32581 + Interview Questions in Mathematics

1.	In the figure, line segment AB meets x - axis at A and y - axis at B. The point P(-3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B. [3 MARKS]
Answer» In the figure, line segment AB meets x - axis at A and y - axis at B. The point P(-3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B. [3 MARKS]

Discussion

2.	Find mean by step deviation method.
Answer» Find mean by step deviation method.

2.

Find mean by step deviation method.

Answer»

Find mean by step deviation method.

Discussion

3.	Consider the points A(4,3) and B(0,1). If a circle is drawn with AB as diameter, then the coordinates of the points where this circle intersects the x-axis are
Answer» Consider the points $A (4, 3)$ and $B (0, 1)$ . If a circle is drawn with AB as diameter, then the coordinates of the points where this circle intersects the $x$ -axis are

Discussion

4.	In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF to the area of the quadrilateral FDCE is:
Answer» In the given figure, AE and BD are two medians of a $△$ ABC meeting at F. The ratio of the area of $△$ ABF to the area of the quadrilateral FDCE is:

4.

In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF to the area of the quadrilateral FDCE is:

Answer»

In the given figure, AE and BD are two medians of a $△$ ABC meeting at F. The ratio of the area of $△$ ABF to the area of the quadrilateral FDCE is:

Discussion

5.	The H.C.F. of 3xy2z3, 3yz2x2 and x2y2z is .
Answer» The H.C.F. of $3 x y^{2} z^{3}$ , $3 y z^{2} x^{2}$ and $x^{2} y^{2} z$ is .

Discussion

6.	Find a quadratic equation whose one of the root is 2 and whose sum of the roots of zero
Answer» Find a quadratic equation whose one of the root is 2 and whose sum of the roots of zero

Discussion

7.	A man invests ₹ 1680 in buying shares of nominal value ₹ 25 at 12% premium. The dividend on the shares is 15% per annum.Calculate 1) the number of shares he buys 2) the dividend he receives annually
Answer» A man invests ₹ 1680 in buying shares of nominal value ₹ 25 at 12% premium. The dividend on the shares is 15% per annum.Calculate 1) the number of shares he buys 2) the dividend he receives annually

7.

A man invests ₹ 1680 in buying shares of nominal value ₹ 25 at 12% premium. The dividend on the shares is 15% per annum.Calculate 1) the number of shares he buys 2) the dividend he receives annually

Answer»

A man invests ₹ 1680 in buying shares of nominal value ₹ 25 at 12% premium. The dividend on the shares is 15% per annum.Calculate

1) the number of shares he buys

2) the dividend he receives annually

Discussion

8.	Prove that 2 sec2θ−sec4θ−2cosec2θ+cosec4θ−tan4θ [3 MARKS]
Answer» Prove that $2 s e c^{2} θ - s e c^{4} θ - 2 c o s e c^{2} θ + c o s e c^{4} θ - t a n^{4} θ$ [3 MARKS]

Discussion

9.	In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.
Answer» In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.

9.

In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.

Answer»

In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.

Discussion

10.	Two dice are thrown. What is the probability that the sum of the numbers appearing on them is prime?
Answer» Two dice are thrown. What is the probability that the sum of the numbers appearing on them is prime?

Discussion

11.	The following figure shows a histogram and the corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.
Answer» The following figure shows a histogram and the corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.

Discussion

12.	Question 131 State whether the statements are True or False. A rhombus can be constructed uniquely, if both diagonals are given.
Answer» Question 131 State whether the statements are True or False. A rhombus can be constructed uniquely, if both diagonals are given.

Discussion

13.	The area of a circle is 98.56cm2. Find its circumference.
Answer» The area of a circle is $98.56 c m^{2}$ . Find its circumference.

Discussion

14.	Solve the following quadratic equation by factorization. 1(x−1)(x−2)+1(x−2)(x−3)+1(x−3)(x−4)=16
Answer» Solve the following quadratic equation by factorization. $\frac{1}{(x - 1) (x - 2)} + \frac{1}{(x - 2) (x - 3)} + \frac{1}{(x - 3) (x - 4)} = \frac{1}{6}$

Discussion

15.	Let α&β be the zeros of a polynomial p(x). If α+β=24 & α−β=8, then find quadratic polynomial.
Answer» Let $α & β$ be the zeros of a polynomial p(x). If $α + β = 24 & α - β = 8$ , then find quadratic polynomial.

