32581 + Interview Questions in Mathematics

1.	What is the point of intersection of angle bisectors of a triangle called?
Answer» What is the point of intersection of angle bisectors of a triangle called?

Discussion

2.	PQ and RS are two chords of circles which intersects each other at right angle at T. If PT= 8cm, RT= (√41- 3) cm and TP = 2TQ then radius of the circle is (RT
Answer» PQ and RS are two chords of circles which intersects each other at right angle at T. If PT= 8cm, RT= (√41- 3) cm and TP = 2TQ then radius of the circle is (RT

Discussion

3.	If 0.4 of a number is equal to 0.06 of another number, the ratio of the number is:
Answer» If 0.4 of a number is equal to 0.06 of another number, the ratio of the number is:

Discussion

4.	If 5x - 3 ≤ 5 + 3x ≤ 4x + 2, solve for x and represent it on the number line x ∈ R
Answer» If 5x - 3 ≤ 5 + 3x ≤ 4x + 2, solve for x and represent it on the number line x ∈ R

Discussion

5.	What must be subtracted from the polynomial f(x) = x4 + 2x3 − 13x2 − 12x + 21 so that the resulting polynomial is exactly divisible by x2 − 4x + 3?
Answer» What must be subtracted from the polynomial f(x) = x⁴ + 2x³ − 13x² − 12x + 21 so that the resulting polynomial is exactly divisible by x² − 4x + 3?

Discussion

6.	Question 2 (i)Formulate the following problems as a pair of equations, and hence find their solutions:Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.
Answer» Question 2 (i) Formulate the following problems as a pair of equations, and hence find their solutions: Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Discussion

7.	Question 13Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.
Answer» Question 13 Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.

Discussion

8.	Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.
Answer» Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Discussion

9.	Which of the following are a pair of linear equations in two variables?
Answer» Which of the following are a pair of linear equations in two variables?

Discussion

10.	The number of terms in an A.P. whose first term is 10, last term is 50 and the sum of all terms is 300, is ___________.
Answer» The number of terms in an A.P. whose first term is 10, last term is 50 and the sum of all terms is 300, is ___________.

Discussion

11.	In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠ OTA = 30o . Then AT = ? (a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm
Answer» In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $∠$ OTA = $30^{o}$ . Then AT = ? (a) 4 cm (b) 2 cm (c) $2 \sqrt{3}$ cm (d) $4 \sqrt{3}$ cm

11.

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠ OTA = 30o . Then AT = ? (a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm

Answer»

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and $∠$ OTA = $30^{o}$ . Then AT = ?

(a) 4 cm (b) 2 cm

(c) $2 \sqrt{3}$ cm (d) $4 \sqrt{3}$ cm

Discussion

12.	The multiplication and division of two like quadratic surds is always a ___ number.
Answer» The multiplication and division of two like quadratic surds is always a ___ number.

Discussion

13.	In the following figure, DE\|\|OQ and DF\|\|OR, show that EF\|\|QR.
Answer» In the following figure, DE\|\|OQ and DF\|\|OR, show that EF\|\|QR.

Discussion

14.	If mth term of an AP is 1n and nth term is 1m then find the sum of its first mn terms. [CBSE 2017]
Answer» If mth term of an AP is $\frac{1}{n}$ and nth term is $\frac{1}{m}$ then find the sum of its first mn terms. [CBSE 2017]

Discussion

15.	A metallic right circular cone 20 cm high and those vertical angle is 60^° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16cm, find the length of the wire
Answer» A metallic right circular cone 20 cm high and those vertical angle is 60^° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16cm, find the length of the wire

Discussion

16.	In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.
Answer» In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

Discussion

17.	To draw a pair of tangents to a circle which are inclined to each other at an angle of 45∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be
Answer» To draw a pair of tangents to a circle which are inclined to each other at an angle of $45^{\circ}$ , it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

Discussion

18.	The locus of a point, equidistant from two given points, is the __ of the line segment joining the two points.
Answer» The locus of a point, equidistant from two given points, is the __ of the line segment joining the two points.

Discussion

19.	Prove the following trignometric identities: √1−cos θ1+cos θ=cosec θ−cot θ
Answer» Prove the following trignometric identities: $\sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = c o s e c θ - c o t θ$

19.

Prove the following trignometric identities: √1−cos θ1+cos θ=cosec θ−cot θ

Answer»

Prove the following trignometric identities:

$\sqrt{\frac{1 - c o s θ}{1 + c o s θ}} = c o s e c θ - c o t θ$

Discussion

20.	If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.
Answer» If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.

