32581 + Interview Questions in Mathematics

1.	f(x) cannot be equal to 5(x5)(35)
Answer» $f (x)$ cannot be equal to $5 (x^{5}) (\frac{3}{5})$

Discussion

2.	If y2+16=2xy, then y′(5)=
Answer» If $y^{2} + 16 = 2 x y,$ then $y^{'} (5) =$

Discussion

3.	From the following Venn diagram, A' is
Answer» From the following Venn diagram, A' is

3.

From the following Venn diagram, A' is

Answer»

From the following Venn diagram, A' is

Discussion

4.	Question 2Which of the following is not a quadratic equation?(a) 2(x−1)2=4x2−2x+1(b) 2x−x2=x2+5(c) (√2x+√3)2=3x2−5x(d) (x2+2x)2=x4+3+4x3
Answer» Question 2 Which of the following is not a quadratic equation? (a) $2 (x - 1)^{2} = 4 x^{2} - 2 x + 1$ (b) $2 x - x^{2} = x^{2} + 5$ (c) ${(\sqrt{2} x + \sqrt{3})}^{2} = 3 x^{2} - 5 x$ (d) $(x^{2} + 2 x)^{2} = x^{4} + 3 + 4 x^{3}$

Discussion

5.	For what value of k, is 3 a zero of the polynomial 2x2 + x + k?
Answer» For what value of k, is 3 a zero of the polynomial 2x² + x + k?

Discussion

6.	If sin^2A +sinA =1 , then cos^6A + cos^4A + cos^2A =
Answer» If sin^2A +sinA =1 , then cos^6A + cos^4A + cos^2A =

Discussion

7.	If AB, AC, PQ are tangents in the given figure and AB = 5 cm, find the perimeter of Δ APQ.
Answer» If AB, AC, PQ are tangents in the given figure and AB = 5 cm, find the perimeter of Δ APQ.

Discussion

8.	If p has n+1 and q has n fair coins then probability that p has more heads than q
Answer» If p has n+1 and q has n fair coins then probability that p has more heads than q

Discussion

9.	Choose the correct answer in each of the following questions:The 7th term of an AP is −1 and its 16th term is 17. The nth term of the AP is [CBSE 2014](a) (3n + 8) (b) (4n − 7) (c) (15 − 2n) (d) (2n − 15)
Answer» Choose the correct answer in each of the following questions: The 7th term of an AP is −1 and its 16th term is 17. The nth term of the AP is [CBSE 2014] (a) (3n + 8) (b) (4n − 7) (c) (15 − 2n) (d) (2n − 15)

Discussion

10.

Compute the median for each of the following data:(i) Marks No. of students Less than 10 Less than 30 Less than 50 Less than 70 Less than 90 Less than 110 Less than 130 Less than 150 0 10 25 43 65 87 96 100 (ii) Marks No. of students More than 150 More than 140 More than 130 More than 120 More than 110 More than 100 More than 90 More than 80 0 12 27 60 105 124 141 150

Answer» Compute the median for each of the following data:

(i)

Marks	No. of students
Less than 10 Less than 30 Less than 50 Less than 70 Less than 90 Less than 110 Less than 130 Less than 150	0 10 25 43 65 87 96 100

(ii)

Marks	No. of students
More than 150 More than 140 More than 130 More than 120 More than 110 More than 100 More than 90 More than 80	0 12 27 60 105 124 141 150

Discussion

11.	A solid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is _________.
Answer» A solid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is _________.

Discussion

12.	The mid-point P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also, find the value of y. [CBSE 2014]
Answer» The mid-point P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also, find the value of y. [CBSE 2014]

Discussion

13.	The altitude of a right triangle is 7 cm less than its base x and its hypotenuse is 13 cm. Identify the quadratic representation of the given statement.
Answer» The altitude of a right triangle is 7 cm less than its base x and its hypotenuse is 13 cm. Identify the quadratic representation of the given statement.

Discussion

14.	In a partnership business, the capital that Arav invested is double the capital that Zoya had invested. The ratio of their period of investment is 12:13. The ratio of their profit is ______.
Answer» In a partnership business, the capital that Arav invested is double the capital that Zoya had invested. The ratio of their period of investment is $\frac{1}{2} : \frac{1}{3}$ . The ratio of their profit is ______.

Discussion

15.	Product of two consecutive natural number is 56. Find the smaller number.
Answer» Product of two consecutive natural number is 56. Find the smaller number.