Discussion

16.	By Investing ₹ 8400 in a company paying 10 percent dividend, an income of ₹ 400 is received. What price is paid for each ₹ 100 share ?
Answer» By Investing ₹ 8400 in a company paying 10 percent dividend, an income of ₹ 400 is received. What price is paid for each ₹ 100 share ?

Discussion

17.	If the hcf of 657 and 963 is expressible in the form of 657 x and 963 y . find x and y
Answer» If the hcf of 657 and 963 is expressible in the form of 657 x and 963 y . find x and y

Discussion

18.	A rectangle of length “a” and breadth “b” is revolved 360∘ about its length. The volume of the resulting cylinder is
Answer» A rectangle of length “a” and breadth “b” is revolved $360^{\circ}$ about its length. The volume of the resulting cylinder is

Discussion

19.	A 13-m-long ladder reaches a window of a building 12 m above the ground. determine the distance of the foot of the ladder from the building.
Answer» A 13-m-long ladder reaches a window of a building 12 m above the ground. determine the distance of the foot of the ladder from the building.

Discussion

20.	Question 4 Arun bought a car for ₹ 3,50,000 . The next year, the price went up to ₹ 3,70,000 . What was the percentage increase in price?
Answer» Question 4 Arun bought a car for ₹ 3,50,000 . The next year, the price went up to ₹ 3,70,000 . What was the percentage increase in price?

Discussion

21.	PROVE THAT cosAcos(90-A)-sinAsin(90-A)=0
Answer» PROVE THAT cosAcos(90-A)-sinAsin(90-A)=0

Discussion

22.	Let ABC be a hollow cone of radius R, height H and slant height L. Let this cone be cut by a plane A'B' parallel to AB. O' is the centre of base of the cut out cone A'B'C'. Find the ratio of the height of cone to the height of frustum.
Answer» Let ABC be a hollow cone of radius R, height H and slant height L. Let this cone be cut by a plane A'B' parallel to AB. O' is the centre of base of the cut out cone A'B'C'. Find the ratio of the height of cone to the height of frustum.

Discussion

23.	A man bought 20 shares of Rs. 50 at 5 discounts, the rate of dividend being 1312 The rate of interest obtained is:
Answer» A man bought 20 shares of Rs. 50 at 5 discounts, the rate of dividend being $13 \frac{1}{2}$ The rate of interest obtained is:

Discussion

24.	Find the value of (,tan1°tan4°tan6°........tan88°).
Answer» Find the value of (,tan1°tan4°tan6°........tan88°).

Discussion

25.	Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angle PAQ and PBQ are supplementary.
Answer» Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angle PAQ and PBQ are supplementary.

25.

Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angle PAQ and PBQ are supplementary.

Answer»

Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angle PAQ and PBQ are supplementary.

Discussion

26.	Find the value of theta (0° < theta < 90°) if:(i) cos 63° sec (90°- theta)= 1 (ii) tan 35° cot(90°-theta)=1.
Answer» Find the value of theta (0° < theta < 90°) if:(i) cos 63° sec (90°- theta)= 1 (ii) tan 35° cot(90°-theta)=1.

Discussion

27.	Rubik's cube has a total surface area of 54 cm2. The area occupied by a single red tile on Rubik's cube is
Answer» Rubik's cube has a total surface area of $54 c m^{2}$ . The area occupied by a single red tile on Rubik's cube is

Discussion

28.	If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.
Answer» If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

Discussion

29.	Find the values of x, y and z if (x529)(47y2)=(91717z)
Answer» Find the values of x, y and z if $(\begin{matrix} x & 5 2 & 9 \end{matrix}) (\begin{matrix} 4 & 7 y & 2 \end{matrix}) = (\begin{matrix} 9 & 17 17 & z \end{matrix})$

Discussion

30.	The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the volume?
Answer» The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the volume?

