32581 + Interview Questions in Mathematics

1.	The volume of a hemisphere of radius r is ______ .
Answer» The volume of a hemisphere of radius r is ______ .

Discussion

2.	The coordinates of centroid of triangle formed by lines 4x+7y =28 whenx=0,y=0
Answer» The coordinates of centroid of triangle formed by lines 4x+7y =28 whenx=0,y=0

Discussion

3.	If 3 is is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a+b , is
Answer» If 3 is is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a+b , is

Discussion

4.	In the following figure, AB, CD and EF are perpendicular to the straight line BDF. If AB = x units and CD = z units and EF = y units, then which of the following is/are true?
Answer» In the following figure, AB, CD and EF are perpendicular to the straight line BDF. If AB = x units and CD = z units and EF = y units, then which of the following is/are true?

4.

In the following figure, AB, CD and EF are perpendicular to the straight line BDF. If AB = x units and CD = z units and EF = y units, then which of the following is/are true?

Answer»

In the following figure, AB, CD and EF are perpendicular to the straight line BDF.

If AB = x units and CD = z units and EF = y units, then which of the following is/are true?

Discussion

5.	A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins , respectively . The dimension of the cuboid are 10 cm × 5 cm×4 cm . The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm . The edge of the cubical depression is 3 cm . Find the volume of the wood in the entire stand.
Answer» A pen stand made of wood is in the shape of a cuboid with four conical depression and a cubical depression to hold the pens and pins , respectively . The dimension of the cuboid are $10 cm \times 5 cm \times 4 cm$ . The radius of each of the conical depression is 0.5 cm and the depth is 2.1 cm . The edge of the cubical depression is 3 cm . Find the volume of the wood in the entire stand.

Discussion

6.	Draw a square whose vertices are (2,2), (4,2), (4,4) and (2,4). Reflect the square in the y-axis and then reflect the image in the origin. What single transformation would give the same result?
Answer» Draw a square whose vertices are (2,2), (4,2), (4,4) and (2,4). Reflect the square in the y-axis and then reflect the image in the origin. What single transformation would give the same result?

Discussion

7.	Two different dice are thrown together. Find the probability that(i) the sum of the numbers appeared is less than 7. [CBSE 2011](ii) the product of the numbers appeared is less than 18. [CBSE 2017]
Answer» Two different dice are thrown together. Find the probability that (i) the sum of the numbers appeared is less than 7. [CBSE 2011] (ii) the product of the numbers appeared is less than 18. [CBSE 2017]

Discussion

8.	Which term of the AP = 21, 18, 15, ... is -81?
Answer» Which term of the AP = 21, 18, 15, ... is -81?

Discussion

9.	If one of the zeroes of a quadratic polynomial (k−1)x2+kx+1 is -3, then the value of k is .
Answer» If one of the zeroes of a quadratic polynomial $(k - 1) x^{2} + k x + 1$ is -3, then the value of k is .

Discussion

10.	Use Euclid’s division algorithm to find the HCF of:
Answer» Use Euclid’s division algorithm to find the HCF of:

10.

Use Euclid’s division algorithm to find the HCF of:

Answer»

Use Euclid’s division algorithm to find the HCF of:

Discussion

11.	Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is(i) an odd number(ii) a perfect square number(iii) divisible by 5(iv) a prime number less than 20 [CBSE 2014]
Answer» Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is (i) an odd number (ii) a perfect square number (iii) divisible by 5 (iv) a prime number less than 20 [CBSE 2014]

Discussion

12.	If (tan x +sec x)(tan y + sec y)(tanz +sec z) = (sec x - tan x )(sec y - tan y ) (secz - tan z) = K, then the value of K is
Answer» If (tan x +sec x)(tan y + sec y)(tanz +sec z) = (sec x - tan x )(sec y - tan y ) (secz - tan z) = K, then the value of K is

Discussion

13.	Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation. a) 64455 b) 133125
Answer» Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation. a) $\frac{64}{455}$ b) $\frac{13}{3125}$

13.

Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation. a) 64455 b) 133125

Answer»

Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation.

a) $\frac{64}{455}$ b) $\frac{13}{3125}$

Discussion

14.	4 A polynomial has property that 3f(x)+7f(2016/x)=2x. The value of f(8) is
Answer» 4 A polynomial has property that 3f(x)+7f(2016/x)=2x. The value of f(8) is

Discussion

15.	Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x), q(x) + r(x), where degree r(x) = 0.
Answer» Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x), q(x) + r(x), where degree r(x) = 0.

Discussion

16.	If the equation x2+2(k+2)x+9k=0 has equal roots, then values of k are __________.
Answer» If the equation $x^{2} + 2 (k + 2) x + 9 k = 0$ has equal roots, then values of k are __________.

Discussion

17.	In a farm, a heap of paddy is in the form of a cone with slant height 13 m and height 12 m. What is the area of canvas needed to protect it from sun and rain?
Answer» In a farm, a heap of paddy is in the form of a cone with slant height 13 m and height 12 m. What is the area of canvas needed to protect it from sun and rain?

Discussion

18.	On comparing the ratios a1a2, b1b2 and c1c2, and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide :(i) 5x − 4y + 8 = 07x + 6y − 9 = 0(ii) 9x + 3y + 12 = 018x + 6y + 24 = 0(iii) 6x − 3y + 10 = 02x − y + 9 = 0
Answer» On comparing the ratios $\frac{a_{1}}{a_{2}}, \frac{b_{1}}{b_{2}} and \frac{c_{1}}{c_{2}}$ , and without drawing them, find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincide : (i) 5x − 4y + 8 = 0 7x + 6y − 9 = 0 (ii) 9x + 3y + 12 = 0 18x + 6y + 24 = 0 (iii) 6x − 3y + 10 = 0 2x − y + 9 = 0

Discussion

19.	Question 162 Find the values of x and y in the following kite.
Answer» Question 162 Find the values of x and y in the following kite.

Discussion

20.	If LM ∥ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?___
Answer» If LM $∥$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?___

20.

If LM ∥ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?___

Answer»

If LM $∥$ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?___

Discussion

21.	Solve the following systems of equations:xyx+y=65xyy-x=6,where x + y ≠ 0, y − x ≠ 0
Answer» Solve the following systems of equations: $\frac{x y}{x + y} = \frac{6}{5} \frac{x y}{y - x} = 6,$ where x + y ≠ 0, y − x ≠ 0

Discussion

22.	Three numbers are in AP such that their sum is 15 then find the second term.
Answer» Three numbers are in AP such that their sum is 15 then find the second term.

Discussion

23.	The angle of elevation of a ladder leaning against a wall is 60∘ and the foot of the ladder is 9.5m away from the wall. Find the length of the ladder.
Answer» The angle of elevation of a ladder leaning against a wall is $60^{\circ}$ and the foot of the ladder is 9.5m away from the wall. Find the length of the ladder.

Discussion

24.	If the radius and the slant height of the cone are in the ratio of 4:7and its curved surface area is 792 cm^2 then its radius is
Answer» If the radius and the slant height of the cone are in the ratio of 4:7and its curved surface area is 792 cm^2 then its radius is

Discussion

25.	Question 2 (i)For which values of ‘a’ and ‘b’ does the following pair of linear equations have an infinite number of solutions?2x + 3y =7(a - b)x + (a + b)y = 3a +b - 2
Answer» Question 2 (i) For which values of ‘a’ and ‘b’ does the following pair of linear equations have an infinite number of solutions? 2x + 3y =7 (a - b)x + (a + b)y = 3a +b - 2

Discussion

26.	Question 3 (iii) In an AP: (iii) Given a12=37,d=3, find a and S12.
Answer» Question 3 (iii) In an AP: (iii) Given $a_{12} = 37, d = 3$ , find a and $S_{12}$ .

