24740 + Interview Questions in Mathematics

1.	Four curves i.e.a) y=x3b) y=x7c) y=x2 andd) y=x6are depicted in the following graph. Which polynomial is represented by Graph 4?
Answer» Four curves i.e. a) $y = x^{3}$ b) $y = x^{7}$ c) $y = x^{2}$ and d) $y = x^{6}$ are depicted in the following graph. Which polynomial is represented by Graph 4?

Discussion

2.	24. A can hit a target four times in 5 shots ; B three times in 4 shots and C twice in 3 shots . They fire a volley ; what is the probability that 2 shots at least hit ? And if two hit , what is the probability that it is C who has missed ?
Answer» 24. A can hit a target four times in 5 shots ; B three times in 4 shots and C twice in 3 shots . They fire a volley ; what is the probability that 2 shots at least hit ? And if two hit , what is the probability that it is C who has missed ?

Discussion

3.	Which of the following rational numbers is a non-terminating and repeating decimal?
Answer» Which of the following rational numbers is a non-terminating and repeating decimal?

Discussion

4.	If the points (–2, 1) and (–1, – 2) are on the opposite sides of the line 2x + y + a = 0, then the set of values of a is _________.
Answer» If the points (–2, 1) and (–1, – 2) are on the opposite sides of the line 2x + y + a = 0, then the set of values of a is _________.

Discussion

5.	A point Of is taken inside a quadrilateral ABCD such that it's distances from the angular points D and B are equal. Show that OA and OC are in one and same straight line.
Answer» A point Of is taken inside a quadrilateral ABCD such that it's distances from the angular points D and B are equal. Show that OA and OC are in one and same straight line.

Discussion

6.	In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that(i) area (PQRS) = area (ABRS) (ii) area (AXS) =12 area (PQRS)
Answer» In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) area (PQRS) $=$ area (ABRS) (ii) area (AXS) $= \frac{1}{2}$ area (PQRS)

6.

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that(i) area (PQRS) = area (ABRS) (ii) area (AXS) =12 area (PQRS)

Answer»

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that

(i) area (PQRS) $=$ area (ABRS)

(ii) area (AXS) $= \frac{1}{2}$ area (PQRS)

Discussion

7.	In triangle ABC, D is a point on BC such that BD:CD = 3:2. If area of triangle ABC=40cm^2. Then find the area of triangle ACD.
Answer» In triangle ABC, D is a point on BC such that BD:CD = 3:2. If area of triangle ABC=40cm^2. Then find the area of triangle ACD.

Discussion

8.	24xy2z26yz2=
Answer» $\frac{24 x y^{2} z^{2}}{6 y z^{2}} =$

Discussion

9.	If 2x+2f(x)=2, then the domain of the function f(x) is
Answer» If $2^{x} + 2^{f (x)} = 2,$ then the domain of the function $f (x)$ is

Discussion

10.	In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then show that area of(△BPC) = area of (△DPQ).
Answer» In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then show that area of( $△$ BPC) = area of ( $△$ DPQ).

Discussion

11.	A. A Booker prize won by Salman Rushdie for his writing 'Midnight's Children', turned Indian writing in English for the better. B. Although International recognition came to Rabindranath Tagore much earlier, it was Rushdie's book that affected Indian literature in a way that nothing else in this century has done. C. It was 'Midnight Children's success which gave a whole generation of Indians who had literary inclinations the confidence to embark on literary careers. D. Rushdie's influence lies in the fact that he made India - rather Indian themes, locales and characters - written about in English popular, even trendy. E. Rushdie's 'Midnight Children' convinced publishers, both in India and in the west that there was a market for books in English written by Indians.
Answer» A. A Booker prize won by Salman Rushdie for his writing 'Midnight's Children', turned Indian writing in English for the better. B. Although International recognition came to Rabindranath Tagore much earlier, it was Rushdie's book that affected Indian literature in a way that nothing else in this century has done. C. It was 'Midnight Children's success which gave a whole generation of Indians who had literary inclinations the confidence to embark on literary careers. D. Rushdie's influence lies in the fact that he made India - rather Indian themes, locales and characters - written about in English popular, even trendy. E. Rushdie's 'Midnight Children' convinced publishers, both in India and in the west that there was a market for books in English written by Indians.