Discussion

21.	If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be(a) 0(b) p − q(c) p + q(d) −(p + q)
Answer» If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be (a) 0 (b) p − q (c) p + q (d) −(p + q)

Discussion

22.	The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.
Answer» The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.

Discussion

23.	Question 75 What is the product of 5129 and its reciprocal?
Answer» Question 75 What is the product of $\frac{5}{129}$ and its reciprocal?

23.

Question 75 What is the product of 5129 and its reciprocal?

Answer»

Question 75

What is the product of $\frac{5}{129}$ and its reciprocal?

Discussion

24.	If the distance between the points A (4, p) and B(1, 0) is 5 then (a) p = 4 only (b) p = -4 only (c) p = ±4 (d) p = 0
Answer» If the distance between the points A (4, p) and B(1, 0) is 5 then (a) p = 4 only (b) p = -4 only (c) p = $\pm$ 4 (d) p = 0

24.

If the distance between the points A (4, p) and B(1, 0) is 5 then (a) p = 4 only (b) p = -4 only (c) p = ±4 (d) p = 0

Answer»

If the distance between the points A (4, p) and B(1, 0) is 5 then

(a) p = 4 only (b) p = -4 only (c) p = $\pm$ 4 (d) p = 0

Discussion

25.	If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.
Answer» If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.

Discussion

26.	The difference between the circumference and radius of a circle is 37 cm. Using π=227, find the circumference of the circle.
Answer» The difference between the circumference and radius of a circle is 37 cm. Using $π = \frac{22}{7}$ , find the circumference of the circle.

Discussion

27.	Which of the following is not a complementary event?
Answer» Which of the following is not a complementary event?

Discussion

28.

If the mean of the following distribution is 2.6, then the value of y is Variable (x): 1 2 3 4 5 Frequency 4 5 y 1 2 (a) 3(b) 8(c) 13(d) 24

Answer» If the mean of the following distribution is 2.6, then the value of y is

Variable (x):	1	2	3	4	5
Frequency	4	5	y	1	2

(a) 3

(b) 8

(c) 13

(d) 24

Discussion

29.	If sin A=941, compute cos A and tan A.
Answer» If $\sin A = \frac{9}{41}$ , compute cos A and tan A.

Discussion

30.	Question 2 (ii)Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
Answer» Question 2 (ii) Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method: Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Discussion

31.	On plotting the points O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC and CO which of the following figure is formed?(a) Square(b) Rectangle(c) Trapezium(d) Rhombus
Answer» On plotting the points O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC and CO which of the following figure is formed? (a) Square (b) Rectangle (c) Trapezium (d) Rhombus

Discussion

32.	There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.
Answer» There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

Discussion

33.	Question 5 (i) The following table gives the life times of neon lamps: Length (in hours)Number of lamps300−40014400−50056500−60060600−70086700−80074800−90062900−100048 (i) Represent the given information with the help of a histogram.
Answer» Question 5 (i) The following table gives the life times of neon lamps: $\begin{matrix} Length (in hours) & Number of lamps 300 - 400 & 14 400 - 500 & 56 500 - 600 & 60 600 - 700 & 86 700 - 800 & 74 800 - 900 & 62 900 - 1000 & 48 \end{matrix}$ (i) Represent the given information with the help of a histogram.

Discussion

34.	If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?
Answer» If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?

Discussion

35.	What is the slope of the line passing through the points (0, –4) and ( –6, 2)?-1
Answer» What is the slope of the line passing through the points (0, –4) and ( –6, 2)? -1

Discussion

36.	Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)
Answer» Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Discussion

37.	a wire of resis†an ce 20ohm is bent to form a complete c8rcle the resis†an ce between two diametrically opposite points a and b as shown in the figure,is
Answer» a wire of resis†an ce 20ohm is bent to form a complete c8rcle the resis†an ce between two diametrically opposite points a and b as shown in the figure,is

Discussion

38.	If one card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, then the probability of a diamond card is
Answer» If one card is drawn from a well shuffled deck of $52$ cards. If each outcome is equally likely, then the probability of a diamond card is

Discussion

39.	I have doubt with question no 2 from ex 3.1 . In this question the equation 3x+6y=3900, x+3y=1300 if I divide first equation by 3 I get x+2y=1300. So how it possible that x+3y=1300 and x+2y=1300 both rhs is same but not LHS. Please explain this question
Answer» I have doubt with question no 2 from ex 3.1 . In this question the equation 3x+6y=3900, x+3y=1300 if I divide first equation by 3 I get x+2y=1300. So how it possible that x+3y=1300 and x+2y=1300 both rhs is same but not LHS. Please explain this question

Discussion

40.	If A and B are two events such that P(A/B) = p, P(A) = p, PB=13 and PA∪B=59, then p = _____________.
Answer» If A and B are two events such that P(A/B) = p, P(A) = p, $P (B) = \frac{1}{3} and P (A \cup B) = \frac{5}{9},$ then p = _____________.

