24740 + Interview Questions in Mathematics

1.	If x < 3 & y > 7, then the value \|x−y\| is greater than:
Answer» If x < 3 & y > 7, then the value $\| x - y \|$ is greater than:

Discussion

2.	Find 4 rational number between 1/5 and 1/6
Answer» Find 4 rational number between 1/5 and 1/6

Discussion

3.	Surface area of a sphere is changing at the rate of 16pi cm^2/sec. When the radius is 4cm. Find the rate at which radius is changing.
Answer» Surface area of a sphere is changing at the rate of 16pi cm^2/sec. When the radius is 4cm. Find the rate at which radius is changing.

Discussion

4.	The relation between the number of books read (y) and the number of days(x) is given by y = 2x. Which of the following table of data is plotted in the given graph?
Answer» The relation between the number of books read (y) and the number of days(x) is given by y = 2x. Which of the following table of data is plotted in the given graph?

Discussion

5.	If (4x-3) and (2x+3) are the factors of f(x)= 16x³-ax²-36x+b the value of a and b are?
Answer» If (4x-3) and (2x+3) are the factors of f(x)= 16x³-ax²-36x+b the value of a and b are?

Discussion

6.	A point whose abscissa and ordinate are 2 and −5 respectively, lies in(a) First quadrant(b) Second quadrant(c) Third quadrant(d) Fourth quadrant
Answer» A point whose abscissa and ordinate are 2 and −5 respectively, lies in (a) First quadrant (b) Second quadrant (c) Third quadrant (d) Fourth quadrant

Discussion

7.	In how many years will Rs. 7,000 amount to Rs. 9,317 at 10 per cent per annum compound interest ?
Answer» In how many years will Rs. 7,000 amount to Rs. 9,317 at 10 per cent per annum compound interest ?

Discussion

8.	An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel in cm2.781.86
Answer» An oil funnel made of tin sheet consists of a 10 cm long cylindrical portion attached to a frustum of a cone. If the total height is 22 cm, the diameter of the cylindrical portion is 8 cm and diameter of the top of the funnel is 18 cm, find the area of the tin sheet required to make the funnel in $c m^{2}$ . 781.86

Discussion

9.	If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height( π=3.14)
Answer» If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height ( $π = 3.14$ )

Discussion

10.	The distribution of the heights of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table:Height110115x1120121125Number of students6814f143
Answer» The distribution of the heights of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table: $\begin{matrix} H e i g h t & 110 & 115 & x_{1} & 120 & 121 & 125 N u m b e r o f s t u d e n t s & 6 & 8 & 14 & f_{1} & 4 & 3 \end{matrix}$

Discussion

11.	In figure AB \|\| CD. Find the value of x.
Answer» In figure AB \|\| CD. Find the value of x.

Discussion

12.	In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]
Answer» In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]

12.

In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]

Answer»

In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]

Discussion

13.	Prove the following trigonometric identities.(i) sec θ-1sec θ+1+sec θ+1sec θ-1=2 cosec θ(ii) 1+sin θ1-sin θ+1-sin θ1+sin θ=2 sec θ(iii) 1+cos θ1-cos θ+1-cos θ1+cos θ=2 cosec θ(iv) sec θ-1sec θ+1=sin θ1+cos θ2(v) sinθ+1-cosθcosθ-1+sinθ=1+sinθcosθ
Answer» Prove the following trigonometric identities. (i) $\sqrt{\frac{\sec θ - 1}{\sec θ + 1}} + \sqrt{\frac{\sec θ + 1}{\sec θ - 1}} = 2 cosec θ$ (ii) $\sqrt{\frac{1 + \sin θ}{1 - \sin θ}} + \sqrt{\frac{1 - \sin θ}{1 + \sin θ}} = 2 \sec θ$ (iii) $\sqrt{\frac{1 + \cos θ}{1 - \cos θ}} + \sqrt{\frac{1 - \cos θ}{1 + \cos θ}} = 2 cosec θ$ (iv) $\frac{\sec θ - 1}{\sec θ + 1} = {(\frac{\sin θ}{1 + \cos θ})}^{2}$ (v) $\frac{\sin θ + 1 - \cos θ}{\cos θ - 1 + \sin θ} = \frac{1 + \sin θ}{\cos θ}$

Discussion

14.	Simplify(i) 3-11 3+11(ii) -3+5 -3-5(iii) 3-32(iv) 5-32(v) 5+7 2+5(vi) 5-2 2-3
Answer» Simplify (i) $(3 - \sqrt{11}) (3 + \sqrt{11})$ (ii) $(- 3 + \sqrt{5}) (- 3 - \sqrt{5})$ (iii) ${(3 - \sqrt{3})}^{2}$ (iv) ${(\sqrt{5} - \sqrt{3})}^{2}$ (v) $(5 + \sqrt{7}) (2 + \sqrt{5})$ (vi) $(\sqrt{5} - \sqrt{2}) (\sqrt{2} - \sqrt{3})$

Discussion

15.	The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?
Answer» The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?

