32581 + Interview Questions in Mathematics

1.	A sprinter starts from the point A and runs on the circular track of radius 14 m completing one complete round. The distance covered in one round is equal to:
Answer» A sprinter starts from the point A and runs on the circular track of radius 14 m completing one complete round. The distance covered in one round is equal to:

Discussion

2.	The ratio of sides in two similar triangles is 4:9. What is the ratio of their perimeters?
Answer» The ratio of sides in two similar triangles is 4:9. What is the ratio of their perimeters?

Discussion

3.	In the figure, the circle represents youth, the triangle represents footballers and the rectangle representsathletes. Which letter (s) represent(s) athletes among youths who are not footballers?
Answer» In the figure, the circle represents youth, the triangle represents footballers and the rectangle representsathletes. Which letter (s) represent(s) athletes among youths who are not footballers?

3.

In the figure, the circle represents youth, the triangle represents footballers and the rectangle representsathletes. Which letter (s) represent(s) athletes among youths who are not footballers?

Answer»

In the figure, the circle represents youth, the triangle represents footballers and the rectangle representsathletes. Which letter (s) represent(s) athletes among youths who are not footballers?

Discussion

4.	A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter (D) of the hemisphere is equal to the edge of the cube. The surface area of the remaining solid is:
Answer» A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter (D) of the hemisphere is equal to the edge of the cube. The surface area of the remaining solid is:

Discussion

5.	You are holding a spherical ball of radius 3.5 cm in your fist. You observe that 30% of area is uncovered. Then find the area of the ball uncovered. (Take π=227)
Answer» You are holding a spherical ball of radius 3.5 cm in your fist. You observe that 30% of area is uncovered. Then find the area of the ball uncovered. (Take $π = \frac{22}{7}$ )

Discussion

6.	a train covered A certain distance at a uniform speed if the train would have been 10 km per hour faster it would have taken 2 hours less than the scheduled time and the train was lower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train
Answer» a train covered A certain distance at a uniform speed if the train would have been 10 km per hour faster it would have taken 2 hours less than the scheduled time and the train was lower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train

Discussion

7.	If the numbers are arranged in the descending order, which number shall be in the third position?
Answer» If the numbers are arranged in the descending order, which number shall be in the third position?

Discussion

8.	A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.
Answer» A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.

Discussion

9.	Five arithmetic means are inserted between 6 and 36. Choose the correct numbers among the options.
Answer» Five arithmetic means are inserted between 6 and 36. Choose the correct numbers among the options.

Discussion

10.	(1+tan A)2+(1−tan A)2=
Answer» $(1 + tan A)^{2} + (1 - tan A)^{2} =$

Discussion

11.	The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Can you determine the length and breadth of the rectangle?
Answer» The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Can you determine the length and breadth of the rectangle?

Discussion

12.	Amit deposits Rs 150 per month in a bank for 8 months under Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month.?
Answer» Amit deposits Rs 150 per month in a bank for 8 months under Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month.?

Discussion

13.	Mr. Ram Gopal invested Rs 8,000 in 7% Rs 100 shares at Rs 80. After a year, he sold these shares at Rs 75 each and invested the proceeds (including his dividend) in 18%, Rs 25 shares at Rs 41. Find: (i) his dividend for the first year. (ii) his annual income in the second year. (iii) the percentage increase in his return on his original investment. [4 MARKS]
Answer» Mr. Ram Gopal invested Rs 8,000 in $7 %$ Rs 100 shares at Rs 80. After a year, he sold these shares at Rs 75 each and invested the proceeds (including his dividend) in $18 %$ , Rs 25 shares at Rs 41. Find: (i) his dividend for the first year. (ii) his annual income in the second year. (iii) the percentage increase in his return on his original investment. [4 MARKS]

Discussion

14.	Question 10 Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.
Answer» Question 10 Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Discussion

15.	Matrix A = [aij]m × n is a square matrix if _______
Answer» Matrix $A = [a_{i j}]_{m \times n}$ is a square matrix if _______

Discussion

16.	Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.
Answer» Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

Discussion

17.	The number of real roots of the equation x2−3x+5=0 is:
Answer» The number of real roots of the equation $x^{2} - 3 x + 5 = 0$ is:

Discussion

18.	Solve the quadratic equation x2−9x+20=0.
Answer» Solve the quadratic equation $x^{2} - 9 x + 20 = 0.$

Discussion

19.	A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.
Answer» A train travels a distance of $480 k m$ at a uniform speed. If the speed had been $8 k m / h$ less, then it would have taken $3$ hours more to cover the same distance. Find the speed of the train.

