32581 + Interview Questions in Mathematics

1.	Question 21(iii)Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 7?
Answer» Question 21(iii) Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 7?

Discussion

2.	how to solve (q/x-a - q/x+a)
Answer» how to solve (q/x-a - q/x+a)

Discussion

3.	The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is(a) 5(b) 10(c) 12(d) 14(e) 20
Answer» The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is (a) 5 (b) 10 (c) 12 (d) 14 (e) 20

Discussion

4.	In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then find the value of PS.
Answer» In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then find the value of PS.

Discussion

5.	Find the sum of first 24 terms of the list of numbers whose nth term is given by an=3+2n.
Answer» Find the sum of first $24$ terms of the list of numbers whose $n^{t h}$ term is given by $a_{n} = 3 + 2 n$ .

Discussion

6.	The probability of certain event is:
Answer» The probability of certain event is:

Discussion

7.	If p(x)=x3−3x2−9x−9, find p(0), p(3), p(-3) and p(-1). What do you conclude about the zeros of p(x)? Is 0 a zero p(x)?
Answer» If $p (x) = x^{3} - 3 x^{2} - 9 x - 9$ , find p(0), p(3), p(-3) and p(-1). What do you conclude about the zeros of p(x)? Is 0 a zero p(x)?

Discussion

8.	16.Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second
Answer» 16.Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second

Discussion

9.	In a ΔABC, ∠B=90o, AB=24 cm and BC=7 cm. Find (i) sin A (ii) cos A (iii) sin C (iv) cos C.
Answer» In a $Δ A B C$ , $∠ B = 90^{o}, A B = 24 c m$ and $B C = 7 c m$ . Find (i) sin A (ii) cos A (iii) sin C (iv) cos C.

9.

In a ΔABC, ∠B=90o, AB=24 cm and BC=7 cm. Find (i) sin A (ii) cos A (iii) sin C (iv) cos C.

Answer»

In a $Δ A B C$ , $∠ B = 90^{o}, A B = 24 c m$ and $B C = 7 c m$ .

Find (i) sin A (ii) cos A (iii) sin C (iv) cos C.

Discussion

10.	Which among the following is the solution of 3x+4y=6?
Answer» Which among the following is the solution of $3 x + 4 y = 6 ?$

Discussion

11.	A Ladder makes an angle of 60∘ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length( in meters) is:
Answer» A Ladder makes an angle of $60^{\circ}$ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length( in meters) is:

Discussion

12.	Is −150 a term of 11,8,5,2,...........?
Answer» Is $- 150$ a term of $11, 8, 5, 2, . . . . . . . . . . . ?$

Discussion

13.	Question 15For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?
Answer» Question 15 For what value of n, are the $n^{t h}$ terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

Discussion

14.	Fill In The Blanks A die is thrown 1000 times and the outcomes were recorded as follows: Outcomes: 1 2 3 4 5 6Frequency: 180 150 160 170 150 190If the die is thown once more, then the probability that its show 5 is _________.
Answer» Fill In The Blanks A die is thrown 1000 times and the outcomes were recorded as follows: Outcomes: 1 2 3 4 5 6 Frequency: 180 150 160 170 150 190 If the die is thown once more, then the probability that its show 5 is _________.

Discussion

15.	In triangle ABC, AC=AB and BD is perpendicular to AC prove that BD2+CD2=2AC×CD
Answer» In triangle ABC, AC=AB and BD is perpendicular to AC prove that $B D^{2} + C D^{2} = 2 A C \times C D$

Discussion

16.	Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points
Answer» Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

Discussion

17.	When two dice are thrown simultaneously ,the probability of getting a sum of 12 is___
Answer» When two dice are thrown simultaneously ,the probability of getting a sum of 12 is___

Discussion

18.	The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.
Answer» The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.

Discussion

19.	From a window A, 10 m above ground the angle of elevation of the top of the tower, is where tan = 5/2 and the angle of depression of the foot D of tower is y degrees, where tan y = 1/4. Calculate height of tower CD in meters.
Answer» From a window A, 10 m above ground the angle of elevation of the top of the tower, is where tan = ⁵/₂ and the angle of depression of the foot D of tower is y degrees, where tan y = ¹/₄. Calculate height of tower CD in meters.

19.

From a window A, 10 m above ground the angle of elevation of the top of the tower, is where tan = 5/2 and the angle of depression of the foot D of tower is y degrees, where tan y = 1/4. Calculate height of tower CD in meters.