Discussion

16.	Write the equation representing x-axis.
Answer» Write the equation representing x-axis.

Discussion

17.	The circle x2+y2+4x−4y+4=0 touches
Answer» The circle $x^{2} + y^{2} + 4 x - 4 y + 4 = 0$ touches

Discussion

18.	A dice is thrown once. Find the probability of getting a number less than 3.
Answer» A dice is thrown once. Find the probability of getting a number less than 3.

Discussion

19.	log2(2) is equal to _______ . ___
Answer» $l o g_{2} (2)$ is equal to _______ . ___

Discussion

20.	Factorise64125a3-9625a2+485a-8
Answer» Factorise $\frac{64}{125} a^{3} - \frac{96}{25} a^{2} + \frac{48}{5} a - 8$

Discussion

21.	Two positive integers a and b can be written as a=m2n2 and b=mn2, where m and n are prime numbers. Find the LCM(a, b).
Answer» Two positive integers a and b can be written as $a = m^{2} n^{2}$ and $b = m n^{2}$ , where m and n are prime numbers. Find the LCM(a, b).

Discussion

22.	Which of the following is a polynomial in 1 variable?
Answer» Which of the following is a polynomial in 1 variable?

Discussion

23.

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below: Number of balls Team A Team B 1 − 6 7 − 12 13 − 18 19 − 24 25 − 30 31 − 36 37 − 42 43 − 48 49 − 54 55 − 60 2 1 8 9 4 5 6 10 6 2 5 6 2 10 5 6 3 4 8 10 Represent the data of both the teams on the same graph by frequency polygons.[Hint: First make the class intervals continuous.]

Answer»

The runs scored by two teams A and B on the first 60 balls in a cricket match are given below:

Number of balls

Team A

Team B

1 − 6

7 − 12

13 − 18

19 − 24

25 − 30

31 − 36

37 − 42

43 − 48

49 − 54

55 − 60

2

1

8

9

4

5

6

10

6

2

5

6

2

10

5

6

3

4

8

10

Represent the data of both the teams on the same graph by frequency polygons.

[Hint: First make the class intervals continuous.]

Discussion

24.	In the figures below, find the value of 'x'.
Answer» In the figures below, find the value of 'x'.

Discussion

25.	32. If (5+6+7)(-5+6+7)(5-6+7)(5+6-7)=13K. THEN FIND VALUE OF K
Answer» 32. If (5+6+7)(-5+6+7)(5-6+7)(5+6-7)=13K. THEN FIND VALUE OF K

Discussion

26.	Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) −x+4y=12 (ii) x−y4−5=0 (iii) 2x+3y=9.35
Answer» Express the following linear equations in the form $a x + b y + c = 0$ and indicate the values of a, b and c in each case: (i) $- x + 4 y = 12$ (ii) $x - \frac{y}{4} - 5 = 0$ (iii) $2 x + 3 y = 9.35$

26.

Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) −x+4y=12 (ii) x−y4−5=0 (iii) 2x+3y=9.35

Answer»

Express the following linear equations in the form $a x + b y + c = 0$ and indicate the values of a, b and c in each case:

(i) $- x + 4 y = 12$ (ii) $x - \frac{y}{4} - 5 = 0$ (iii) $2 x + 3 y = 9.35$

Discussion

27.	Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is___
Answer» Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is ___

27.

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is___

Answer»

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is

___

Discussion

28.	Question 2 In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.
Answer» Question 2 In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Discussion

29.	Which of the following are polynomials?
Answer» Which of the following are polynomials?

Discussion

30.	Using thales's theorem prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.
Answer» Using thales's theorem prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Discussion

31.	Question 5If a line segment joining midpoints of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.
Answer» Question 5 If a line segment joining midpoints of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Discussion

32.	Given position vectors ¯a,¯b,¯c of points A, B, C for a triangle. The centroid can be given by
Answer» Given position vectors $¯ a, ¯ b, ¯ c$ of points A, B, C for a triangle. The centroid can be given by

Discussion

33.	Question 3 The value of the expression cosec(75∘+θ)−sec(15∘−θ)−tan(55∘+θ)+cot(35∘−θ) is (A) -1 (B) 0 (C) 1 (D) 32
Answer» Question 3 The value of the expression $c o s e c (75^{\circ} + θ) - s e c (15^{\circ} - θ) - t a n (55^{\circ} + θ) + c o t (35^{\circ} - θ)$ is (A) -1 (B) 0 (C) 1 (D) $\frac{3}{2}$

Discussion

34.	Fill in the blanks:90108 reduced to simplest form .....
Answer» Fill in the blanks: $\frac{90}{108}$ reduced to simplest form .....