Discussion

20.	What is the total outlay of the 11th plan compared to the 10th plan in India?
Answer» What is the total outlay of the 11^th plan compared to the 10^th plan in India?

Discussion

21.	The common ratio of the G.P series 9, 27, 81 is _____.
Answer» The common ratio of the G.P series 9, 27, 81 is _____.

Discussion

22.	A metal sheet of breadth 10cm is used to make a cone of radius 14cm and slant height 20cm. Then length of sheet if 25% of sheet is wasted is .
Answer» A metal sheet of breadth $10 c m$ is used to make a cone of radius $14 c m$ and slant height $20 c m$ . Then length of sheet if $25 %$ of sheet is wasted is .

22.

A metal sheet of breadth 10cm is used to make a cone of radius 14cm and slant height 20cm. Then length of sheet if 25% of sheet is wasted is .

Answer»

A metal sheet of breadth $10 c m$ is used to make a cone of radius $14 c m$ and slant height $20 c m$ . Then length of sheet if $25 %$ of sheet is wasted is .

Discussion

23.	Question 1 (iv) Solve the following pairs of equations by reducing them to a pair of linear equations: 5x−1+1y−2=2 6x−1−3y−2=1
Answer» Question 1 (iv) Solve the following pairs of equations by reducing them to a pair of linear equations: $\frac{5}{x - 1} + \frac{1}{y - 2} = 2$ $\frac{6}{x - 1} - \frac{3}{y - 2} = 1$

Discussion

24.	If α and β are the zeros of the quadratic polynomial f(x)=kx2+4x+4 such that α2+β2=24, find the values of k. [4 MARKS]
Answer» If $α$ and $β$ are the zeros of the quadratic polynomial $f (x) = k x^{2} + 4 x + 4$ such that $α^{2} + β^{2} = 24$ , find the values of $k$ . [4 MARKS]

Discussion

25.	Represent the given set in Roster form. A = {x:x is an integer, −32<x<112}
Answer» Represent the given set in Roster form. A = ${x : x i s a n i n t e g e r, \frac{- 3}{2} < x < \frac{11}{2}}$

25.

Represent the given set in Roster form. A = {x:x is an integer, −32<x<112}

Answer»

Represent the given set in Roster form.

A = ${x : x i s a n i n t e g e r, \frac{- 3}{2} < x < \frac{11}{2}}$

Discussion

26.	Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.
Answer» Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

Discussion

27.	Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) √3,√6,√9,√12, …
Answer» Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) $\sqrt{3}, \sqrt{6}, \sqrt{9}, \sqrt{12}, \dots$

Discussion

28.	Question 12 In figure, arcs are drawn by taking vertices, A, B , and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D,E and F. Find the area of the shaded region. (use π=3.14)
Answer» Question 12 In figure, arcs are drawn by taking vertices, A, B , and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D,E and F. Find the area of the shaded region. (use $π = 3.14$ )

Discussion

29.	If the mean of the following data is 17, then the value of 'p' is ___ xi10p182125fi1015799
Answer» If the mean of the following data is 17, then the value of 'p' is ___ $\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

29.