Discussion

16.	Define a polynomial with real coefficients.
Answer» Define a polynomial with real coefficients.

Discussion

17.	There are two positive integers X & Y. When X is divided by 237, the remainder is 192. When Y is divided by 117 the quotient is the same but the remainder is 108. Find the remainder when the sum of X & Y is divided by 118.
Answer» There are two positive integers $X$ & $Y .$ When $X$ is divided by $237,$ the remainder is $192.$ When Y is divided by $117$ the quotient is the same but the remainder is $108.$ Find the remainder when the sum of $X$ & $Y$ is divided by $118.$

Discussion

18.	If sin θ=2029, find cos θ.
Answer» If $s i n θ = \frac{20}{29}$ , find $c o s θ$ .

Discussion

19.	The nth term of an A.P is given by (−4n + 15), Find the sum of first 20 terms of this A.P.
Answer» The nth term of an A.P is given by (−4n + 15), Find the sum of first 20 terms of this A.P.

Discussion

20.	If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then ∠TOP is ____.
Answer» If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then $∠$ TOP is ____.

Discussion

21.	The area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, find the radius of the inner circle.
Answer» The area enclosed between the concentric circles is 770 cm². If the radius of the outer circle is 21 cm, find the radius of the inner circle.

Discussion

22.	If 0º < θ < 90º and 4secθ + 4cosecθ = 5secθcosecθ, then tanθ can be equal toयदि 0º < θ < 90º तथा 4secθ + 4cosecθ = 5secθcosecθ, तब tanθ बराबर हो सकता है
Answer» If 0º < θ < 90º and 4secθ + 4cosecθ = 5secθcosecθ, then tanθ can be equal to यदि 0º < θ < 90º तथा 4secθ + 4cosecθ = 5secθcosecθ, तब tanθ बराबर हो सकता है

Discussion

23.	In the picture below, PQ, RS, TU are tangents to the circle at A, B, C.How many pairs of equal angles are there in it?
Answer» In the picture below, PQ, RS, TU are tangents to the circle at A, B, C. How many pairs of equal angles are there in it?

23.

In the picture below, PQ, RS, TU are tangents to the circle at A, B, C.How many pairs of equal angles are there in it?

Answer»

In the picture below, PQ, RS, TU are tangents to the circle at A, B, C.

How many pairs of equal angles are there in it?

Discussion

24.	If angle between two radii of a circle is 1300 , the angle between the tangents at the ends of radii is (a) 900 (b) 500 (c) 700 (d) 400
Answer» If angle between two radii of a circle is 130⁰, the angle between the tangents at the ends of radii is (a) 90⁰ (b) 50⁰ (c) 70⁰ (d) 40⁰

Discussion

25.	The denominator of a fraction is greater than its numerator by 11.If 8 is added to both its numerator and denominator,it becomes 34.Find the fraction.
Answer» The denominator of a fraction is greater than its numerator by 11.If 8 is added to both its numerator and denominator,it becomes $\frac{3}{4}$ .Find the fraction.

Discussion

26.	The distance of the point (–4, 7) from y-axis is _________.
Answer» The distance of the point (–4, 7) from y-axis is _________.

Discussion

27.	What is n/2in the equation for sum to 'n' terms
Answer» What is n/2in the equation for sum to 'n' terms

Discussion

28.	The positive numbers x and y satisfy xy = 1. Then the value of x such thatis minimum.
Answer» The positive numbers x and y satisfy xy = 1. Then the value of x such thatis minimum.

Discussion

29.	53. Why is TSA,CSA and volume of frustum are R1+R2 not r1-r2
Answer» 53. Why is TSA,CSA and volume of frustum are R1+R2 not r1-r2

Discussion

30.	What is the probability of picking a red numbered card with number more than 6?
Answer» What is the probability of picking a red numbered card with number more than 6?

Discussion

31.	Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not?(i) R={(2,1),(3,1),(4,2)}(ii) R={2,2),(2,4),(3,3),(4,4)}(iii) R={1,2),(2,3),(3,4),(4,5),(5,6),(6,7)}
Answer» Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not? $(i) R = {(2, 1), (3, 1), (4, 2)}$ $(i i) R = {2, 2), (2, 4), (3, 3), (4, 4)}$ $(i i i) R = {1, 2), (2, 3), (3, 4), (4, 5), (5, 6), (6, 7)}$

Discussion

32.	The mean of first five natural numbers is(a) 5 (b) 4 (c) 3 (d) 6
Answer» The mean of first five natural numbers is (a) 5 (b) 4 (c) 3 (d) 6

Discussion

33.	Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?
Answer» Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?