Discussion

35.	If x=1x−4 , find x−1x
Answer» If $x = \frac{1}{x - 4}$ , find $x - \frac{1}{x}$

Discussion

36.	Which of the following cannot be the probability of an event?(a) 13(b) 35(c) 53(d) 1
Answer» Which of the following cannot be the probability of an event? (a) $\frac{1}{3}$ (b) $\frac{3}{5}$ (c) $\frac{5}{3}$ (d) 1

Discussion

37.	An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOC is(a) 30°(b) 60°(c) 90°(d) 120°
Answer» An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOC is (a) 30° (b) 60° (c) 90° (d) 120°

Discussion

38.	Consider the above Venn-diagram. The set {2,9,10} represents ___.
Answer» Consider the above Venn-diagram. The set ${2, 9, 10}$ represents ___.

38.

Consider the above Venn-diagram. The set {2,9,10} represents ___.

Answer»

Consider the above Venn-diagram. The set ${2, 9, 10}$ represents ___.

Discussion

39.	If pq is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as:(Here, n and m are non-negative integers.)
Answer» If $\frac{p}{q}$ is a rational number with terminating decimal expansion where $p$ and $q$ are coprimes, then $q$ can be represented as: (Here, n and m are non-negative integers.)

Discussion

40.	The consecutive sides of a quadrilateral have(a) no common point(b) one common point(c) two common points(d) infinitely many common points
Answer» The consecutive sides of a quadrilateral have (a) no common point (b) one common point (c) two common points (d) infinitely many common points

Discussion

41.	Jane travelled 47 as many miles on foot as by water and 25 as many miles on horseback as by water. If she covered a total of 3036 miles, how many miles did she travel on foot?
Answer» Jane travelled $\frac{4}{7}$ as many miles on foot as by water and $\frac{2}{5}$ as many miles on horseback as by water. If she covered a total of $3036$ miles, how many miles did she travel on foot?

Discussion

42.	x2+y+z33 + x3-2y3+z3 + -5x6-y34z33
Answer» ${(\frac{x}{2} + y + \frac{z}{3})}^{3} + {(\frac{x}{3} - \frac{2 y}{3} + z)}^{3} + {(- \frac{5 x}{6} - \frac{y}{3} \frac{4 z}{3})}^{3}$

Discussion

43.	Which of the following graph shows the equation y - x = 4?
Answer» Which of the following graph shows the equation y - x = 4?

Discussion

44.	In the diagram above, if CD and PQ are not parallel, then, ∠1= and ∠6=.
Answer» In the diagram above, if $CD$ and $PQ$ are not parallel, then, $∠ 1 =$ and $∠ 6 =$ .

Discussion

45.	Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, then AC = _________ and BD = __________.
Answer» Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, then AC = _________ and BD = __________.

Discussion

46.	The line represented by the equation x = a is perpendicular to ____.
Answer» The line represented by the equation x = a is perpendicular to ____.

Discussion

47.	15 Prove that all angles of equilateral triangle is 60
Answer» 15 Prove that all angles of equilateral triangle is 60

Discussion

48.	If sin theta + cos theta is equal to root 3 then prove that tan theta + cot theta is equal to 1
Answer» If sin theta + cos theta is equal to root 3 then prove that tan theta + cot theta is equal to 1

Discussion

49.	Question 4The range of the data 30, 61, 55, 56, 20, 26, 46, 28, 56 is(a) 26(b) 30(c) 41(d) 61
Answer» Question 4 The range of the data 30, 61, 55, 56, 20, 26, 46, 28, 56 is (a) 26 (b) 30 (c) 41 (d) 61

49.

Question 4The range of the data 30, 61, 55, 56, 20, 26, 46, 28, 56 is(a) 26(b) 30(c) 41(d) 61

Answer»

Question 4

The range of the data 30, 61, 55, 56, 20, 26, 46, 28, 56 is

(a) 26

(b) 30

(c) 41

(d) 61

Discussion

50.	If the volume and the surface area of a sphere is numerically equal , then find its radius
Answer» If the volume and the surface area of a sphere is numerically equal , then find its radius

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If x < 3 & y > 7, then the value |x−y| is greater than:

Find 4 rational number between 1/5 and 1/6

Surface area of a sphere is changing at the rate of 16pi cm^2/sec. When the radius is 4cm. Find the rate at which radius is changing.

The relation between the number of books read (y) and the number of days(x) is given by y = 2x. Which of the following table of data is plotted in the given graph?

If (4x-3) and (2x+3) are the factors of f(x)= 16x³-ax²-36x+b the value of a and b are?