If the mean of the following data is 17, then the value of 'p' is ___ xi10p182125fi1015799

Answer»

If the mean of the following data is 17, then the value of 'p' is ___

$\begin{matrix} x_{i} & 10 & p & 18 & 21 & 25 f_{i} & 10 & 15 & 7 & 9 & 9 \end{matrix}$

Discussion

30.	Factorize √5 x2 + 8x + 3√5 = 0 into the form √5 x2 + px + qx +3√5 = 0.Find the value of p and q.
Answer» Factorize $\sqrt{5}$ $x^{2}$ + 8x + 3 $\sqrt{5}$ = 0 into the form $\sqrt{5}$ $x^{2}$ + px + qx +3 $\sqrt{5}$ = 0.Find the value of p and q.

Discussion

31.	In the given figure, AC is a diameter of the circle. Find the value of x.
Answer» In the given figure, AC is a diameter of the circle. Find the value of $x .$

Discussion

32.	A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the coordinates of point B if AB and BC are parallel to the coordinate axes.
Answer» A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the coordinates of point B if AB and BC are parallel to the coordinate axes.

Discussion

33.	In a right triangle ABC right angled at B , a perpendicular BD is dropped on the hypotenuse such that D divides AC in the ratio 1:2 such that DC>AD. If AC = 9cm, find the length of base BC.
Answer» In a right triangle ABC right angled at B , a perpendicular BD is dropped on the hypotenuse such that D divides AC in the ratio 1:2 such that $D C > A D$ . If AC = 9cm, find the length of base BC.

Discussion

34.	If the value of tanα=52 find the value of cotθ if α+θ=90∘.
Answer» $I f t h e v a l u e o f t a n α = \frac{5}{2}$ $f i n d t h e v a l u e o f c o t θ$ $i f α + θ = 90^{\circ}$ .

Discussion

35.	From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be α & β. The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is
Answer» From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be $α & β$ . The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is

Discussion

36.	Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true?
Answer» Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true?

Discussion

37.	Let α≠β, α2+3=5α and β2=5β−3. The quadratic equation whose roots are αβ and βα will be:
Answer» Let $α \neq β$ , $α^{2} + 3 = 5 α$ and $β^{2} = 5 β - 3$ . The quadratic equation whose roots are $\frac{α}{β}$ and $\frac{β}{α}$ will be:

Discussion

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

Discussion

39.	Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4). [4 MARKS]
Answer» Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4). [4 MARKS]

Discussion

40.	A manufacturer X sells a refrigerator to a trader Y for Rs. 22500. The trader Y sells it to a trader Z at a profit of Rs. 1250 and trader Z sell it to a consumer at a profit of Rs. 1000. If the rate of value added tax (VAT) is 4%, find the total amount of tax (under VAT ) received by the government on the scale of the refrigerator.
Answer» A manufacturer X sells a refrigerator to a trader Y for Rs. 22500. The trader Y sells it to a trader Z at a profit of Rs. 1250 and trader Z sell it to a consumer at a profit of Rs. 1000. If the rate of value added tax (VAT) is $4 %$ , find the total amount of tax (under VAT ) received by the government on the scale of the refrigerator.

Discussion

41.	ABCD is a quadrilateral such that ∠ABC +∠ADC =180∘. Inside the quadrilateral : Statement 1: the circumcircle of △ABC intersects diagonal BD at D. Statement 2: the circumcircle of △ABC intersects BD at D′inside the quadrilateral. Statement 3: the circumcircle of △ABC intersects BD at D′ outside the quadrilateral. Statement 4: the circumcircle of △ABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.
Answer» ABCD is a quadrilateral such that $∠$ ABC $+ ∠$ ADC $= 180^{\circ}$ . Inside the quadrilateral : Statement 1: the circumcircle of $△$ ABC intersects diagonal BD at D. Statement 2: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ inside the quadrilateral. Statement 3: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ outside the quadrilateral. Statement 4: the circumcircle of $△$ ABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.

41.

ABCD is a quadrilateral such that ∠ABC +∠ADC =180∘. Inside the quadrilateral : Statement 1: the circumcircle of △ABC intersects diagonal BD at D. Statement 2: the circumcircle of △ABC intersects BD at D′inside the quadrilateral. Statement 3: the circumcircle of △ABC intersects BD at D′ outside the quadrilateral. Statement 4: the circumcircle of △ABC does not intersect BD at all. Statement 5: ABCD is called cyclic quadrilateral.