Discussion

12.	Question 1Visualize 3.765 on the number line using successive magnification.
Answer» Question 1 Visualize 3.765 on the number line using successive magnification.

Discussion

13.	(3pq+3qr)2−18pq2r = .
Answer» ${(3 p q + 3 q r)}^{2} - 18 p q^{2} r$ = .

Discussion

14.	Observe the construction given below. To construct triangle ABC, the given components are
Answer» Observe the construction given below. To construct triangle ABC, the given components are

Discussion

15.	Question 1(ii)Represent these numbers on the number line:−56
Answer» Question 1(ii) Represent these numbers on the number line: $\frac{- 5}{6}$

Discussion

16.	Abcd is square the bisector of angle DBC cut ac and CD at e and f respectively prove that bfCE=bedf
Answer» Abcd is square the bisector of angle DBC cut ac and CD at e and f respectively prove that bfCE=bedf

Discussion

17.	Proof of Theorem ( Two distinct lines cannot have more than one point in common )
Answer» Proof of Theorem ( Two distinct lines cannot have more than one point in common )

Discussion

18.	How to rationalize -: (a) 2−√3/2+√3 (b) 2√5+3√2/2√5−3√2
Answer» How to rationalize -: (a) 2−√3/2+√3 (b) 2√5+3√2/2√5−3√2

18.

How to rationalize -: (a) 2−√3/2+√3 (b) 2√5+3√2/2√5−3√2

Answer»

How to rationalize -:

(a) 2−√3/2+√3
(b) 2√5+3√2/2√5−3√2

Discussion

19.	8a3 − b3 − 4ax + 2bx
Answer» 8a³ − b³ − 4ax + 2bx

Discussion

20.	The decimal form of 78 is _.
Answer» The decimal form of $\frac{7}{8}$ is _.

Discussion

21.	The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.Class Interval0−1010−2020−3030−4040−50Number of students341315528.75
Answer» The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method. $\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$ 28.75

21.

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.Class Interval0−1010−2020−3030−4040−50Number of students341315528.75

Answer»

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.

$\begin{matrix} C l a s s I n t e r v a l & 0 - 10 & 10 - 20 & 20 - 30 & 30 - 40 & 40 - 50 N u m b e r o f s t u d e n t s & 3 & 4 & 13 & 15 & 5 \end{matrix}$

28.75

Discussion

22.	What is the approximate value of √2 +√3 ?
Answer» What is the approximate value of √2 +√3 ?

Discussion

23.	A farmer has to plough the field for five different types of crops naming A, B, C, D and E in a circular field. If the diameter of the field, where crops A, B and C are grown is 126 units and every other band is 21 units wide. Then, choose the correct option. i) Area of region, where crop A is grown =1386 sq. units ii) Area of region, where crop B is grown =22176 sq. units iii) Area of region, where crops A, B, C and D are grown =5544 sq. units iv) Area of region, where crop E is grown =34650 sq. units
Answer» A farmer has to plough the field for five different types of crops naming $A, B, C, D$ and $E$ in a circular field. If the diameter of the field, where crops $A, B$ and $C$ are grown is 126 units and every other band is 21 units wide. Then, choose the correct option. i) Area of region, where crop $A$ is grown $= 1386$ sq. units ii) Area of region, where crop $B$ is grown $= 22176$ sq. units iii) Area of region, where crops $A, B, C$ and $D$ are grown $= 5544$ sq. units iv) Area of region, where crop $E$ is grown $= 34650$ sq. units

Discussion

24.	How many parts should be shaded in figure B to make it represent the same fraction as the unshaded part of figure A?
Answer» How many parts should be shaded in figure B to make it represent the same fraction as the unshaded part of figure A?

