24740 + Interview Questions in Mathematics

1.	PQRS is a parallelogram. X and Y are midpoints of sides PQ and Rs respectively. If W and Z are points of intersection of SX & PY and XR and YQ respectively. Then show that arΔ YWZ = arΔXWZ
Answer» PQRS is a parallelogram. X and Y are midpoints of sides PQ and Rs respectively. If W and Z are points of intersection of SX & PY and XR and YQ respectively. Then show that ar $Δ Y W Z = a r Δ X W Z$

Discussion

2.	Question 3 ABCD is a rectangle and P, Q, R, S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.
Answer» Question 3 ABCD is a rectangle and P, Q, R, S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Discussion

3.	Factorise x8−y8
Answer» Factorise $x^{8} - y^{8}$

Discussion

4.	Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.
Answer» Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.

Discussion

5.	Question 20 In following figure, the point identified by the coordinates ( -5 , 3 ) is A) T B) R C) L D) S
Answer» Question 20 In following figure, the point identified by the coordinates ( -5 , 3 ) is A) T B) R C) L D) S

Discussion

6.	Question 8 (ii) ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: Diagonal BD bisects ∠B as well as ∠D.
Answer» Question 8 (ii) ABCD is a rectangle in which diagonal AC bisects $∠ A$ as well as $∠ C$ . Show that: Diagonal BD bisects $∠ B$ as well as $∠ D$ .

Discussion

7.	The roots of 2x2–6x+8=0 are ___________.
Answer» The roots of $2 x^{2} - 6 x + 8 = 0$ are ___________.

Discussion

8.	The marked price of a watch is Rs.1600. The shopkeeper gives two successive discounts to the customer, the first being 10%. If the customer pays Rs1224 for the watch, the second discount is,
Answer» The marked price of a watch is Rs.1600. The shopkeeper gives two successive discounts to the customer, the first being 10%. If the customer pays Rs1224 for the watch, the second discount is,

Discussion

9.	The mean and median of the numbers 1, 2, 3,4, y, 8, 9, 10, 12 and x written in increasing order are both 10, then the values of x and y are _____.
Answer» The mean and median of the numbers 1, 2, 3,4, $y$ , 8, 9, 10, 12 and $x$ written in increasing order are both 10, then the values of $x$ and $y$ are _____.

Discussion

10.	∑nn=11log2n (a)=
Answer» $\sum_{n = 1}^{n} \frac{1}{l o g_{2^{n}} (a)} =$

Discussion

11.	Question 119 (xi) Write two integers whose product is smaller than both the integers.
Answer» Question 119 (xi) Write two integers whose product is smaller than both the integers.

11.

Question 119 (xi) Write two integers whose product is smaller than both the integers.

Answer»

Question 119 (xi)

Write two integers whose product is smaller than both the integers.

Discussion

12.	For the equation \|x2\|+\|x\|−6=0, the roots are
Answer» For the equation $\| x^{2} \| + \| x \| - 6 = 0$ , the roots are

Discussion

13.	Question 4 Degree of the zero polynomial is A) 0 B) 1 C) Any natural number D) Not defined
Answer» Question 4 Degree of the zero polynomial is A) 0 B) 1 C) Any natural number D) Not defined

Discussion

14.	Question 9 (v) Classify 1.101001000100001… as rational or irrational.
Answer» Question 9 (v) Classify 1.101001000100001… as rational or irrational.

Discussion

15.	Find the solution of the pair of linear equations x+2y=5 and 7x+3y=13.
Answer» Find the solution of the pair of linear equations $x + 2 y = 5$ and $7 x + 3 y = 13.$

Discussion

16.	Question 8 ABCD is a rectangle formed by points A (-1,-1), B(-1,4), C(5,4) and D(5,-1). P, Q, R, and S are mid-points of AB, BC, CD, and DA respectively. Is the quadrilateral PQRS a square, rectangle or rhombus? Justify your answer.
Answer» Question 8 ABCD is a rectangle formed by points A (-1,-1), B(-1,4), C(5,4) and D(5,-1). P, Q, R, and S are mid-points of AB, BC, CD, and DA respectively. Is the quadrilateral PQRS a square, rectangle or rhombus? Justify your answer.

Discussion

17.	ABCD is a parallelogram and DM ⊥ BM as shown in the figure. Find ∠CDM (in degrees).60
Answer» ABCD is a parallelogram and DM ⊥ BM as shown in the figure. Find $∠ C D M$ (in degrees). 60

Discussion

18.	If an alphabet is picked from the word MISSIMMIPPI what is the probability that an alphabet 'M' is picked?
Answer» If an alphabet is picked from the word MISSIMMIPPI what is the probability that an alphabet 'M' is picked?