Discussion

31.	If sum of n terms is given by Sn = 3n2 + 5n, then the common difference of this AP is:
Answer» If sum of n terms is given by S_n = 3n² + 5n, then the common difference of this AP is:

Discussion

32.	To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is
Answer» To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

Discussion

33.	2 cubes of volume 64 cm3 are joined end to end. Find the surface area of resulting cuboid.
Answer» 2 cubes of volume 64 cm³ are joined end to end. Find the surface area of resulting cuboid.

Discussion

34.	In order to obtain an income of ₹ 650 from 10% stock at ₹ 96, one must make an investment of:
Answer» In order to obtain an income of ₹ 650 from $10 %$ stock at ₹ 96, one must make an investment of:

Discussion

35.	If a straight line parallel to the side BC of ΔABC intersects the sides AB and AC at the points D and E respectively, then which of the following is/are correct?
Answer» If a straight line parallel to the side BC of $Δ A B C$ intersects the sides AB and AC at the points D and E respectively, then which of the following is/are correct?

Discussion

36.	a) Meenu buys a TV for Rs 10,260 including sales tax. If the list price of the TV is Rs 9,500. Find the rate of sales tax charged. b) Ms. Chawla goes to a shop to buy a leather coat which costs Rs 735.The rate of sales tax is 5%. She tells the shopkeeper to reduce the price of the coat, such that she has to pay only Rs 735 inclusive of sales tax. Find the reduction needed in the price of the coat? [6 MARKS]
Answer» a) Meenu buys a TV for Rs 10,260 including sales tax. If the list price of the TV is Rs 9,500. Find the rate of sales tax charged. b) Ms. Chawla goes to a shop to buy a leather coat which costs Rs 735.The rate of sales tax is 5%. She tells the shopkeeper to reduce the price of the coat, such that she has to pay only Rs 735 inclusive of sales tax. Find the reduction needed in the price of the coat? [6 MARKS]

Discussion

37.	The line segment parallel to any sides of a triangle divides other two sides of the triangle ___ .
Answer» The line segment parallel to any sides of a triangle divides other two sides of the triangle ___ .

Discussion

38.	In what ratio does the median of a triangle divide its sides? 1 : __ __
Answer» In what ratio does the median of a triangle divide its sides? 1 : __ __

Discussion

39.	Which are the possible remainders on dividing any number with 4?
Answer» Which are the possible remainders on dividing any number with 4?

Discussion

40.	In the given figure, PQRS is a cyclic quadrilateral in a circle with centre O. If ∠PSR=130∘. Find ∠QPR.
Answer» In the given figure, PQRS is a cyclic quadrilateral in a circle with centre O. If $∠ P S R = 130^{\circ}$ . Find $∠ Q P R$ .

Discussion

41.	Raj was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?
Answer» Raj was given a linear programming problem to solve in an interview. The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The interviewer told him one of the four points given below is the optimal solution for the problem and theorem 1 in linear programming would help him to find the answer. Which of the following points is the optimal solution?

Discussion

42.	In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P. The tangent at P cuts AB at M. Which of the following options are correct?
Answer» In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P. The tangent at P cuts AB at M. Which of the following options are correct?

42.

In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P. The tangent at P cuts AB at M. Which of the following options are correct?

Answer»

In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P.

The tangent at P cuts AB at M. Which of the following options are correct?

Discussion

43.	144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?
Answer» 144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?

Discussion

44.	In a circle of radius 35 cm, an arc subtends an angle of 72∘ at the centre. Find the length of the arc and area of the sector.
Answer» In a circle of radius 35 cm, an arc subtends an angle of $72^{\circ}$ at the centre. Find the length of the arc and area of the sector.