Answer»

ABCD is a quadrilateral such that $∠$ ABC $+ ∠$ ADC $= 180^{\circ}$ . Inside the quadrilateral :

Statement 1: the circumcircle of $△$ ABC intersects diagonal BD at D.

Statement 2: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ inside the quadrilateral.

Statement 3: the circumcircle of $△$ ABC intersects BD at $D^{^{'}}$ outside the quadrilateral.

Statement 4: the circumcircle of $△$ ABC does not intersect BD at all.

Statement 5: ABCD is called cyclic quadrilateral.

Discussion

42.	What are composure prime and even numbers
Answer» What are composure prime and even numbers

Discussion

43.	Sam's cubicle is exactly of the shape of a cube with side 6 m. The total surface area of the cubicle neglecting the thickness is
Answer» Sam's cubicle is exactly of the shape of a cube with side 6 m. The total surface area of the cubicle neglecting the thickness is

Discussion

44.	A man in a boat rowing away froma lighthouse 150 m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60∘ to 45∘. Find the speed of the boat.
Answer» A man in a boat rowing away froma lighthouse 150 m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from $60^{\circ} t o 45^{\circ}$ . Find the speed of the boat.

Discussion

45.	Pratik takes 8 hours to travel 36km down stream and to return to the same spot. The speed of boat in still water is 12 km per hour.Find the speed of water current.
Answer» Pratik takes 8 hours to travel 36km down stream and to return to the same spot. The speed of boat in still water is 12 km per hour.Find the speed of water current.

Discussion

46.	A spherical shell of lead whose external radius is 9 cm is melted and recast into a right circular cylinder 8 cm high and 12 cm in diameter. Find the diameter of the shell. [4 MARKS]
Answer» A spherical shell of lead whose external radius is 9 cm is melted and recast into a right circular cylinder 8 cm high and 12 cm in diameter. Find the diameter of the shell. [4 MARKS]

Discussion

47.	12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is:
Answer» 12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is:

Discussion

48.	Show that (3x+4)1 is any positive odd integer.
Answer» Show that (3x+4)1 is any positive odd integer.

Discussion

49.	Polynomial will have zeroes
Answer» Polynomial will have zeroes

49.

Polynomial will have zeroes

Answer»

Polynomial will have zeroes

Discussion

50.	The area of a sector of a circle of radius 5 cm is 5π cm2. The angle contained by the sector will be
Answer» The area of a sector of a circle of radius 5 cm is 5π cm². The angle contained by the sector will be

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

A sprinter starts from the point A and runs on the circular track of radius 14 m completing one complete round. The distance covered in one round is equal to:

The ratio of sides in two similar triangles is 4:9. What is the ratio of their perimeters?

In the figure, the circle represents youth, the triangle represents footballers and the rectangle representsathletes. Which letter (s) represent(s) athletes among youths who are not footballers?

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter (D) of the hemisphere is equal to the edge of the cube. The surface area of the remaining solid is:

You are holding a spherical ball of radius 3.5 cm in your fist. You observe that 30% of area is uncovered. Then find the area of the ball uncovered. (Take π=227)

a train covered A certain distance at a uniform speed if the train would have been 10 km per hour faster it would have taken 2 hours less than the scheduled time and the train was lower by 10 km per hour it would have taken 3 hours more than the scheduled time find the distance covered by the train

If the numbers are arranged in the descending order, which number shall be in the third position?

A card is drawn at random from a pack of 52 cards. Find the probability that the card drawn is neither a heart nor a king.

Five arithmetic means are inserted between 6 and 36. Choose the correct numbers among the options.

(1+tan A)2+(1−tan A)2=

The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and breadth by 2 units, the area is increased by 67 square units. Can you determine the length and breadth of the rectangle?

Amit deposits Rs 150 per month in a bank for 8 months under Recurring Deposit Scheme. What will be the maturity value of his deposits, if the rate of interest is 8% per annum and interest is calculated at the end of every month.?