Discussion

19.	Question 6 In the figure, LM is a line parallel to the y-axis at a distance of 3 units. a. What are the coordinates of the points P, R and Q? b. What is the difference between the abscissa of the points L and M?
Answer» Question 6 In the figure, LM is a line parallel to the y-axis at a distance of 3 units. a. What are the coordinates of the points P, R and Q? b. What is the difference between the abscissa of the points L and M?

Discussion

20.	Question 2 (i) AD is an altitude of an isosceles triangles ABC in which AB = AC. Show that AD bisets BC
Answer» Question 2 (i) AD is an altitude of an isosceles triangles ABC in which AB = AC. Show that AD bisets BC

Discussion

21.	Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16cm×8cm×8cm. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [use π−31.4]
Answer» Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions $16 c m \times 8 c m \times 8 c m$ . when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. $[u s e π - 31.4]$

Discussion

22.	There is a tent in conical shape. The slant height of the tent is 14 m. If the curved surface area of cone is 308 m2 then base area of tent is
Answer» There is a tent in conical shape. The slant height of the tent is $14 m .$ If the curved surface area of cone is $308 m^{2}$ then base area of tent is

22.

There is a tent in conical shape. The slant height of the tent is 14 m. If the curved surface area of cone is 308 m2 then base area of tent is

Answer»

There is a tent in conical shape. The slant height of the tent is $14 m .$ If the curved surface area of cone is $308 m^{2}$ then base area of tent is

Discussion

23.	Find the unique solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13.
Answer» Find the unique solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13.

Discussion

24.	Which of the the following product is rational?
Answer» Which of the the following product is rational?

24.

Which of the the following product is rational?

Answer»

Which of the the following product is rational?

Discussion

25.	In the figure, OP and OQ are opposite rays then value of ∠DOC is
Answer» In the figure, OP and OQ are opposite rays then value of ∠DOC is

25.

In the figure, OP and OQ are opposite rays then value of ∠DOC is

Answer»

In the figure, OP and OQ are opposite rays then value of ∠DOC is

Discussion

26.	Solve the following pair of equations: 2x + y = 7 3x + 2y = 12 Choose the correct answer from the given options.
Answer» Solve the following pair of equations: 2x + y = 7 3x + 2y = 12 Choose the correct answer from the given options.

Discussion

27.	Suppose f (x) is a polynomial of degree 5 and with leading coefficient 2009. Suppose further that f (1)=1, f (2)=3,f (3)=5,f (4)=7,f (5)=9. What is the value of f (6).
Answer» Suppose f (x) is a polynomial of degree 5 and with leading coefficient 2009. Suppose further that f (1)=1, f (2)=3,f (3)=5,f (4)=7,f (5)=9. What is the value of f (6).

Discussion

28.	a-c=25 and a=b. Show that b-c= 25
Answer» a-c=25 and a=b. Show that b-c= 25

Discussion

29.	Question 2 The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?
Answer» Question 2 The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per $m^{2}$ per year. A company hired one of its walls for 3 months. How much rent did it pay?

Discussion

30.	Question 51 Fill in the blanks to make the statement true. 1 cm2=___ mm2
Answer» Question 51 Fill in the blanks to make the statement true. $1 c m^{2} =$ ___ $m m^{2}$

Discussion

31.	How many cubes of side 2 cm can be fit into cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively? [3 MARKS]
Answer» How many cubes of side 2 cm can be fit into cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively? [3 MARKS]

Discussion

32.	Question 8 If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r , then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle is this statement false? Why?
Answer» Question 8 If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r , then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle is this statement false? Why?

Discussion

33.	A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the total surface area of the cylindrical tin is
Answer» A cricket ball of radius $r$ is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the total surface area of the cylindrical tin is

Discussion

34.	The radius of the circle given above is 7cm and the angle subtended by the arc is 60∘. If the area of ΔOAB is 21cm2, then the area of segment APB is___ .(Take the value of π as 227)
Answer» The radius of the circle given above is 7cm and the angle subtended by the arc is $60^{\circ}$ . If the area of $Δ$ OAB is $21 {c m}^{2}$ , then the area of segment APB is___ .(Take the value of $π$ as $\frac{22}{7}$ )

Discussion

35.	The area of a parallelogram of the given dimensions is:
Answer» The area of a parallelogram of the given dimensions is:

35.

The area of a parallelogram of the given dimensions is:

Answer»

The area of a parallelogram of the given dimensions is:

Discussion

36.	A line which intersects 2 or more lines is called a __.
Answer» A line which intersects 2 or more lines is called a __.

Discussion

37.	On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.
Answer» On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.

37.

On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.

Answer»

On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.