Discussion

45.	If three points (x1,y1),(x2,y2),(x3,y3) lie on the same line, prove that y2−y3x2x3+y3−y1x3x1+y1−y2x1x2=0.
Answer» If three points $(x_{1}, y_{1}), (x_{2}, y_{2}), (x_{3}, y_{3})$ lie on the same line, prove that $\frac{y_{2} - y_{3}}{x_{2} x_{3}} + \frac{y_{3} - y_{1}}{x_{3} x_{1}} + \frac{y_{1} - y_{2}}{x_{1} x_{2}} = 0.$

Discussion

46.	100 students record how far they can run in one minute. The results are shown in the table : Distance(d metres)frequency0−2005200−25020250−30050300−40025 Estimate the median.
Answer» 100 students record how far they can run in one minute. The results are shown in the table : $\begin{matrix} Distance(d metres) & frequency 0 - 200 & 5 200 - 250 & 20 250 - 300 & 50 300 - 400 & 25 \end{matrix}$ Estimate the median.

46.

100 students record how far they can run in one minute. The results are shown in the table : Distance(d metres)frequency0−2005200−25020250−30050300−40025 Estimate the median.

Answer»

100 students record how far they can run in one minute.

The results are shown in the table :

$\begin{matrix} Distance(d metres) & frequency 0 - 200 & 5 200 - 250 & 20 250 - 300 & 50 300 - 400 & 25 \end{matrix}$

Estimate the median.

Discussion

47.	Factorize x3+3x2−28x and verify the relationship between the zeroes and coefficients.
Answer» Factorize $x^{3} + 3 x^{2} - 28 x$ and verify the relationship between the zeroes and coefficients.

Discussion

48.	The 17th term of an AP exceeds its 10th term by 21. The common difference fo the AP is (a) 3 (2) (c) -3 (d) -2
Answer» The 17th term of an AP exceeds its 10th term by 21. The common difference fo the AP is (a) 3 (2) (c) -3 (d) -2

Discussion

49.	For what value of k does the system of equations x+2y=5,3x+ky+15=0 have (i) a unique solution,(ii) no solution?
Answer» For what value of k does the system of equations $x + 2 y = 5, 3 x + k y + 15 = 0$ have (i) a unique solution,(ii) no solution?

Discussion

50.	If tan θ=34, find: sin θ
Answer» If $t a n θ = \frac{3}{4}$ , find: $s i n θ$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

In the figure, line segment AB meets x - axis at A and y - axis at B. The point P(-3, 4) on AB divides it in the ratio 2 : 3. Find the coordinates of A and B. [3 MARKS]

Find mean by step deviation method.

Consider the points A(4,3) and B(0,1). If a circle is drawn with AB as diameter, then the coordinates of the points where this circle intersects the x-axis are

In the given figure, AE and BD are two medians of a △ABC meeting at F. The ratio of the area of △ ABF to the area of the quadrilateral FDCE is:

The H.C.F. of 3xy2z3, 3yz2x2 and x2y2z is .

Find a quadratic equation whose one of the root is 2 and whose sum of the roots of zero

A man invests ₹ 1680 in buying shares of nominal value ₹ 25 at 12% premium. The dividend on the shares is 15% per annum.Calculate 1) the number of shares he buys 2) the dividend he receives annually

Prove that 2 sec2θ−sec4θ−2cosec2θ+cosec4θ−tan4θ [3 MARKS]

In the given diagram, a circle is inscribed in a right angled triangle such that AF = 6 cm and EC = 15 cm. Find the difference between CD and BD.

Two dice are thrown. What is the probability that the sum of the numbers appearing on them is prime?

The following figure shows a histogram and the corresponding frequency polygon. The data shows the number of victims suffering from a disease 'X' in various months of 2012. Identify the correct statement(s) among the following.

Question 131 State whether the statements are True or False. A rhombus can be constructed uniquely, if both diagonals are given.

The area of a circle is 98.56cm2. Find its circumference.

Solve the following quadratic equation by factorization. 1(x−1)(x−2)+1(x−2)(x−3)+1(x−3)(x−4)=16

Let α&amp;β be the zeros of a polynomial p(x). If α+β=24 &amp; α−β=8, then find quadratic polynomial.

By Investing ₹ 8400 in a company paying 10 percent dividend, an income of ₹ 400 is received. What price is paid for each ₹ 100 share ?