Answer»

From a window A, 10 m above ground the angle of elevation of the top of the tower, is where tan = ⁵/₂ and the angle of depression of the foot D of tower is y degrees, where tan y = ¹/₄. Calculate height of tower CD in meters.

Discussion

20.	Two circles of radii 5 cm and 3 cm have their centres 10 cm apart. Draw a direct common tangent to the circle.
Answer» Two circles of radii 5 cm and 3 cm have their centres 10 cm apart. Draw a direct common tangent to the circle.

Discussion

21.	Rectify the following errors found in the books of Mr. Aryan by passing entries:(i) The purchase of ₹ 610 from Kabir was entered into sales book but Kabir's personal account was rightly credited.(ii) Sale of old furniture of ₹ 2,500 was credited to sales account as ₹ 250.(iii) An item of ₹ 500 relating to prepaid insurance account was omitted to be brought forward from the previous year's books.(iv) ₹ 220 discount received from a creditor had been duly entered in his account but not posted to discount received account.
Answer» Rectify the following errors found in the books of Mr. Aryan by passing entries: (i) The purchase of ₹ 610 from Kabir was entered into sales book but Kabir's personal account was rightly credited. (ii) Sale of old furniture of ₹ 2,500 was credited to sales account as ₹ 250. (iii) An item of ₹ 500 relating to prepaid insurance account was omitted to be brought forward from the previous year's books. (iv) ₹ 220 discount received from a creditor had been duly entered in his account but not posted to discount received account.

Discussion

22.	Given tan(A+B)=√3 and tan(A−B)=1√3 If B<A<90∘, then, A = ___ B = ___ (If your answer is 20∘, then type 20)
Answer» Given $t a n (A + B) = \sqrt{3}$ and $t a n (A - B) = \frac{1}{\sqrt{3}}$ If $B < A < 90^{\circ}$ , then, A = ___ B = ___ (If your answer is $20^{\circ}$ , then type 20)

Discussion

23.	Prove that 2+3 is an irrational number .
Answer» Prove that $\sqrt{2} + \sqrt{3}$ is an irrational number .

Discussion

24.	2log5+1\2log9-log3=logx then find value of x?
Answer» 2log5+1\2log9-log3=logx then find value of x?

Discussion

25.	Find the volume of the figure.
Answer» Find the volume of the figure.

25.

Find the volume of the figure.

Answer»

Find the volume of the figure.

Discussion

26.	In the above figure, the radius of the circle, a is .
Answer» In the above figure, the radius of the circle, a is .

Discussion

27.	What is the largest number that divides each one of 1152 and 1664 exactly ? (a) 32 (b) 64 (c) 128 (d) 256
Answer» What is the largest number that divides each one of 1152 and 1664 exactly ? (a) 32 (b) 64 (c) 128 (d) 256

27.

What is the largest number that divides each one of 1152 and 1664 exactly ? (a) 32 (b) 64 (c) 128 (d) 256

Answer»

What is the largest number that divides each one of 1152 and 1664 exactly ?

(a) 32 (b) 64 (c) 128 (d) 256

Discussion

28.	If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in cm2) is
Answer» If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in $c m^{2}$ ) is

Discussion

29.	From the top of a 120 m high tower, a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° and 45°. Find the distance between the cars. (Take 3=1.732 )
Answer» From the top of a 120 m high tower, a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° and 45°. Find the distance between the cars. (Take $\sqrt{3} = 1.732$ )

Discussion

30.	More than One Answer Typeएक से अधिक उत्तर प्रकार के प्रश्नWhich of the following figure/s has/have exactly 32 triangles and 16 squares?निम्नलिखित में से कौनसा/कौनसे चित्र/चित्रों में ठीक 32 त्रिभुज व 16 वर्ग है/हैं?
Answer» More than One Answer Type एक से अधिक उत्तर प्रकार के प्रश्न Which of the following figure/s has/have exactly 32 triangles and 16 squares? निम्नलिखित में से कौनसा/कौनसे चित्र/चित्रों में ठीक 32 त्रिभुज व 16 वर्ग है/हैं?

Discussion

31.	Find out the slope of line B from thegiven graph.From the following equations, has same slope as line B.
Answer» Find out the slope of line B from the given graph. From the following equations, has same slope as line B.

Discussion

32.	Find the equation of the line whose -intercept is 8 and -intercept is -12.
Answer» Find the equation of the line whose -intercept is 8 and -intercept is -12.

