24740 + Interview Questions in Mathematics

1.	If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find : (i) radius of its base (ii) volume of the cylinder [Use π = 3.14]
Answer» If the lateral surface of a cylinder is 94.2 $c m^{2}$ and its height is 5 cm, find : (i) radius of its base (ii) volume of the cylinder [Use $π$ = 3.14]

1.

If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find : (i) radius of its base (ii) volume of the cylinder [Use π = 3.14]

Answer»

If the lateral surface of a cylinder is 94.2 $c m^{2}$ and its height is 5 cm, find :

(i) radius of its base

(ii) volume of the cylinder [Use $π$ = 3.14]

Discussion

2.	Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.
Answer» Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.

2.

Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.

Answer»

Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.

Discussion

3.	Give two rational numbers lying between 0.515115111511115...0.5353353335...
Answer» Give two rational numbers lying between 0.515115111511115...0.5353353335...

Discussion

4.	How to construct a triangle when all three sides are given?
Answer» How to construct a triangle when all three sides are given?

Discussion

5.	∆ ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on same side of BC . If AD is extended to intersect BC at P show that AP is the perpendicular bisector of BC
Answer» ∆ ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on same side of BC . If AD is extended to intersect BC at P show that AP is the perpendicular bisector of BC

Discussion

6.	In the figure, the value of x that will make AOB, a straight line is
Answer» In the figure, the value of x that will make AOB, a straight line is

6.

In the figure, the value of x that will make AOB, a straight line is

Answer»

In the figure, the value of x that will make AOB, a straight line is

Discussion

7.	Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.
Answer» Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

Discussion

8.	Factrorise 25x2+4y2+9z2−20xy−12yz+30xz
Answer» Factrorise $25 x^{2} + 4 y^{2} + 9 z^{2} - 20 x y - 12 y z + 30 x z$

Discussion

9.	A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape be 7 cm.
Answer» A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape be 7 cm.

Discussion

10.	If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral
Answer» If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral

Discussion

11.	Simplify: (−2)3×(−10)3
Answer» Simplify: $(- 2)^{3} \times (- 10)^{3}$

Discussion

12.	If (x+a)(x+b)=x2+5x+6,what is the value of (a−b) if (a−b)>0?
Answer» $If (x + a) (x + b) = x^{2} + 5 x + 6, what is the value of (a - b) if (a - b) > 0 ?$

Discussion

13.	In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division. f(x) = x3+4x2−3x+10, g(x) = x + 4
Answer» In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division. f(x) = $x^{3} + 4 x^{2} - 3 x + 10$ , g(x) = x + 4

13.

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division. f(x) = x3+4x2−3x+10, g(x) = x + 4

Answer»

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division.

f(x) = $x^{3} + 4 x^{2} - 3 x + 10$ , g(x) = x + 4

Discussion

14.	The distance of the point (p, q, r) from x axis is _______________________.
Answer» The distance of the point (p, q, r) from x axis is _______________________.

Discussion

15.	How many circles can be drawn passing through two points?
Answer» How many circles can be drawn passing through two points?

Discussion

16.	A juiceseller has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses of radius 3 cm up to a height of 8 cm, and sold for ₹ 15 each. How much money does he received by selling the juice completely?
Answer» A juiceseller has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses of radius 3 cm up to a height of 8 cm, and sold for ₹ 15 each. How much money does he received by selling the juice completely?

Discussion

17.	The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x ? (a) x22π (b) x2√π (c) √2xx (d) π2x
Answer» The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x ? (a) $\frac{x^{2}}{2 π}$ (b) $\frac{x}{2 \sqrt{π}}$ (c) $\frac{\sqrt{2 x}}{x}$ (d) $\frac{π}{2 x}$

17.

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x ? (a) x22π (b) x2√π (c) √2xx (d) π2x

Answer»

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x ?

