from the remaining pack. Find the probability of getting a black face card.

Discussion

32.	If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then
Answer» If the sum of the areas of two circles with radii R₁ and R₂ is equal to the area of a circle of radius R, then

Discussion

33.	A circle of radius r is inscribed in a triangle of area ′Δ′. If the semi-perimeter of the triangle is s, then the correct relation is
Answer» A circle of radius r is inscribed in a triangle of area $^{'} Δ^{'}$ . If the semi-perimeter of the triangle is s, then the correct relation is

Discussion

34.	Find the roots of the quadratic equation 2x2 - 7x + 3 = 0 by the method of completion of squares.
Answer» Find the roots of the quadratic equation ${2 x}^{2}$ - 7 $x$ + 3 = 0 by the method of completion of squares.

Discussion

35.	A 6 m tall man finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.
Answer» A 6 m tall man finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Discussion

36.	Find the remainder when x2 + 4x + 5 is divided by (2x + 2)
Answer» Find the remainder when $x^{2}$ + 4x + 5 is divided by (2x + 2)

Discussion

37.	If the seventh term of an AP is 19 and its ninth term is 17, find its 63rd term.
Answer» If the seventh term of an AP is $\frac{1}{9}$ and its ninth term is $\frac{1}{7}$ , find its $63^{r d}$ term.

Discussion

38.	If the slopes of two lines are equal, then the lines are __ to each other.
Answer» If the slopes of two lines are equal, then the lines are __ to each other.

Discussion

39.	You bought a pen and three refills for rupees 25 and your friend wbought 2 pens and a refill for rupees 25. Try to represent the solution as equations. Can you find the cost of a pen and a refill separately?
Answer» You bought a pen and three refills for rupees 25 and your friend wbought 2 pens and a refill for rupees 25. Try to represent the solution as equations. Can you find the cost of a pen and a refill separately?

Discussion

40.	Match the following graphs to their nature of roots: i) Real and distinct roots ii) Non-real roots iii) Real and equal roots
Answer» Match the following graphs to their nature of roots: i) Real and distinct roots ii) Non-real roots iii) Real and equal roots

Discussion

41.	How many natural numbers between 1 and 900 are NOT multiples of any of the numbers 2, 3, or 5?
Answer» How many natural numbers between 1 and 900 are NOT multiples of any of the numbers 2, 3, or 5?

Discussion

42.	Find the roots of the Following equation: (i) x2−3x−4=0 By Factorization (ii) 5x2−6x=8 By Completing squares (iii) 4x2−2x=5 By Completing squares
Answer» Find the roots of the Following equation: (i) $x^{2} - 3 x - 4 = 0$ By Factorization (ii) $5 x^{2} - 6 x = 8$ By Completing squares (iii) $4 x^{2} - 2 x = 5$ By Completing squares

42.

Find the roots of the Following equation: (i) x2−3x−4=0 By Factorization (ii) 5x2−6x=8 By Completing squares (iii) 4x2−2x=5 By Completing squares

Answer»

Find the roots of the Following equation:

(i) $x^{2} - 3 x - 4 = 0$ By Factorization

(ii) $5 x^{2} - 6 x = 8$ By Completing squares

(iii) $4 x^{2} - 2 x = 5$ By Completing squares

Discussion

43.	Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (iii)2x2−6x+3=0
Answer» Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; $(i i i) 2 x^{2} - 6 x + 3 = 0$

Discussion

44.	Use the Remainder Theorem to find which of the following is a factor of 2x3+3x2−5x−6 (a) x+1 (ii) 2x-1 (iii) x+2
Answer» Use the Remainder Theorem to find which of the following is a factor of $2 x^{3} + 3 x^{2} - 5 x - 6$ (a) x+1 (ii) 2x-1 (iii) x+2

Discussion

45.	In a Math test two students while solving a quadratic equation committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and got the roots as 12 and 4. But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.
Answer» In a Math test two students while solving a quadratic equation committed the following mistakes: (i) One of them made a mistake in the constant term and got the roots as 5 and 9. (ii) Another one committed an error in the coefficient of x and got the roots as 12 and 4. But, in the meantime, they realised that they are wrong and they managed to get it right jointly. Find the correct quadratic equation.