Discussion

33.	If x ( /2 , ) Show that sin (cosx) < cos (sinx)
Answer» If x ( /2 , ) Show that sin (cosx) < cos (sinx)

Discussion

34.	The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?
Answer» The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

Discussion

35.	Simplify the following:3n×9n+13n−1×9n−1
Answer» Simplify the following: $\frac{3^{n} \times 9^{n + 1}}{3^{n - 1} \times 9^{n - 1}}$

Discussion

36.	A semi circular sheet of metal of diameter 28cm is bent into an open conical cup , find the depth and capacity of the cup
Answer» A semi circular sheet of metal of diameter 28cm is bent into an open conical cup , find the depth and capacity of the cup

Discussion

37.	17. integrate 1/(sinx +secx)
Answer» 17. integrate 1/(sinx +secx)

Discussion

38.	The probability to be a year younger next year is ___.
Answer» The probability to be a year younger next year is ___.

Discussion

39.	Question 7The tangents to the circumcircle of an isosceles ΔABC at A, which AB=AC, is parallel to BC.
Answer» Question 7 The tangents to the circumcircle of an isosceles $Δ$ ABC at A, which AB=AC, is parallel to BC.

Discussion

40.	Choose the correct answer of the following question:If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is(a) 20 cm (b) 125 cm (c) 813 cm (d) 16 cm [CBSE 2013C]
Answer» Choose the correct answer of the following question: If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is (a) 20 cm (b) $12 \sqrt{5}$ cm (c) $8 \sqrt{13}$ cm (d) 16 cm [CBSE 2013C]

Discussion

41.	In measuring the sides of a rectangle, errors of 5% and 3% in excess are made. The error percentage in the calculated area is ____.
Answer» In measuring the sides of a rectangle, errors of $5 %$ and $3 %$ in excess are made. The error percentage in the calculated area is ____.

Discussion

42.	Question 2 (i)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
Answer» Question 2 (i) Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Discussion

43.	Determine the ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8), also find the value of m.
Answer» Determine the ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8), also find the value of m.

Discussion

44.	Solve the following systems of equations graphically:2x + 3y = 4x − y + 3 = 0
Answer» Solve the following systems of equations graphically: 2x + 3y = 4 x − y + 3 = 0

Discussion

45.	If f(x) = [x]2 − 5 [x] + 6, then the set of values of x satisfying f(x) = 0 is __________ .
Answer» If f(x) = [x]² − 5 [x] + 6, then the set of values of x satisfying f(x) = 0 is __________ .

Discussion

46.	Prove that the points (a, b) , (a1,b1) and (a−a1,b−b1) are collinear if ab1=a1b.
Answer» Prove that the points (a, b) , $(a_{1}, b_{1})$ and $(a - a_{1}, b - b_{1})$ are collinear if $a b_{1} = a_{1} b$ .

Discussion

47.	Is the relation 2sin x=a+1/a possible for any x where a is any positive integer. Explain
Answer» Is the relation 2sin x=a+1/a possible for any x where a is any positive integer. Explain

Discussion

48.	One of the roots of the equation (x+1a)2−b2=0 is .
Answer» One of the roots of the equation $(x + \frac{1}{a})^{2} - b^{2} = 0$ is .

Discussion

49.	A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)
Answer» A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm². (Use π = 3.14)

Discussion

50.	1. Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis.
Answer» 1. Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Question 21(iii)Two dice are thrown together. Find the probability that the product of the numbers on the top of the dice is 7?

how to solve (q/x-a - q/x+a)

The number of terms of the A.P. 3, 7, 11, 15, ... to be taken so that the sum is 406 is(a) 5(b) 10(c) 12(d) 14(e) 20

In the given figure, PS is a tangent and line PR is a secant to the circle. If PQ = 4.9 cm and QR = 5.1cm, then find the value of PS.

Find the sum of first 24 terms of the list of numbers whose nth term is given by an=3+2n.

The probability of certain event is:

If p(x)=x3−3x2−9x−9, find p(0), p(3), p(-3) and p(-1). What do you conclude about the zeros of p(x)? Is 0 a zero p(x)?

16.Water flows through a horizontal pipe of varying area of cross section at the rate 15 cubic meter per minute. Find the radius of the pipe where water flows with a velocity 3 meter per second

In a ΔABC, ∠B=90o, AB=24 cm and BC=7 cm. Find (i) sin A (ii) cos A (iii) sin C (iv) cos C.