(a) $\frac{x^{2}}{2 π}$ (b) $\frac{x}{2 \sqrt{π}}$

(c) $\frac{\sqrt{2 x}}{x}$ (d) $\frac{π}{2 x}$

Discussion

18.	Question 1 An isosceles right triangle has area 8cm2. The length of its hypotenuse is
Answer» Question 1 An isosceles right triangle has area $8 c m^{2}$ . The length of its hypotenuse is

Discussion

19.	If A and B are subsets of a set X, then (A∩(X−B))∪B is equal to
Answer» If $A$ and $B$ are subsets of a set $X,$ then $(A \cap (X - B)) \cup B$ is equal to

Discussion

20.	M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.
Answer» M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

Discussion

21.	Prove that the triangle formed by the points of contact of the sides of a given triangle with excircles correponding to these sides is equivalent to the triangle formed by the points of contact of the sides of the triangle with the inscribed circle
Answer» Prove that the triangle formed by the points of contact of the sides of a given triangle with excircles correponding to these sides is equivalent to the triangle formed by the points of contact of the sides of the triangle with the inscribed circle

Discussion

22.	Find the value of x in degrees from the given figure if ∠AOB=70∘ and AB=CD.70
Answer» Find the value of $x$ in degrees from the given figure if $∠ A O B = 70^{\circ}$ and $A B = C D .$ 70

Discussion

23.	Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and 3a - 2b = 1
Answer» Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and 3a - 2b = 1

Discussion

24.	The average mark obtained by all students in Electric Machines is___
Answer» The average mark obtained by all students in Electric Machines is___

Discussion

25.	Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by ABCD.
Answer» Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by ABCD.

25.

Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by ABCD.

Answer»

Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by ABCD.

Discussion

26.	Question 2:Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
Answer» Question 2: Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

26.

Question 2:Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Answer»

Question 2:

Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

Discussion

27.	AB and CD are respectively the smallest and largest sides of a quadrilateral ABCD. Show that ∠A > ∠C and∠B > ∠D.
Answer» AB and CD are respectively the smallest and largest sides of a quadrilateral ABCD. Show that ∠A > ∠C and ∠B > ∠D.

Discussion

28.	The coefficient of x53 in the expansion of 100∑m=0 100Cm(x−3)100−m2m is
Answer» The coefficient of $x^{53}$ in the expansion of $100 \sum m = 0$ $^{100} C_{m}$ $(x - 3)^{100 - m} 2^{m}$ is

Discussion

29.	In which of the following figure, the triangle formed by the line segment DE using the sides of the triangle ABC is similar to the triangle ABC?
Answer» In which of the following figure, the triangle formed by the line segment DE using the sides of the triangle ABC is similar to the triangle ABC?

Discussion

30.	Which of the following is irrational number?
Answer» Which of the following is irrational number?

Discussion

31.	In the given figure , AD is the median, then ∠BAD is:
Answer» In the given figure , AD is the median, then ∠BAD is:

31.

In the given figure , AD is the median, then ∠BAD is:

Answer»

In the given figure , AD is the median, then ∠BAD is:

Discussion

32.	Construct the following quadrilaterals of given measures.(1) In ☐ MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58°, m∠O = 105°, m∠R = 90°.(2) Construct ☐ DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm.(3) In ☐ ABCD l(AB) = 6.4 cm, l(BC) = 4.8 cm, m∠A = 70°, m∠B = 50°, m∠C = 140°.(4) Construct ☐ LMNO such that l(LM) = l(LO) = 6 cm, l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.
Answer» Construct the following quadrilaterals of given measures. (1) In ☐ MORE, l(MO) = 5.8 cm, l(OR) = 4.4 cm, m∠M = 58 $°$ , m∠O = 105 $°$ , m∠R = 90 $°$ . (2) Construct ☐ DEFG such that l(DE) = 4.5 cm, l(EF) = 6.5 cm, l(DG) = 5.5 cm, l(DF) = 7.2 cm, l(EG) = 7.8 cm. (3) In ☐ ABCD l(AB) = 6.4 cm, l(BC) = 4.8 cm, m∠A = 70 $°$ , m∠B = 50 $°$ , m∠C = 140 $°$ . (4) Construct ☐ LMNO such that l(LM) = l(LO) = 6 cm, l(ON) = l(NM) = 4.5 cm, l(OM) = 7.5 cm.

Discussion

33.	The mean of 10 numbers 7×8,10×10,13×12,16×14,.... is
Answer» The mean of $10$ numbers $7 \times 8, 10 \times 10, 13 \times 12, 16 \times 14, . . . .$ is

Discussion

34.	If two parallel lines are intersected by a transversal, then each pair of corresponding angles are_______.
Answer» If two parallel lines are intersected by a transversal, then each pair of corresponding angles are_______.

Discussion

35.	In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.
Answer» In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.