If the hcf of 657 and 963 is expressible in the form of 657 x and 963 y . find x and y

A rectangle of length “a” and breadth “b” is revolved 360∘ about its length. The volume of the resulting cylinder is

A 13-m-long ladder reaches a window of a building 12 m above the ground. determine the distance of the foot of the ladder from the building.

Question 4 Arun bought a car for ₹ 3,50,000 . The next year, the price went up to ₹ 3,70,000 . What was the percentage increase in price?

PROVE THAT cosAcos(90-A)-sinAsin(90-A)=0

Let ABC be a hollow cone of radius R, height H and slant height L. Let this cone be cut by a plane A'B' parallel to AB. O' is the centre of base of the cut out cone A'B'C'. Find the ratio of the height of cone to the height of frustum.

A man bought 20 shares of Rs. 50 at 5 discounts, the rate of dividend being 1312 The rate of interest obtained is:

Find the value of (,tan1°tan4°tan6°........tan88°).

Two circles intersect each other at points A and B. Their common tangent touches the circles at points P and Q as shown in the figure. Show that the angle PAQ and PBQ are supplementary.

Find the value of theta (0° &lt; theta &lt; 90°) if:(i) cos 63° sec (90°- theta)= 1 (ii) tan 35° cot(90°-theta)=1.

Rubik's cube has a total surface area of 54 cm2. The area occupied by a single red tile on Rubik's cube is

If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x.

Find the values of x, y and z if (x529)(47y2)=(91717z)

The solid object is composed of a hemisphere and a cone surmounted on it. If the common radius is 7m and height of the cone is 1m, what is the volume?

If sum of n terms is given by Sn = 3n2 + 5n, then the common difference of this AP is:

To draw a pair of tangents to a circle which are inclined to each other at an angle of 35°, it is required to draw tangents at the end points of those two radii of the circle, the angle between which is

2 cubes of volume 64 cm3 are joined end to end. Find the surface area of resulting cuboid.

In order to obtain an income of ₹ 650 from 10% stock at ₹ 96, one must make an investment of:

If a straight line parallel to the side BC of ΔABC intersects the sides AB and AC at the points D and E respectively, then which of the following is/are correct?

The line segment parallel to any sides of a triangle divides other two sides of the triangle ___ .

In what ratio does the median of a triangle divide its sides? 1 : __ __

Which are the possible remainders on dividing any number with 4?

In the given figure, PQRS is a cyclic quadrilateral in a circle with centre O. If ∠PSR=130∘. Find ∠QPR.​​​​​​

In the figure, the tangent from A touches the circle at B. BC is diameter. The line AC cuts the circle at P. The tangent at P cuts AB at M. Which of the following options are correct?

144 cartons of Coke Cans and 90 cartons of Pepsi Cans are to be stacked in a Canteen. If each stack is of the same height and is to contain cartons of the same drink, what would be the greatest number of cartons each stack would have?

In a circle of radius 35 cm, an arc subtends an angle of 72∘ at the centre. Find the length of the arc and area of the sector.

If three points (x1,y1),(x2,y2),(x3,y3) lie on the same line, prove that y2−y3x2x3+y3−y1x3x1+y1−y2x1x2=0.

100 students record how far they can run in one minute. The results are shown in the table : Distance(d metres)frequency0−2005200−25020250−30050300−40025 Estimate the median.

Factorize x3+3x2−28x and verify the relationship between the zeroes and coefficients.

The 17th term of an AP exceeds its 10th term by 21. The common difference fo the AP is (a) 3 (2) (c) -3 (d) -2

For what value of k does the system of equations x+2y=5,3x+ky+15=0 have (i) a unique solution,(ii) no solution?

If tan θ=34, find: sin θ

Let α&β be the zeros of a polynomial p(x). If α+β=24 & α−β=8, then find quadratic polynomial.

Find the value of theta (0° < theta < 90°) if:(i) cos 63° sec (90°- theta)= 1 (ii) tan 35° cot(90°-theta)=1.

In what ratio does the median of a triangle divide its sides? 1 :

In the given figure, PQRS is a cyclic quadrilateral in a circle with centre O. If ∠PSR=130∘. Find ∠QPR.