Discussion

34.	Express the given pattern as a sequence.
Answer» Express the given pattern as a sequence.

Discussion

35.	Question 7 (v)Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.(e) If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.
Answer» Question 7 (v) Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC. (e) If $A (x_{1}, y_{1}), B (x_{2}, y_{2}) a n d C (x_{3}, y_{3})$ are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

Discussion

36.	In the circle given, OP = 1 unit and ∠POQ = θ. Which side represents cos θ?
Answer» In the circle given, OP = 1 unit and ∠POQ = θ. Which side represents $c o s θ$ ?

Discussion

37.	Question 8Any point on the line y = x is of the form:A) (a, a)B) (0, a)C) (a, 0)D) (a, -a)
Answer» Question 8 Any point on the line y = x is of the form: A) (a, a) B) (0, a) C) (a, 0) D) (a, -a)

Discussion

38.	Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and is in the direction .
Answer» Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and is in the direction .

Discussion

39.	Question 9 (ii) 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: Number of lettersNumber of surnames1−464−6306−8448−121612−204 (ii) Write the class interval in which the maximum number of surname lie.
Answer» Question 9 (ii) 100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows: $\begin{matrix} Number of letters & Number of surnames 1 - 4 & 6 4 - 6 & 30 6 - 8 & 44 8 - 12 & 16 12 - 20 & 4 \end{matrix}$ (ii) Write the class interval in which the maximum number of surname lie.

Discussion

40.	The number of integers n such that 1less than or equal to n less than or equal to 200 and nn is a perfect square is ?
Answer» The number of integers n such that 1less than or equal to n less than or equal to 200 and nⁿis a perfect square is ?

Discussion

41.	Two spheres of same material are heated up to same temperature and then allowed to cool in same surrounding. If their radii are in the ratio of 4:7 then ratio of their initial rate of cooling is? 1) 2:7 2) 7:2 3) 4:7 4) 7:4
Answer» Two spheres of same material are heated up to same temperature and then allowed to cool in same surrounding. If their radii are in the ratio of 4:7 then ratio of their initial rate of cooling is? 1) 2:7 2) 7:2 3) 4:7 4) 7:4

Discussion

42.	Complete the following statements:(i) Probability of an event E + Probability of the event ‘not E’ = _______.(ii) The probability of an event that cannot happen is _________. Such as event is called _________.(iii) The probability of an event that is certain to happen is _________. Such as event is called ________.(iv) The sum of the probabilities of all the elementary events of an experiment is _________.(v) The probability of an event is greater than or equal to _______ and less than or equal to _______.
Answer» Complete the following statements: (i) Probability of an event E + Probability of the event ‘not E’ = _______. (ii) The probability of an event that cannot happen is _________. Such as event is called _________. (iii) The probability of an event that is certain to happen is _________. Such as event is called ________. (iv) The sum of the probabilities of all the elementary events of an experiment is _________. (v) The probability of an event is greater than or equal to _______ and less than or equal to _______.

42.

Complete the following statements:(i) Probability of an event E + Probability of the event ‘not E’ = ___.(ii) The probability of an event that cannot happen is _. Such as event is called _.(iii) The probability of an event that is certain to happen is _. Such as event is called .(iv) The sum of the probabilities of all the elementary events of an experiment is _.(v) The probability of an event is greater than or equal to _ and less than or equal to _____.

Answer»

Complete the following statements:

(i) Probability of an event E + Probability of the event ‘not E’ = _______.

(ii) The probability of an event that cannot happen is _________. Such as event is called _________.

(iii) The probability of an event that is certain to happen is _________. Such as event is called ________.

(iv) The sum of the probabilities of all the elementary events of an experiment is _________.

(v) The probability of an event is greater than or equal to _______ and less than or equal to _______.

Discussion

43.	If 1x+2,1x+3,1x+5 are in A.P. Then, x =(a) 5(b) 3(c) 1(d) 2
Answer» If $\frac{1}{x + 2}, \frac{1}{x + 3}, \frac{1}{x + 5}$ are in A.P. Then, x = (a) 5 (b) 3 (c) 1 (d) 2

Discussion

44.	In the following figure, shows a sector of a circle, centre O, containing an angle 0°. Prove that:(i) Perimeter of the shaded region is tan θ+secθ+πθ180-1(ii) Area of the shaded region is r22tanθ-πθ180
Answer» In the following figure, shows a sector of a circle, centre O, containing an angle 0°. Prove that: (i) Perimeter of the shaded region is $(\tan θ + s e c θ + \frac{πθ}{180} - 1)$ (ii) Area of the shaded region is $\frac{r^{2}}{2} (\tan θ - \frac{πθ}{180})$

Discussion

45.	Find the angle of elevation of the sun when the shadow of a 10m long pole is 10√3 m.
Answer» Find the angle of elevation of the sun when the shadow of a 10m long pole is 10 $\sqrt{3}$ m.