Discussion

27.	A chord of length 5 cm subtends an angle of 60∘ at the centre of a circle. The area of the sector of the same circle which is subtending central angle of 120∘ at the centre, is
Answer» A chord of length $5 cm$ subtends an angle of $60^{\circ}$ at the centre of a circle. The area of the sector of the same circle which is subtending central angle of $120^{\circ}$ at the centre, is

Discussion

28.	Find the sum(1) 4 ⊕5 3(2) 5 ⊕7 4(3) (3 ⊕7 6) ⊕7 4(4) (10 ⊕12 2) ⊕12 3
Answer» Find the sum (1) 4 ⊕₅ 3 (2) 5 ⊕₇ 4 (3) (3 ⊕₇ 6) ⊕₇ 4 (4) (10 ⊕₁₂ 2) ⊕₁₂ 3

28.

Find the sum(1) 4 ⊕5 3(2) 5 ⊕7 4(3) (3 ⊕7 6) ⊕7 4(4) (10 ⊕12 2) ⊕12 3

Answer»

Find the sum

(1) 4 ⊕₅ 3

(2) 5 ⊕₇ 4

(3) (3 ⊕₇ 6) ⊕₇ 4

(4) (10 ⊕₁₂ 2) ⊕₁₂ 3

Discussion

29.	Show that the points A(1,2),B(1,6),C(1+2√3,4) are vertices of an equilateral triangle.
Answer» Show that the points $A (1, 2), B (1, 6), C (1 + 2 \sqrt{3}, 4)$ are vertices of an equilateral triangle.

Discussion

30.	In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region.[Use π = 3.14]
Answer» In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region. [Use π = 3.14]

Discussion

31.	Question 5: Draw a rough figure and label suitably in the following case: (a) Line l contains E and F but not D.
Answer» Question 5: Draw a rough figure and label suitably in the following case: (a) Line l contains E and F but not D.

Discussion

32.	A man travels 600 km partly by train and partly by car. If the covers 400 km by train and the rest by car, it takes him 6 hours 30 minutes. But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.
Answer» A man travels 600 km partly by train and partly by car. If the covers 400 km by train and the rest by car, it takes him 6 hours 30 minutes. But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

Discussion

33.	The following data shows monthly savings of 100 families . Find the Mode of the Monthly SavingsMonthly savings(Rs)Number of families1000−2000142000−3000153000−4000214000−5000275000−600025
Answer» The following data shows monthly savings of 100 families . Find the Mode of the Monthly Savings $\begin{matrix} Monthly savings(Rs) & Number of families 1000 - 2000 & 14 2000 - 3000 & 15 3000 - 4000 & 21 4000 - 5000 & 27 5000 - 6000 & 25 \end{matrix}$

33.

The following data shows monthly savings of 100 families . Find the Mode of the Monthly SavingsMonthly savings(Rs)Number of families1000−2000142000−3000153000−4000214000−5000275000−600025

Answer»

The following data shows monthly savings of 100 families . Find the Mode of the Monthly Savings

$\begin{matrix} Monthly savings(Rs) & Number of families 1000 - 2000 & 14 2000 - 3000 & 15 3000 - 4000 & 21 4000 - 5000 & 27 5000 - 6000 & 25 \end{matrix}$

Discussion

34.	A solid cylinder and a solid cone have equal bases and equal heights. If the radius and height be in the ratio 4 : 3, the ratio of the total surface area of the cylinder to that of the cone is __________.
Answer» A solid cylinder and a solid cone have equal bases and equal heights. If the radius and height be in the ratio 4 : 3, the ratio of the total surface area of the cylinder to that of the cone is __________.

Discussion

35.	Show that x=−bcad is a solution of the quadratic equation ad2(axb+2cd)x+bc2=0.
Answer» Show that $x = - \frac{b c}{a d}$ is a solution of the quadratic equation $a d^{2} (\frac{a x}{b} + \frac{2 c}{d}) x + b c^{2} = 0$ .

Discussion

36.	A manufacturer of furniture sells a sofa set to a retailer for Rs.23000. The retailer, in turn sells sofa set to a customer for Rs.29500. find the VAT rate as percent, if the retailer pays Rs.250 as VAT.
Answer» A manufacturer of furniture sells a sofa set to a retailer for Rs.23000. The retailer, in turn sells sofa set to a customer for Rs.29500. find the VAT rate as percent, if the retailer pays Rs.250 as VAT.