Discussion

46.	If the meas of the following distribution is 27, find the value of P, Class0−1010−2020−3030−4040−50Frequency8P121310
Answer» If the meas of the following distribution is 27, find the value of P, $\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 F r e q u e n c y & 8 & P & 12 & 13 & 10 \end{matrix}$

46.

If the meas of the following distribution is 27, find the value of P, Class0−1010−2020−3030−4040−50Frequency8P121310

Answer»

If the meas of the following distribution is 27, find the value of P,

$\begin{matrix} C l a s s & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 F r e q u e n c y & 8 & P & 12 & 13 & 10 \end{matrix}$

Discussion

47.	The area of a rectangular plot is 528m2. The length of the plot (in metres) is one metre more than twice its breadth. Find the length and the breadth of the plot.
Answer» The area of a rectangular plot is $528 m^{2} .$ The length of the plot (in metres) is one metre more than twice its breadth. Find the length and the breadth of the plot.

Discussion

48.	A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. Find the angle subtended by the fence with the center of the garden. It is given that cos(53∘) = 35.
Answer» A circular garden of radius 10m has a straight line fence between the two points on the boundary of the garden. The fence lies inside the garden arena. This fence separates the walking area which is a small region from the plants. The fence is at a distance of 6 m from the centre of the garden. Find the angle subtended by the fence with the center of the garden. It is given that cos( $53^{\circ}$ ) = $\frac{3}{5}$ .

Discussion

49.	If one root of equation ax2+bx+c=0 is reciprocal of other, then value of c is:
Answer» If one root of equation $a x^{2} + b x + c = 0$ is reciprocal of other, then value of c is:

Discussion

50.	Which of the following statements are true? 1) No tangents can be drawn to a circle from an interior point. 2) Only two tangents, at most, can be drawn to a circle from an exterior point.
Answer» Which of the following statements are true? 1) No tangents can be drawn to a circle from an interior point. 2) Only two tangents, at most, can be drawn to a circle from an exterior point.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A ladder is placed along a wall of a house such that its upper end is touching the top of the wall. The foot of the ladder is 2 m away from the wall and the ladder is making an angle of 60∘ with the level of the ground. Determine the height of the wall.

Find the area of a parallelogram ABCD if three of its vertices are A (2, 4), B (2+√3,5) and C (2, 6).

Which one of the following is solution for p(x)= (x-1) (x+6) ?

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?

A contractor plans to install two slides for the children to play in a park. She prefers to have a slide whose top is at a height of √3m and is inclined at an angle of 60∘ to the ground. What should be the length of the slide?

Find the number of values of x satisfying 3x−3≤7x+5 and 5−x≥(x4)−(54),where x ϵ N.

What is the probability of getting a 7 when a die is rolled once?

Find the equation of a straight line passing through the intersection of 2x+5y-4=0 with X axis and perpendicular to the line 3x-7y+8=0

Question 112 (i) Social Studies Application remembering that 1 AD came immediately after 1 BC, while solving following problems take 1 BC as -1 and 1 AD as +1 The Greece-Roman era, when Greece and Rome ruled Egypt, started in the year 330 BC and ended in the year 395 AD. How long did this era last?

If n ' is a rational number and √y is irrational then prove that x+√y is rational?

If x=a,and y=b is the solution of the equation 2x+y=3 and x-y=3. Find the values of a and b. ​​​​​

If a,b belongs to C are the distinct roots of the equation x^2-x+1=0 then find a^101+b^107 is

Construct a circle in a regular hexagon of side 3 cm. [3 MARKS]

Hello Please help me with the following Is interest charged on a current account? Regards Nikita

When a polynomial f(x) is divided by (x-1) the remainder is 5 and when it is divided by (x-2),the remainder is 7.Find the remainder when it is divided by (x-1)(x-2).