Discussion

38.	Question 5 (vii) Find 1.07 × 0.02
Answer» Question 5 (vii) Find 1.07 $\times$ 0.02

Discussion

39.	Question 9 (ii) Solve the following pairs of equation x3+y4=4, 5x6−y8=4
Answer» Question 9 (ii) Solve the following pairs of equation $\frac{x}{3} + \frac{y}{4} = 4, \frac{5 x}{6} - \frac{y}{8} = 4$

Discussion

40.	Marks of students of a Class are represented in the frequency polygon shown below. Grade A is given to a student if he got at least 15 marks in the test. How many students got the grade A?14
Answer» Marks of students of a Class are represented in the frequency polygon shown below. Grade A is given to a student if he got at least 15 marks in the test. How many students got the grade A? 14

Discussion

41.	The length of a rectangle is increased buy 10 % while its breadth is decreased by 10%. What is the consequent percentage change in the area of the rectangle?
Answer» The length of a rectangle is increased buy 10 % while its breadth is decreased by 10%. What is the consequent percentage change in the area of the rectangle?

Discussion

42.	Given the area of rectangle is A=25a2−35a+69. The length is given as (5a−3).Find the width of the rectangle.
Answer» $Given the area of rectangle is A = 25 a^{2} - 35 a + 69. The length is given as (5 a - 3) . Find the width of the rectangle.$

Discussion

43.	Using the information given in the figure, find the values of x and y.
Answer» Using the information given in the figure, find the values of x and y.

43.

Using the information given in the figure, find the values of x and y.

Answer»

Using the information given in the figure, find the values of x and y.

Discussion

44.	In two triangles ABC and DEF, it is given that ∠A=∠D, ∠B=∠E and ∠C=∠F. Are the two triangles necessarily congruent?
Answer» In two triangles ABC and DEF, it is given that $∠ A = ∠ D, ∠ B = ∠ E a n d ∠ C = ∠ F .$ Are the two triangles necessarily congruent?

44.

In two triangles ABC and DEF, it is given that ∠A=∠D, ∠B=∠E and ∠C=∠F. Are the two triangles necessarily congruent?

Answer»

In two triangles ABC and DEF, it is given that $∠ A = ∠ D, ∠ B = ∠ E a n d ∠ C = ∠ F .$

Are the two triangles necessarily congruent?

Discussion

45.	Determine (8x)x,if 9x+2=240+9x.
Answer» $D e t e r m i n e (8 x)^{x}, i f 9^{x + 2} = 240 + 9^{x} .$

Discussion

46.	If two straight lines intersect each other prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.
Answer» If two straight lines intersect each other prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

Discussion

47.	What is 216−23?
Answer» What is $216^{\frac{- 2}{3}}$ ?

Discussion

48.	The zeros of the polynomial p(x)=3x2−1 are (a) 13 and 3 (b) 1√3 and √3 (c) −1√3 and √3 (d) 1√3 and −1√3
Answer» The zeros of the polynomial $p (x) = 3 x^{2} - 1$ are (a) $\frac{1}{3}$ and 3 (b) $\frac{1}{\sqrt{3}}$ and $\sqrt{3}$ (c) $\frac{- 1}{\sqrt{3}}$ and $\sqrt{3}$ (d) $\frac{1}{\sqrt{3}}$ and $\frac{- 1}{\sqrt{3}}$

Discussion

49.	Determine the mode of the following values of a variable. 23, 15, 25, 40, 27, 25, 22, 25, 20
Answer» Determine the mode of the following values of a variable. 23, 15, 25, 40, 27, 25, 22, 25, 20

Discussion

50.	The equation of the y - axis is (a) x = 0 (b) y = 0 (c) x = y (d) x + y = 0
Answer» The equation of the y - axis is (a) x = 0 (b) y = 0 (c) x = y (d) x + y = 0

50.

The equation of the y - axis is (a) x = 0 (b) y = 0 (c) x = y (d) x + y = 0

Answer»

The equation of the y - axis is

(a) x = 0

(b) y = 0

(c) x = y

(d) x + y = 0

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

PQRS is a parallelogram. X and Y are midpoints of sides PQ and Rs respectively. If W and Z are points of intersection of SX &amp; PY and XR and YQ respectively. Then show that arΔ YWZ = arΔXWZ

Question 3 ABCD is a rectangle and P, Q, R, S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus.

Factorise x8−y8

Find the area of the triangle whose base measures 24 cm and the corresponding height measures 14.5 cm.

Question 20 In following figure, the point identified by the coordinates ( -5 , 3 ) is A) T B) R C) L D) S

Question 8 (ii) ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: Diagonal BD bisects ∠B as well as ∠D.

The roots of 2x2–6x+8=0 are ___________.

The marked price of a watch is Rs.1600. The shopkeeper gives two successive discounts to the customer, the first being 10%. If the customer pays Rs1224 for the watch, the second discount is,

The mean and median of the numbers 1, 2, 3,4, y, 8, 9, 10, 12 and x written in increasing order are both 10, then the values of x and y are _____.

∑nn=11log2n (a)=

Question 119 (xi) Write two integers whose product is smaller than both the integers.