Discussion

37.	what is fog and gof function
Answer» what is fog and gof function

Discussion

38.	If a and b are the roots of the equation x^2-ax+b=0 then find a and b
Answer» If a and b are the roots of the equation x^2-ax+b=0 then find a and b

Discussion

39.	π is(a) a rational number(b) an integer(c) an irrational number(d) a whole number
Answer» π is (a) a rational number (b) an integer (c) an irrational number (d) a whole number

Discussion

40.	Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.
Answer» Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Discussion

41.	Question 15Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.
Answer» Question 15 Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

Discussion

42.	A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.
Answer» A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

Discussion

43.	how to solve nine persons were to pay equal amount to a certain fund . if there were 3 persons less then each would have to contribute four rupees more . what is the amount of the fund ?
Answer» how to solve nine persons were to pay equal amount to a certain fund . if there were 3 persons less then each would have to contribute four rupees more . what is the amount of the fund ?

Discussion

44.	5. Find the maximum value of a cos theta+b sin (theta+alpha) (a,beta,theta are constants.)
Answer» 5. Find the maximum value of a cos theta+b sin (theta+alpha) (a,beta,theta are constants.)

Discussion

45.	On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is
Answer» On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

Discussion

46.	the angle made by \overrightarrow A =2icap+2jcap with negative x axis is why the angle is not 135degre??
Answer» the angle made by \overrightarrow A =2icap+2jcap with negative x axis is why the angle is not 135degre??

Discussion

47.	For a right angled triangle, if the sum of the length of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotensuse and the side is
Answer» For a right angled triangle, if the sum of the length of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotensuse and the side is

Discussion

48.	A person standing on a boat at point A sees a submarine at point B, making an angle of depression of 60°. After some time, the submarine travels 232 m and moves to point C. Now, the angle of depression becomes 30°. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [tan 30° = 0.57, tan 60° =1.73 ]
Answer» A person standing on a boat at point A sees a submarine at point B, making an angle of depression of 60°. After some time, the submarine travels $232 m$ and moves to point C. Now, the angle of depression becomes 30°. Find the distance the boat has to travel to reach a point that is exactly above the submarine. [tan 30° $=$ 0.57, tan 60° $=$ 1.73 ]

Discussion

49.	94. Prove that the points (3,0) (6,4) and (-1,3) are the vertices of right angled isosceles triangle?
Answer» 94. Prove that the points (3,0) (6,4) and (-1,3) are the vertices of right angled isosceles triangle?

Discussion

50.	If f(x) = 2x + 3, what is f(7)?
Answer» If f(x) = 2x + 3, what is f(7)?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The volume of a hemisphere of radius r is ______ .

The coordinates of centroid of triangle formed by lines 4x+7y =28 whenx=0,y=0

If 3 is is the least prime factor of number a and 7 is the least prime factor of number b, then the least prime factor of a+b , is

In the following figure, AB, CD and EF are perpendicular to the straight line BDF. If AB = x units and CD = z units and EF = y units, then which of the following is/are true?

Draw a square whose vertices are (2,2), (4,2), (4,4) and (2,4). Reflect the square in the y-axis and then reflect the image in the origin. What single transformation would give the same result?

Two different dice are thrown together. Find the probability that(i) the sum of the numbers appeared is less than 7. [CBSE 2011](ii) the product of the numbers appeared is less than 18. [CBSE 2017]

Which term of the AP = 21, 18, 15, ... is -81?

If one of the zeroes of a quadratic polynomial (k−1)x2+kx+1 is -3, then the value of k is .

Use Euclid’s division algorithm to find the HCF of:

Cards numbered from 11 to 60 are kept in a box. If a card is drawn at random from the box, find the probability that the number on the drawn card is(i) an odd number(ii) a perfect square number(iii) divisible by 5(iv) a prime number less than 20 [CBSE 2014]

If (tan x +sec x)(tan y + sec y)(tanz +sec z) = (sec x - tan x )(sec y - tan y ) (secz - tan z) = K, then the value of K is

Without actual division, state whether the following rational numbers will have terminating or non-terminating decimal representation. a) 64455 b) 133125

4 A polynomial has property that 3f(x)+7f(2016/x)=2x. The value of f(8) is

Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x), q(x) + r(x), where degree r(x) = 0.