Discussion

46.	If one root of equation z2 - (11 + i)z + k +3i = 0 is 3.Find the other root. K ϵ Z
Answer» If one root of equation $z^{2}$ - (11 + i)z + k +3i = 0 is 3.Find the other root. K $ϵ$ Z

Discussion

47.	Q45) India and United States (US) signed Inter Governmental Agreement (IGA) to implement the Foreign Account Tax Compliance Act (FATCA) 1) The agreement will promote transparency on tax matters between the two countries. 2) FATCA is an Indian Act to curb money laundering Which of the above statement(s) is/ are correct?
Answer» Q45) India and United States (US) signed Inter Governmental Agreement (IGA) to implement the Foreign Account Tax Compliance Act (FATCA) 1) The agreement will promote transparency on tax matters between the two countries. 2) FATCA is an Indian Act to curb money laundering Which of the above statement(s) is/ are correct?

47.

Q45) India and United States (US) signed Inter Governmental Agreement (IGA) to implement the Foreign Account Tax Compliance Act (FATCA) 1) The agreement will promote transparency on tax matters between the two countries. 2) FATCA is an Indian Act to curb money laundering Which of the above statement(s) is/ are correct?

Answer»

Q45) India and United States (US) signed Inter Governmental Agreement (IGA) to implement the Foreign Account Tax Compliance Act (FATCA)

1) The agreement will promote transparency on tax matters between the two countries.

2) FATCA is an Indian Act to curb money laundering

Which of the above statement(s) is/ are correct?

Discussion

48.	polynomial ax^3+3x^2-26 and 2x^3-5x+a,when divided by (x-4),leave remainder r1 and r2 respectively. find value of a, if r1 + r2 = 0.
Answer» polynomial ax^3+3x^2-26 and 2x^3-5x+a,when divided by (x-4),leave remainder r1 and r2 respectively. find value of a, if r1 + r2 = 0.

Discussion

49.	13. reflection of point (4,-13) about line 5x+y+6=0 ?
Answer» 13. reflection of point (4,-13) about line 5x+y+6=0 ?

Discussion

50.	Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length (5π3) cm
Answer» Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length $(\frac{5 π}{3}) c m$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

f(x) cannot be equal to 5(x5)(35)

If y2+16=2xy, then y′(5)=

From the following Venn diagram, A' is

Question 2Which of the following is not a quadratic equation?(a) 2(x−1)2=4x2−2x+1(b) 2x−x2=x2+5(c) (√2x+√3)2=3x2−5x(d) (x2+2x)2=x4+3+4x3

For what value of k, is 3 a zero of the polynomial 2x2 + x + k?

If sin^2A +sinA =1 , then cos^6A + cos^4A + cos^2A =

If AB, AC, PQ are tangents in the given figure and AB = 5 cm, find the perimeter of Δ APQ.

If p has n+1 and q has n fair coins then probability that p has more heads than q

Choose the correct answer in each of the following questions:The 7th term of an AP is −1 and its 16th term is 17. The nth term of the AP is [CBSE 2014](a) (3n + 8) (b) (4n − 7) (c) (15 − 2n) (d) (2n − 15)

A solid ball is exactly fitted inside the cuboidal box of side a. The volume of the ball is _________.

The mid-point P of the line segment joining the points A(−10, 4) and B(−2, 0) lies on the line segment joining the points C(−9, −4) and D(−4, y). Find the ratio in which P divides CD. Also, find the value of y. [CBSE 2014]

The altitude of a right triangle is 7 cm less than its base x and its hypotenuse is 13 cm. Identify the quadratic representation of the given statement.

In a partnership business, the capital that Arav invested is double the capital that Zoya had invested. The ratio of their period of investment is 12:13. The ratio of their profit is ______.

Product of two consecutive natural number is 56. Find the smaller number.

Define a polynomial with real coefficients.

There are two positive integers X &amp; Y. When X is divided by 237, the remainder is 192. When Y is divided by 117 the quotient is the same but the remainder is 108. Find the remainder when the sum of X &amp; Y is divided by 118.