Question 10 Prove that a diameter AB of a circle bisects all those chords which are parallel to the tangent at the point A.

Matrix A = [aij]m × n is a square matrix if _______

Prove that the tangents drawn at the ends of a chord of a circle make equal angles with the chord.

The number of real roots of the equation x2−3x+5=0 is:

Solve the quadratic equation x2−9x+20=0.

A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km/h less, then it would have taken 3 hours more to cover the same distance. Find the speed of the train.

What is the total outlay of the 11th plan compared to the 10th plan in India?

The common ratio of the G.P series 9, 27, 81 is _____.

A metal sheet of breadth 10cm is used to make a cone of radius 14cm and slant height 20cm. Then length of sheet if 25% of sheet is wasted is .

Question 1 (iv) Solve the following pairs of equations by reducing them to a pair of linear equations: 5x−1+1y−2=2 6x−1−3y−2=1

If α and β are the zeros of the quadratic polynomial f(x)=kx2+4x+4 such that α2+β2=24, find the values of k. [4 MARKS]

Represent the given set in Roster form. A = {x:x is an integer, −32&lt;x&lt;112}

Two circles of radii 5 cm and 3 cm are concentric. Calculate the length of a chord of the outer circle which touches the inner circle.

Question 4 (xiii) Which of the following are APs? If they form an A.P. find the common difference d and write three more terms. (xiii) √3,√6,√9,√12, …

Question 12 In figure, arcs are drawn by taking vertices, A, B , and C of an equilateral triangle of side 10 cm, to intersect the sides BC, CA and AB at their respective mid-points D,E and F. Find the area of the shaded region. (use π=3.14)

If the mean of the following data is 17, then the value of 'p' is ___ xi10p182125fi1015799

Factorize √5 x2 + 8x + 3√5 = 0 into the form √5 x2 + px + qx +3√5 = 0.Find the value of p and q.

In the given figure, AC is a diameter of the circle. Find the value of x.

A right triangle is formed by connecting the 3 coordinates A, B and C as shown in figure. Find the coordinates of point B if AB and BC are parallel to the coordinate axes.

In a right triangle ABC right angled at B , a perpendicular BD is dropped on the hypotenuse such that D divides AC in the ratio 1:2 such that DC&gt;AD. If AC = 9cm, find the length of base BC.

If the value of tanα=52 find the value of cotθ if α+θ=90∘.

From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be α &amp; β. The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is

Given that P(x) and Q(x) are polynomials of degree 3 with real coefficients, which one of the following is not true?

Let α≠β, α2+3=5α and β2=5β−3. The quadratic equation whose roots are αβ and βα will be:

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

Find the coordinates of points which trisect the line segment joining (1, –2) and (–3, 4). [4 MARKS]

What are composure prime and even numbers

Sam's cubicle is exactly of the shape of a cube with side 6 m. The total surface area of the cubicle neglecting the thickness is

A man in a boat rowing away froma lighthouse 150 m high, takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60∘ to 45∘. Find the speed of the boat.

Pratik takes 8 hours to travel 36km down stream and to return to the same spot. The speed of boat in still water is 12 km per hour.Find the speed of water current.

A spherical shell of lead whose external radius is 9 cm is melted and recast into a right circular cylinder 8 cm high and 12 cm in diameter. Find the diameter of the shell. [4 MARKS]

12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is:

Show that (3x+4)1 is any positive odd integer.

Polynomial will have zeroes

The area of a sector of a circle of radius 5 cm is 5π cm2. The angle contained by the sector will be

Represent the given set in Roster form. A = {x:x is an integer, −32<x<112}

In a right triangle ABC right angled at B , a perpendicular BD is dropped on the hypotenuse such that D divides AC in the ratio 1:2 such that DC>AD. If AC = 9cm, find the length of base BC.

From an aeroplane vertically above a horizontal road, the angles of depression of two friends standing on either side of the aeroplane are observed to be α & β. The distance between the two friends is 1 m. The height (in metres) of the aeroplane from the ground is