Discussion

41.	The cost price of 12 pens is equal to selling price of 10 pens. Find the profit percentage.
Answer» The cost price of 12 pens is equal to selling price of 10 pens. Find the profit percentage.

Discussion

42.	In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD ∥ CF. [2 MARKS]
Answer» In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD $∥$ CF. [2 MARKS]

42.

In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD ∥ CF. [2 MARKS]

Answer»

In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD $∥$ CF. [2 MARKS]

Discussion

43.	The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.
Answer» The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.

Discussion

44.	Column AColumn B(a) sin(90−A)(i) cos A(b) tan(90−A) (ii) cosec A(c) sec(90−A)(iii) cot A
Answer» $\begin{matrix} C o l u m n A & C o l u m n B (a) s i n (90 - A) & (i) c o s A (b) t a n (90 - A) & (i i) c o s e c A (c) s e c (90 - A) & (i i i) c o t A \end{matrix}$

Discussion

45.	In an isosceles ∆ABC, the base AB is produced both the ways to P and Q such that AP ✕ BQ = AC2. Prove that ∆APC ∼ ∆BCQ.
Answer» In an isosceles ∆ABC, the base AB is produced both the ways to P and Q such that AP ✕ BQ = AC². Prove that ∆APC ∼ ∆BCQ.

Discussion

46.	Solve, using cross-multiplication 5x+4y+14=0 3x=−10−4y
Answer» Solve, using cross-multiplication $5 x + 4 y + 14 = 0$ $3 x = - 10 - 4 y$

46.

Solve, using cross-multiplication 5x+4y+14=0 3x=−10−4y

Answer»

Solve, using cross-multiplication

$5 x + 4 y + 14 = 0$
$3 x = - 10 - 4 y$

Discussion

47.	If one root of the quadratic equation having rational coefficients is a+√b, then find the other.
Answer» If one root of the quadratic equation having rational coefficients is a+√b, then find the other.

Discussion

48.	For what value k , do the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 reperesent coincident lines ?(a) 12 (b) -12 (c) 2 (d) - 2
Answer» For what value k , do the equations $3 x - y + 8 = 0$ and $6 x - k y + 16 = 0$ reperesent coincident lines ? (a) $\frac{1}{2}$ (b) $- \frac{1}{2}$ (c) 2 (d) $- 2$

Discussion

49.	Find the median of the following cumulative frequency distribution:xfrequencyCumulative frequency221134233925458135482156930684347843884240
Answer» Find the median of the following cumulative frequency distribution: $\begin{matrix} x & f r e q u e n c y & C u m u l a t i v e f r e q u e n c y 22 & 1 & 1 34 & 2 & 3 39 & 2 & 5 45 & 8 & 13 54 & 8 & 21 56 & 9 & 30 68 & 4 & 34 78 & 4 & 38 84 & 2 & 40 \end{matrix}$

Discussion

50.	Standing on the side of a railway track a man found that two trains of same length crossed him in opposite directions in 18sec and 12 sec respectively . What time will the trains take to cross each other ?
Answer» Standing on the side of a railway track a man found that two trains of same length crossed him in opposite directions in 18sec and 12 sec respectively . What time will the trains take to cross each other ?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

What is the point of intersection of angle bisectors of a triangle called?

PQ and RS are two chords of circles which intersects each other at right angle at T. If PT= 8cm, RT= (√41- 3) cm and TP = 2TQ then radius of the circle is (RT

If 0.4 of a number is equal to 0.06 of another number, the ratio of the number is:

If 5x - 3 ≤ 5 + 3x ≤ 4x + 2, solve for x and represent it on the number line x ∈ R

What must be subtracted from the polynomial f(x) = x4 + 2x3 − 13x2 − 12x + 21 so that the resulting polynomial is exactly divisible by x2 − 4x + 3?

Question 2 (i)Formulate the following problems as a pair of equations, and hence find their solutions:Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

Question 13Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the center of the circle.

Metallic spheres of radii 6 cm, 8 cm and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Which of the following are a pair of linear equations in two variables?

The number of terms in an A.P. whose first term is 10, last term is 50 and the sum of all terms is 300, is ___________.

In the given figure, AT is a tangent to the circle with centre O such that OT = 4 cm and ∠ OTA = 30o . Then AT = ? (a) 4 cm (b) 2 cm (c) 2√3 cm (d) 4√3 cm

The multiplication and division of two like quadratic surds is always a ___ number.