If sin θ=2029, find cos θ.

The nth term of an A.P is given by (−4n + 15), Find the sum of first 20 terms of this A.P.

If two tangents PT and PS are drawn to a circle with centre O and radius 'r' from an external point P and OP=2r then ∠TOP is ____.

The area enclosed between the concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, find the radius of the inner circle.

If 0º &lt; θ &lt; 90º and 4secθ + 4cosecθ = 5secθcosecθ, then tanθ can be equal toयदि 0º &lt; θ &lt; 90º तथा 4secθ + 4cosecθ = 5secθcosecθ, तब tanθ बराबर हो सकता है

In the picture below, PQ, RS, TU are tangents to the circle at A, B, C.How many pairs of equal angles are there in it?

If angle between two radii of a circle is 1300 , the angle between the tangents at the ends of radii is (a) 900 (b) 500 (c) 700 (d) 400

The denominator of a fraction is greater than its numerator by 11.If 8 is added to both its numerator and denominator,it becomes 34.Find the fraction.

The distance of the point (–4, 7) from y-axis is _________.

What is n/2in the equation for sum to 'n' terms

The positive numbers x and y satisfy xy = 1. Then the value of x such thatis minimum.

53. Why is TSA,CSA and volume of frustum are R1+R2 not r1-r2

What is the probability of picking a red numbered card with number more than 6?

Examine each of the following relations given below and state in each case, giving reasons whether it is a function or not?(i) R={(2,1),(3,1),(4,2)}(ii) R={2,2),(2,4),(3,3),(4,4)}(iii) R={1,2),(2,3),(3,4),(4,5),(5,6),(6,7)}

The mean of first five natural numbers is(a) 5 (b) 4 (c) 3 (d) 6

Two brands of chocolates are available in packs of 24 and 15 respectively. If I need to buy an equal number of chocolates of both kinds, what is the least number of boxes of each kind I would need to buy?

Express the given pattern as a sequence.

Question 7 (v)Let A (4, 2), B (6, 5) and C (1, 4) be the vertices of triangle ABC.(e) If A(x1,y1),B(x2,y2) and C(x3,y3) are the vertices of triangle ABC, find the coordinates of the centroid of the triangle.

In the circle given, OP = 1 unit and ∠POQ = θ. Which side represents cos θ?

Question 8Any point on the line y = x is of the form:A) (a, a)B) (0, a)C) (a, 0)D) (a, -a)

Find the equation of the line in vector and in Cartesian form that passes through the point with position vector and is in the direction .

The number of integers n such that 1less than or equal to n less than or equal to 200 and nn is a perfect square is ?

Two spheres of same material are heated up to same temperature and then allowed to cool in same surrounding. If their radii are in the ratio of 4:7 then ratio of their initial rate of cooling is? 1) 2:7 2) 7:2 3) 4:7 4) 7:4

If 1x+2,1x+3,1x+5 are in A.P. Then, x =(a) 5(b) 3(c) 1(d) 2

In the following figure, shows a sector of a circle, centre O, containing an angle 0°. Prove that:(i) Perimeter of the shaded region is tan θ+secθ+πθ180-1(ii) Area of the shaded region is r22tanθ-πθ180​

Find the angle of elevation of the sun when the shadow of a 10m long pole is 10√3 m.

If one root of equation z2 - (11 + i)z + k +3i = 0 is 3.Find the other root. K ϵ Z

polynomial ax^3+3x^2-26 and 2x^3-5x+a,when divided by (x-4),leave remainder r1 and r2 respectively. find value of a, if r1 + r2 = 0.

13. reflection of point (4,-13) about line 5x+y+6=0 ?

Find the angle subtended at the centre of a circle of radius 5 cm by an arc of length (5π3) cm

There are two positive integers X & Y. When X is divided by 237, the remainder is 192. When Y is divided by 117 the quotient is the same but the remainder is 108. Find the remainder when the sum of X & Y is divided by 118.

If 0º < θ < 90º and 4secθ + 4cosecθ = 5secθcosecθ, then tanθ can be equal toयदि 0º < θ < 90º तथा 4secθ + 4cosecθ = 5secθcosecθ, तब tanθ बराबर हो सकता है

In the following figure, shows a sector of a circle, centre O, containing an angle 0°. Prove that:(i) Perimeter of the shaded region is tan θ+secθ+πθ180-1(ii) Area of the shaded region is r22tanθ-πθ180