30th term of the AP: 10,7,4,..., is

If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be

What is the remainder when 4x3 - 7x + 6 is divided by x – 1?

Sin(45o – A) cos(45o - B) + cos(45o – A) sin(45o – B)

The sum of three numbers in an A.P is 12 and the sum of their cubes is 288. Find the numbers.

If A and B are the angles of a right angled triangle ABC, right angled at C, then 1+cot2A=

Seven times a two digit number is equal to four times the number obtained by reversing the order of digits. if the difference between the digits is 3. find the two digit number.

The marked price of a bike is ₹ 46000 and is offered at a discount of 5%. If the sales tax is charged at a rate of 10%, find the selling price of the bike.

In a circle, O is the centre and ∠COD is a right angle. AC=BD and CD is the tangent at P. Which of the following are true, if the radius of the circle is 1 m?

Let M be a 3×3 matrix satisying M⎡⎢⎣010⎤⎥⎦=⎡⎢⎣−123⎤⎥⎦,M⎡⎢⎣1−10⎤⎥⎦=⎡⎢⎣11−1⎤⎥⎦,and M⎡⎢⎣111⎤⎥⎦=⎡⎢⎣0012⎤⎥⎦. Then, the sum of the diagonal entries of M is ___

In each of the following find the value of k for which the given value is a soluton of the given equation (i)7x2+kx−3=0,x=23(ii)x2−x(a+b)+k=0,x=a(iii)kx2+√2x−4=0,x=√2(iv)x23ax+k=0,x=−a

The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

Mean proportional of 10√m and 40√m is

Which of the following quadratic equation have equal roots?

All the three face cards of spade are removed from a well shuffled pack of 52 cards &amp; card is drawn from the remaining pack. Find the probability of getting a black face card.

If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then

A circle of radius r is inscribed in a triangle of area ′Δ′. If the semi-perimeter of the triangle is s, then the correct relation is

Find the roots of the quadratic equation 2x2 - 7x + 3 = 0 by the method of completion of squares.

A 6 m tall man finds that the angle of elevation of a 24 m high pillar and the angle of depression of its base are complementary angles. Find the distance of the man from the pillar.

Find the remainder when x2 + 4x + 5 is divided by (2x + 2)

If the seventh term of an AP is 19 and its ninth term is 17, find its 63rd term.

If the slopes of two lines are equal, then the lines are __ to each other.

You bought a pen and three refills for rupees 25 and your friend wbought 2 pens and a refill for rupees 25. Try to represent the solution as equations. Can you find the cost of a pen and a refill separately?

Match the following graphs to their nature of roots: i) Real and distinct roots ii) Non-real roots iii) Real and equal roots

How many natural numbers between 1 and 900 are NOT multiples of any of the numbers 2, 3, or 5?

Find the roots of the Following equation: (i) x2−3x−4=0 By Factorization (ii) 5x2−6x=8 By Completing squares (iii) 4x2−2x=5 By Completing squares

Find the nature of the roots of the following quadratic equations. If the real roots exist, find them; (iii)2x2−6x+3=0

Use the Remainder Theorem to find which of the following is a factor of 2x3+3x2−5x−6 (a) x+1 (ii) 2x-1 (iii) x+2

If the meas of the following distribution is 27, find the value of P, Class0−1010−2020−3030−4040−50Frequency8P121310

The area of a rectangular plot is 528m2. The length of the plot (in metres) is one metre more than twice its breadth. Find the length and the breadth of the plot.

If one root of equation ax2+bx+c=0 is reciprocal of other, then value of c is:

Which of the following statements are true? 1) No tangents can be drawn to a circle from an interior point. 2) Only two tangents, at most, can be drawn to a circle from an exterior point.

If x=a,and y=b is the solution of the equation 2x+y=3 and x-y=3. Find the values of a and b.

All the three face cards of spade are removed from a well shuffled pack of 52 cards & card is drawn from the remaining pack. Find the probability of getting a black face card.