Discussion

36.	Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.
Answer» Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

Discussion

37.	In triangle ABC, CD perpendicular to AB,CA=2AD and BD=3AC. Prove that angle BCA =90∘
Answer» In triangle ABC, CD perpendicular to AB,CA=2AD and BD=3AC. Prove that angle BCA $= 90^{\circ}$

Discussion

38.	Two circles of radii5cm and 3 cm intersect at two points and the distance between their centres is 4cm. Find the length of the common chord.
Answer» Two circles of radii5cm and 3 cm intersect at two points and the distance between their centres is 4cm. Find the length of the common chord.

Discussion

39.	The decimal expansion of pi is:
Answer» The decimal expansion of pi is:

Discussion

40.	227 is a rational number but pi is an irrational number. Comment on this. [3 MARKS]
Answer» $\frac{22}{7}$ is a rational number but pi is an irrational number. Comment on this. [3 MARKS]

Discussion

41.	In the figure, AB\|\|CD\|\|EF and GH\|\|KL. Find ∠HKL.
Answer» In the figure, AB\|\|CD\|\|EF and GH\|\|KL. Find $∠ H K L$ .

Discussion

42.	In a huge park people are concentrated at three points (see the given figure)A: where there are different slides and swings for children,B: near which a man-made lake is situated,C: which is near to a large parking and exit.Where should an ice-cream parlour be set up so that maximum number of persons can approach it?(Hint: The parlor should be equidistant from A, B and C)
Answer» In a huge park people are concentrated at three points (see the given figure) A: where there are different slides and swings for children, B: near which a man-made lake is situated, C: which is near to a large parking and exit. Where should an ice-cream parlour be set up so that maximum number of persons can approach it? (Hint: The parlor should be equidistant from A, B and C)

42.

In a huge park people are concentrated at three points (see the given figure)A: where there are different slides and swings for children,B: near which a man-made lake is situated,C: which is near to a large parking and exit.Where should an ice-cream parlour be set up so that maximum number of persons can approach it?(Hint: The parlor should be equidistant from A, B and C)

Answer»

In a huge park people are concentrated at three points (see the given figure)

A: where there are different slides and swings for children,

B: near which a man-made lake is situated,

C: which is near to a large parking and exit.

Where should an ice-cream parlour be set up so that maximum number of persons can approach it?

(Hint: The parlor should be equidistant from A, B and C)

Discussion

43.	Arc BAD is called the:
Answer» Arc BAD is called the:

43.

Arc BAD is called the:

Answer»

Arc BAD is called the:

Discussion

44.	In ▢ABCD, seg AD \|\| seg BC. Diagonal AC and diagonal BD intersect each other in point P. Then show that APPD=PCBP
Answer» In ▢ABCD, seg AD \|\| seg BC. Diagonal AC and diagonal BD intersect each other in point P. Then show that $\frac{AP}{PD} = \frac{PC}{BP}$

Discussion

45.	For constructing a triangle with a given base, a base angle and difference between the other two sides, a ___ bisector is required.
Answer» For constructing a triangle with a given base, a base angle and difference between the other two sides, a ___ bisector is required.

Discussion

46.	Questions and their alternative answers are given. Choose the correct alternative answer.(1) Find the circumference of a circle whose area is 1386 cm2.(A) 132 cm2(B) 132 cm(C) 42 cm(D) 21 cm2 (2) The side of a cube is 4 m . If it is doubled, how many times will be the volume of the new cube, as compared with the original cube?(A) Two times(B) Three times(C) Four times(D) Eight times
Answer» Questions and their alternative answers are given. Choose the correct alternative answer. (1) Find the circumference of a circle whose area is 1386 cm². (A) 132 cm² (B) 132 cm (C) 42 cm (D) 21 cm² (2) The side of a cube is 4 m . If it is doubled, how many times will be the volume of the new cube, as compared with the original cube? (A) Two times (B) Three times (C) Four times (D) Eight times

Discussion

47.	What is the difference between an axiom and postulates
Answer» What is the difference between an axiom and postulates

Discussion

48.	The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use π = 22/7).
Answer» The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm², find its radius. (Use $π$ = 22/7).

Discussion

49.	We can write 347 as:
Answer» We can write 347 as:

Discussion

50.	If ABCD is a rhombus, then which of the following statements are correct?
Answer» If ABCD is a rhombus, then which of the following statements are correct?