If the equation x2+2(k+2)x+9k=0 has equal roots, then values of k are __________.

In a farm, a heap of paddy is in the form of a cone with slant height 13 m and height 12 m. What is the area of canvas needed to protect it from sun and rain?

Question 162 Find the values of x and y in the following kite.

If LM ∥ AB, AL=x-3, AC=2x, BM=x-2, BC=2x+3. What is value of AC?___

Solve the following systems of equations:xyx+y=65xyy-x=6,where x + y ≠ 0, y − x ≠ 0

Three numbers are in AP such that their sum is 15 then find the second term.

The angle of elevation of a ladder leaning against a wall is 60∘ and the foot of the ladder is 9.5m away from the wall. Find the length of the ladder.

If the radius and the slant height of the cone are in the ratio of 4:7and its curved surface area is 792 cm^2 then its radius is

Question 2 (i)For which values of ‘a’ and ‘b’ does the following pair of linear equations have an infinite number of solutions?2x + 3y =7(a - b)x + (a + b)y = 3a +b - 2

Question 3 (iii) In an AP: (iii) Given a12=37,d=3, find a and S12.

A chord of length 5 cm subtends an angle of 60∘ at the centre of a circle. The area of the sector of the same circle which is subtending central angle of 120∘ at the centre, is

Find the sum(1) 4 ⊕5 3(2) 5 ⊕7 4(3) (3 ⊕7 6) ⊕7 4(4) (10 ⊕12 2) ⊕12 3

Show that the points A(1,2),B(1,6),C(1+2√3,4) are vertices of an equilateral triangle.

In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region.[Use π = 3.14]

Question 5: Draw a rough figure and label suitably in the following case: (a) Line l contains E and F but not D.

A man travels 600 km partly by train and partly by car. If the covers 400 km by train and the rest by car, it takes him 6 hours 30 minutes. But, if the travels 200 km by train and the rest by car, he takes half an hour longer. Find the speed of the train and that of the car.

The following data shows monthly savings of 100 families . Find the Mode of the Monthly SavingsMonthly savings(Rs)Number of families1000−2000142000−3000153000−4000214000−5000275000−600025

A solid cylinder and a solid cone have equal bases and equal heights. If the radius and height be in the ratio 4 : 3, the ratio of the total surface area of the cylinder to that of the cone is __________.

Show that x=−bcad is a solution of the quadratic equation ad2(axb+2cd)x+bc2=0.

A manufacturer of furniture sells a sofa set to a retailer for Rs.23000. The retailer, in turn sells sofa set to a customer for Rs.29500. find the VAT rate as percent, if the retailer pays Rs.250 as VAT.

what is fog and gof function

If a and b are the roots of the equation x^2-ax+b=0 then find a and b

π is(a) a rational number(b) an integer(c) an irrational number(d) a whole number

Find the coordinates of the points which divide the line segment joining A (- 2, 2) and B (2, 8) into four equal parts.

Question 15Foot of a 10m long ladder leaning against a vertical wall is 6m away from the base of the wall. Find the height of the point on the wall where the top of the ladder reaches.

A passenger train takes 2 hours less for a journey of 300 km if its speed is increased by 5 km/hr from its usual speed. Find its usual speed.

how to solve nine persons were to pay equal amount to a certain fund . if there were 3 persons less then each would have to contribute four rupees more . what is the amount of the fund ?

5. Find the maximum value of a cos theta+b sin (theta+alpha) (a,beta,theta are constants.)

On dividing f(x) = x³ - 3x² + x + 2 by a polynomial g(x) the quotient and remainder q(x) and r(x) are (x – 2) and (-2x + 4) respectively, then g(x) is

the angle made by \overrightarrow A =2icap+2jcap with negative x axis is why the angle is not 135degre??

For a right angled triangle, if the sum of the length of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotensuse and the side is

94. Prove that the points (3,0) (6,4) and (-1,3) are the vertices of right angled isosceles triangle?

If f(x) = 2x + 3, what is f(7)?