For the equation |x2|+|x|−6=0, the roots are

Question 4 Degree of the zero polynomial is A) 0 B) 1 C) Any natural number D) Not defined

Question 9 (v) Classify 1.101001000100001… as rational or irrational.

Find the solution of the pair of linear equations x+2y=5 and 7x+3y=13.

Question 8 ABCD is a rectangle formed by points A (-1,-1), B(-1,4), C(5,4) and D(5,-1). P, Q, R, and S are mid-points of AB, BC, CD, and DA respectively. Is the quadrilateral PQRS a square, rectangle or rhombus? Justify your answer.

ABCD is a parallelogram and DM ⊥ BM as shown in the figure. Find ∠CDM (in degrees).60

If an alphabet is picked from the word MISSIMMIPPI what is the probability that an alphabet 'M' is picked?

Question 6 In the figure, LM is a line parallel to the y-axis at a distance of 3 units. a. What are the coordinates of the points P, R and Q? b. What is the difference between the abscissa of the points L and M?

Question 2 (i) AD is an altitude of an isosceles triangles ABC in which AB = AC. Show that AD bisets BC

Metal spheres, each of radius 2 cm, are packed into a rectangular box of internal dimensions 16cm×8cm×8cm. when 16 spheres are packed the box is filled with preservative liquid. Find the volume of this liquid. Give your answer to the nearest integer. [use π−31.4]

There is a tent in conical shape. The slant height of the tent is 14 m. If the curved surface area of cone is 308 m2 then base area of tent is

Find the unique solution of the pair of linear equations x + 2y = 5, 7x + 3y = 13.

Which of the the following product is rational?

In the figure, OP and OQ are opposite rays then value of ∠DOC is

Solve the following pair of equations: 2x + y = 7 3x + 2y = 12 Choose the correct answer from the given options.

Suppose f (x) is a polynomial of degree 5 and with leading coefficient 2009. Suppose further that f (1)=1, f (2)=3,f (3)=5,f (4)=7,f (5)=9. What is the value of f (6).

a-c=25 and a=b. Show that b-c= 25

Question 2 The triangular side walls of a flyover have been used for advertisement. The sides of the walls are 122m, 22m, and 120m (see the given figure). The advertisements yield an earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?

Question 51 Fill in the blanks to make the statement true. 1 cm2=___ mm2

How many cubes of side 2 cm can be fit into cuboid box having length, breadth and height of 8cm, 12 cm and 10 cm respectively? [3 MARKS]

Question 8 If the length of an arc of a circle of radius r is equal to that of an arc of a circle of radius 2r , then the angle of the corresponding sector of the first circle is double the angle of the corresponding sector of the other circle is this statement false? Why?

A cricket ball of radius r is exactly fitted in a cylindrical tin as shown in the figure below. The ratio of surface areas of cricket ball to the total surface area of the cylindrical tin is

The radius of the circle given above is 7cm and the angle subtended by the arc is 60∘. If the area of ΔOAB is 21cm2, then the area of segment APB is___ .(Take the value of π as 227)

The area of a parallelogram of the given dimensions is:

A line which intersects 2 or more lines is called a __.

On a sunny day, a person who is 5 feet tall casts a 3 feet long shadow. Find the height of a nearby flagpole which casts a 12 feet long shadow.

Question 5 (vii) Find 1.07 × 0.02

Question 9 (ii) Solve the following pairs of equation x3+y4=4, 5x6−y8=4

Marks of students of a Class are represented in the frequency polygon shown below. Grade A is given to a student if he got at least 15 marks in the test. How many students got the grade A?14

The length of a rectangle is increased buy 10 % while its breadth is decreased by 10%. What is the consequent percentage change in the area of the rectangle?

Given the area of rectangle is A=25a2−35a+69. The length is given as (5a−3).Find the width of the rectangle.

Using the information given in the figure, find the values of x and y.

In two triangles ABC and DEF, it is given that ∠A=∠D, ∠B=∠E and ∠C=∠F. Are the two triangles necessarily congruent?

Determine (8x)x,if 9x+2=240+9x.

If two straight lines intersect each other prove that the ray opposite to the bisector of one of the angles thus formed bisects the vertically opposite angle.

What is 216−23?

The zeros of the polynomial p(x)=3x2−1 are (a) 13 and 3 (b) 1√3 and √3 (c) −1√3 and √3 (d) 1√3 and −1√3

Determine the mode of the following values of a variable. 23, 15, 25, 40, 27, 25, 22, 25, 20

The equation of the y - axis is (a) x = 0 (b) y = 0 (c) x = y (d) x + y = 0

PQRS is a parallelogram. X and Y are midpoints of sides PQ and Rs respectively. If W and Z are points of intersection of SX & PY and XR and YQ respectively. Then show that arΔ YWZ = arΔXWZ