Which among the following is the solution of 3x+4y=6?

A Ladder makes an angle of 60∘ with the ground when placed against a wall. If the foot of the ladder is 2 m away from the wall, then the length( in meters) is:

Is −150 a term of 11,8,5,2,...........?

Question 15For what value of n, are the nth terms of two APs 63, 65, 67, and 3, 10, 17, … equal?

Fill In The Blanks A die is thrown 1000 times and the outcomes were recorded as follows: Outcomes: 1 2 3 4 5 6Frequency: 180 150 160 170 150 190If the die is thown once more, then the probability that its show 5 is _________.

In triangle ABC, AC=AB and BD is perpendicular to AC prove that BD2+CD2=2AC×CD

Let the opposite angular points of a square be (3, 4) and (1, –1). Find the coordinates of the remaining angular points

When two dice are thrown simultaneously ,the probability of getting a sum of 12 is___

The sum of the 2nd and the 7th terms of an AP is 30. If its 15th term is 1 less than twice its 8th term, find the AP.

From a window A, 10 m above ground the angle of elevation of the top of the tower, is where tan = 5/2 and the angle of depression of the foot D of tower is y degrees, where tan y = 1/4. Calculate height of tower CD in meters.

Two circles of radii 5 cm and 3 cm have their centres 10 cm apart. Draw a direct common tangent to the circle.

Given tan(A+B)=√3 and tan(A−B)=1√3 If B&lt;A&lt;90∘, then, A = ___ B = ___ (If your answer is 20∘, then type 20)

Prove that 2+3 is an irrational number .

2log5+1\2log9-log3=logx then find value of x?

Find the volume of the figure.

In the above figure, the radius of the circle, a is .

What is the largest number that divides each one of 1152 and 1664 exactly ? (a) 32 (b) 64 (c) 128 (d) 256

If the dimensions of a cuboid are 3 cm, 4 cm and 10 cm, then its surface area( in cm2) is

From the top of a 120 m high tower, a man observes two cars on the opposite sides of the tower and in straight line with the base of tower with angles of depression as 60° and 45°. Find the distance between the cars. (Take 3=1.732 )

Find out the slope of line B from thegiven graph.From the following equations, has same slope as line B.

Find the equation of the line whose -intercept is 8 and -intercept is -12.

If x ( /2 , ) Show that sin (cosx) < cos (sinx)

The diameter of a football is 24 cm. What is the volume of air inside 50 such footballs?

Simplify the following:3n×9n+13n−1×9n−1

A semi circular sheet of metal of diameter 28cm is bent into an open conical cup , find the depth and capacity of the cup

17. integrate 1/(sinx +secx)

The probability to be a year younger next year is ___.

Question 7The tangents to the circumcircle of an isosceles ΔABC at A, which AB=AC, is parallel to BC.

Choose the correct answer of the following question:If the height of a bucket in the shape of frustum of a cone is 16 cm and the diameters of its two circular ends are 40 cm and 16 cm, then its slant height is(a) 20 cm (b) 125 cm (c) 813 cm (d) 16 cm [CBSE 2013C]

In measuring the sides of a rectangle, errors of 5% and 3% in excess are made. The error percentage in the calculated area is ____.

Question 2 (i)Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.

Determine the ratio in which the point P (m, 6) divides the join A (-4, 3) and B (2, 8), also find the value of m.

Solve the following systems of equations graphically:2x + 3y = 4x − y + 3 = 0

If f(x) = [x]2 − 5 [x] + 6, then the set of values of x satisfying f(x) = 0 is __________ .

Prove that the points (a, b) , (a1,b1) and (a−a1,b−b1) are collinear if ab1=a1b.

Is the relation 2sin x=a+1/a possible for any x where a is any positive integer. Explain

One of the roots of the equation (x+1a)2−b2=0 is .

A bucket has top and bottom diameter of 40 cm and 20 cm respectively. Find the volume of the bucket if its depth is 12 cm. Also, find the cost of tin sheet used for making the bucket at the rate of Rs. 1.20 per dm2 . (Use π = 3.14)

1. Show graphically that the system of linear equations 5x – y = 14 ; x – 2y =1 has a unique solution. Write the coordinates where line x – 2y =1 intersects the X-axis.

Given tan(A+B)=√3 and tan(A−B)=1√3 If B<A<90∘, then, A = _ B = _ (If your answer is 20∘, then type 20)