In the following figure, DE||OQ and DF||OR, show that EF||QR.

If mth term of an AP is 1n and nth term is 1m then find the sum of its first mn terms. [CBSE 2017]

A metallic right circular cone 20 cm high and those vertical angle is 60^° is cut into two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained be drawn into a wire of diameter 1/16cm, find the length of the wire

In the given figure, PA and PB are tangents to the circle from an external point P. CD is another tangent touching the circle at Q. If PA = 12 cm, QC = QD = 3 cm, then find PC + PD.

To draw a pair of tangents to a circle which are inclined to each other at an angle of 45∘, it is required to draw tangents at end points of those two radii of the circle, the angle between them should be

The locus of a point, equidistant from two given points, is the __ of the line segment joining the two points.

Prove the following trignometric identities: √1−cos θ1+cos θ=cosec θ−cot θ

If the mid-point of the line joining (3, 4) and (k, 7) is (x, y) and 2x + 2y + 1 = 0 find the value of k.

If the sum of P terms of an A.P. is q and the sum of q terms is p, then the sum of p + q terms will be(a) 0(b) p − q(c) p + q(d) −(p + q)

The slant height of the frustum of a cone is 4 cm and the circumferences of its circular ends are 18 cm and 6 cm. Find curved surface area of the frustum.

Question 75 What is the product of 5129 and its reciprocal?

If the distance between the points A (4, p) and B(1, 0) is 5 then (a) p = 4 only (b) p = -4 only (c) p = ±4 (d) p = 0

If both 'x' and 'y' are natural numbers, the equation 2x + 5y = 7 will have a unique solution.

The difference between the circumference and radius of a circle is 37 cm. Using π=227, find the circumference of the circle.

Which of the following is not a complementary event?

If the mean of the following distribution is 2.6, then the value of y is Variable (x): 1 2 3 4 5 Frequency 4 5 y 1 2 (a) 3(b) 8(c) 13(d) 24

If sin A=941, compute cos A and tan A.

Question 2 (ii)Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

On plotting the points O(0, 0), A(3, 0), B(3, 4), C(0, 4) and joining OA, AB, BC and CO which of the following figure is formed?(a) Square(b) Rectangle(c) Trapezium(d) Rhombus

There are 5 green, 6 black and 7 white balls in a bag. A ball is drawn at random from the bag. Find the probability that it is not white.

Question 5 (i) The following table gives the life times of neon lamps: Length (in hours)Number of lamps300−40014400−50056500−60060600−70086700−80074800−90062900−100048 (i) Represent the given information with the help of a histogram.

If the altitude of two similar triangles are in the ratio 2 : 3, what is the ratio of their areas?

What is the slope of the line passing through the points (0, –4) and ( –6, 2)?-1

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

a wire of resis†an ce 20ohm is bent to form a complete c8rcle the resis†an ce between two diametrically opposite points a and b as shown in the figure,is

If one card is drawn from a well shuffled deck of 52 cards. If each outcome is equally likely, then the probability of a diamond card is

I have doubt with question no 2 from ex 3.1 . In this question the equation 3x+6y=3900, x+3y=1300 if I divide first equation by 3 I get x+2y=1300. So how it possible that x+3y=1300 and x+2y=1300 both rhs is same but not LHS. Please explain this question

If A and B are two events such that P(A/B) = p, P(A) = p, PB=13 and PA∪B=59, then p = _____________.

The cost price of 12 pens is equal to selling price of 10 pens. Find the profit percentage.

In figure A, B, C, and D, E, F are two sets of collinear points, Prove that AD ∥ CF. [2 MARKS]

The value of p for which the points (–1, 3), (2, p), (5, –1) are collinear is ____.

Column AColumn B(a) sin(90−A)(i) cos A(b) tan(90−A) (ii) cosec A(c) sec(90−A)(iii) cot A

In an isosceles ∆ABC, the base AB is produced both the ways to P and Q such that AP ✕ BQ = AC2. Prove that ∆APC ∼ ∆BCQ.

Solve, using cross-multiplication 5x+4y+14=0 3x=−10−4y

If one root of the quadratic equation having rational coefficients is a+√b, then find the other.

For what value k , do the equations 3x - y + 8 = 0 and 6x - ky + 16 = 0 reperesent coincident lines ?(a) 12 (b) -12 (c) 2 (d) - 2

Find the median of the following cumulative frequency distribution:xfrequencyCumulative frequency221134233925458135482156930684347843884240

Standing on the side of a railway track a man found that two trains of same length crossed him in opposite directions in 18sec and 12 sec respectively . What time will the trains take to cross each other ?