A point whose abscissa and ordinate are 2 and −5 respectively, lies in(a) First quadrant(b) Second quadrant(c) Third quadrant(d) Fourth quadrant

In how many years will Rs. 7,000 amount to Rs. 9,317 at 10 per cent per annum compound interest ?

If the ratio of radius of base and height of a cone is 5:12 and its volume is 314 cubic metre. Find its perpendicular height and slant height( π=3.14)

The distribution of the heights of 50 children are given. If the mean height for the distribution is 117.8 cm, then complete the following table:Height110115x1120121125Number of students6814f143

In figure AB || CD. Find the value of x.

In a circular table cover of radius 12 cm, a design is formed leaving an equilateral triangle ABC in the middle as shown in figure. Find the area of the design. [4 MARKS]

Prove the following trigonometric identities.(i) sec θ-1sec θ+1+sec θ+1sec θ-1=2 cosec θ(ii) 1+sin θ1-sin θ+1-sin θ1+sin θ=2 sec θ(iii) 1+cos θ1-cos θ+1-cos θ1+cos θ=2 cosec θ(iv) sec θ-1sec θ+1=sin θ1+cos θ2(v) sinθ+1-cosθcosθ-1+sinθ=1+sinθcosθ

Simplify(i) 3-11 3+11(ii) -3+5 -3-5(iii) 3-32(iv) 5-32(v) 5+7 2+5(vi) 5-2 2-3

The mid points of an equilateral triangle of side 10 cm are joined to form a triangle. What type of triangle is obtained by joining the mid points?

Write the equation representing x-axis.

The circle x2+y2+4x−4y+4=0 touches

A dice is thrown once. Find the probability of getting a number less than 3.

log2(2) is equal to _______ . ___

Factorise64125a3-9625a2+485a-8

Two positive integers a and b can be written as a=m2n2 and b=mn2, where m and n are prime numbers. Find the LCM(a, b).

Which of the following is a polynomial in 1 variable?

In the figures below, find the value of 'x'.

32. If (5+6+7)(-5+6+7)(5-6+7)(5+6-7)=13K. THEN FIND VALUE OF K

Express the following linear equations in the form ax+by+c=0 and indicate the values of a, b and c in each case:(i) −x+4y=12 (ii) x−y4−5=0 (iii) 2x+3y=9.35

Points P and Q are two points in the coordinate plane. The x-coordinate of the point equidistant from the points P and Q and lying on the line y = -1 is___

Question 2 In a triangle locate a point in its interior which is equidistant from all the sides of the triangle.

Which of the following are polynomials?

Using thales's theorem prove that the line joining the mid-points of any two sides of a triangle is parallel to the third side.

Question 5If a line segment joining midpoints of two chords of a circle passes through the centre of the circle, prove that the two chords are parallel.

Given position vectors ¯a,¯b,¯c of points A, B, C for a triangle. The centroid can be given by

Question 3 The value of the expression cosec(75∘+θ)−sec(15∘−θ)−tan(55∘+θ)+cot(35∘−θ) is (A) -1 (B) 0 (C) 1 (D) 32

Fill in the blanks:90108 reduced to simplest form .....

If x=1x−4 , find x−1x

Which of the following cannot be the probability of an event?(a) 13(b) 35(c) 53(d) 1

An equilateral triangle ABC is inscribed in a circle with centre O. The measures of ∠BOC is(a) 30°(b) 60°(c) 90°(d) 120°

Consider the above Venn-diagram. The set {2,9,10} represents ___.

If pq is a rational number with terminating decimal expansion where p and q are coprimes, then q can be represented as:(Here, n and m are non-negative integers.)

The consecutive sides of a quadrilateral have(a) no common point(b) one common point(c) two common points(d) infinitely many common points

Jane travelled 47 as many miles on foot as by water and 25 as many miles on horseback as by water. If she covered a total of 3036 miles, how many miles did she travel on foot?

x2+y+z33 + x3-2y3+z3 + -5x6-y34z33

Which of the following graph shows the equation y - x = 4?

In the diagram above, if CD and PQ are not parallel, then, ∠1= and ∠6=.

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, then AC = _________ and BD = __________.

The line represented by the equation x = a is perpendicular to ____.

15 Prove that all angles of equilateral triangle is 60

If sin theta + cos theta is equal to root 3 then prove that tan theta + cot theta is equal to 1

Question 4The range of the data 30, 61, 55, 56, 20, 26, 46, 28, 56 is(a) 26(b) 30(c) 41(d) 61

If the volume and the surface area of a sphere is numerically equal , then find its radius

log2(2) is equal to _____ . _

Diagonals AC and BD of a parallelogram ABCD intersect each other at O. If OA = 3 cm and OD = 2 cm, then AC = _ and BD = __.