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, find : (i) radius of its base (ii) volume of the cylinder [Use π = 3.14]

Prove that in a triangle, a line dividing two sides proportionally is parallel to the third side.

Give two rational numbers lying between 0.515115111511115...0.5353353335...

How to construct a triangle when all three sides are given?

∆ ABC and ∆DBC are two isosceles triangles on the same base BC and vertices A and D are on same side of BC . If AD is extended to intersect BC at P show that AP is the perpendicular bisector of BC

In the figure, the value of x that will make AOB, a straight line is

Prove that the circles described on the four sides of a rhombus as diameters, pass through the point of intersection of its diagonals.

Factrorise 25x2+4y2+9z2−20xy−12yz+30xz

A cylinder of same height and radius is placed on the top of a hemisphere. Find the curved surface area of the shape if the length of the shape be 7 cm.

If the vertices of a triangle have integral coordinates, prove that the triangle cannot be equilateral

Simplify: (−2)3×(−10)3

If (x+a)(x+b)=x2+5x+6,what is the value of (a−b) if (a−b)&gt;0?

In each of the following, using the remainder Theorem, find the remainder when f(x) is divided by g(x) and verify the result y actual division. f(x) = x3+4x2−3x+10, g(x) = x + 4

The distance of the point (p, q, r) from x axis is _______________________.

How many circles can be drawn passing through two points?

A juiceseller has a large cylindrical vessel of base radius 15 cm filled up to a height of 32 cm with orange juice. The juice is filled in small cylindrical glasses of radius 3 cm up to a height of 8 cm, and sold for ₹ 15 each. How much money does he received by selling the juice completely?

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x ? (a) x22π (b) x2√π (c) √2xx (d) π2x

Question 1 An isosceles right triangle has area 8cm2. The length of its hypotenuse is

If A and B are subsets of a set X, then (A∩(X−B))∪B is equal to

M (-2, y) is a point equidistant from the coordinates A(5,7) and B(3,-4). Find the value of y.

Prove that the triangle formed by the points of contact of the sides of a given triangle with excircles correponding to these sides is equivalent to the triangle formed by the points of contact of the sides of the triangle with the inscribed circle

Find the value of x in degrees from the given figure if ∠AOB=70∘ and AB=CD.70

Find value of a and b if y = 1 and x = 2 is solution of linear equation ax + by = 3 and 3a - 2b = 1

The average mark obtained by all students in Electric Machines is___

Four points A, B, C, and D are given on circle. Line segment AB and CD are parallel. Find the area of the figure formed by ABCD.

Question 2:Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.

AB and CD are respectively the smallest and largest sides of a quadrilateral ABCD. Show that ∠A > ∠C and∠B > ∠D.

The coefficient of x53 in the expansion of 100∑m=0 100Cm(x−3)100−m2m is

In which of the following figure, the triangle formed by the line segment DE using the sides of the triangle ABC is similar to the triangle ABC?

Which of the following is irrational number?

In the given figure , AD is the median, then ∠BAD is:

The mean of 10 numbers 7×8,10×10,13×12,16×14,.... is

If two parallel lines are intersected by a transversal, then each pair of corresponding angles are_______.

In Δ ABC, BD⊥ AC and CE ⊥ AB. If BD and CE intersect at O, prove that ∠BOC = 180° − A.

Diagonals AC and BD of a quadrilateral ABCD intersect at O in such a way that ar (AOD) = ar (BOC). Prove that ABCD is a trapezium.

In triangle ABC, CD perpendicular to AB,CA=2AD and BD=3AC. Prove that angle BCA =90∘

Two circles of radii5cm and 3 cm intersect at two points and the distance between their centres is 4cm. Find the length of the common chord.

The decimal expansion of pi is:

227 is a rational number but pi is an irrational number. Comment on this. [3 MARKS]

In the figure, AB||CD||EF and GH||KL. Find ∠HKL.

Arc BAD is called the:

In ▢ABCD, seg AD || seg BC. Diagonal AC and diagonal BD intersect each other in point P. Then show that APPD=PCBP

For constructing a triangle with a given base, a base angle and difference between the other two sides, a ___ bisector is required.

What is the difference between an axiom and postulates

The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm2, find its radius. (Use π = 22/7).

We can write 347 as:

If ABCD is a rhombus, then which of the following statements are correct?

If (x+a)(x+b)=x2+5x+6,what is the value of (a−b) if (a−b)>0?