Discussion

25.	Simplify:15 - (6 + 6 × 6) ÷ (9 + 5)
Answer» Simplify: 15 - (6 + 6 × 6) ÷ (9 + 5)

Discussion

26.	the length of a focal chord of the parabola y^2 =4ax at a dis†an ce b from the vertex is c. Then 1. a^2=bc 2. a^3=b^2c 3. b^2=ac 3. b^2c=4a^{}
Answer» the length of a focal chord of the parabola y^2 =4ax at a dis†an ce b from the vertex is c. Then 1. a^2=bc 2. a^3=b^2c 3. b^2=ac 3. b^2c=4a^{}

Discussion

27.	If one of the factors of the polynomial (3x3+25x2+36x−36) is (x+3), then find the other factors using synthetic division.
Answer» If one of the factors of the polynomial $(3 x^{3} + 25 x^{2} + 36 x - 36) is (x + 3),$ then find the other factors using synthetic division.

Discussion

28.	ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.
Answer» ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

Discussion

29.	In figure, AX bisects ∠BAC as well as ∠BDC. State the three facts needed to ensure that △ACD ≅ △ABD
Answer» In figure, AX bisects $∠$ BAC as well as $∠$ BDC. State the three facts needed to ensure that $△$ ACD $≅$ $△$ ABD

Discussion

30.	In ΔABC,∠B=90∘. Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.
Answer» In $Δ A B C, ∠ B = 90^{\circ}$ . Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

30.

In ΔABC,∠B=90∘. Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

Answer»

In $Δ A B C, ∠ B = 90^{\circ}$ . Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

Discussion

31.	The distance of the point in (1,-2,3) from the plane x-y+z=5 measured parallel to the line x/2=y/3=(z-1)/6is
Answer» The distance of the point in (1,-2,3) from the plane x-y+z=5 measured parallel to the line x/2=y/3=(z-1)/6is

Discussion

32.	What is walli's theoram
Answer» What is walli's theoram

Discussion

33.	Find the value of 5√16×5√2.
Answer» Find the value of $\sqrt[5]{16} \times \sqrt[5]{2}$ .

Discussion

34.	Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel, If the distance between AB and CD is 3 cm, find the radius of the circle.
Answer» Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel, If the distance between AB and CD is 3 cm, find the radius of the circle.

Discussion

35.	Factorize: a4−2a3−4a+8
Answer» Factorize: $a^{4} - 2 a^{3} - 4 a + 8$

Discussion

36.	In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)1. 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 by actual division: (1−8) 1. f(x) = x³ + 4x² − 3x + 10, g(x) = x + 4

Discussion

37.	In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. [4 MARKS]
Answer» In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. [4 MARKS]

Discussion

38.	You have been asked to plot graphs of the following equations: Equation 1: 3x+2y=1 Equation 2: y−2x=2 Fill the following tables (find p, q, r, s) which you will use to plot the graphs: Equation 1: x05ypq Equation 2: xrsy05
Answer» You have been asked to plot graphs of the following equations: Equation 1: $3 x + 2 y = 1$ Equation 2: $y - 2 x = 2$ Fill the following tables (find p, q, r, s) which you will use to plot the graphs: Equation 1: $\begin{matrix} x & 0 & 5 y & p & q \end{matrix}$ Equation 2: $\begin{matrix} x & r & s y & 0 & 5 \end{matrix}$

Discussion

39.	In the given figure, ABCD is a quadrilateral in which diagonals AC and BD intersect at a point E then,
Answer» In the given figure, ABCD is a quadrilateral in which diagonals AC and BD intersect at a point E then,

Discussion

40.	The diagonals of a rectangle ABCD intersect at O. If ∠BOC=68∘, then ∠ODA is
Answer» The diagonals of a rectangle ABCD intersect at O. If $∠ B O C = 68^{\circ}$ , then $∠ O D A$ is

Discussion

41.	Find the solution for the given equation x+y−82 = x+2y−148 = 3x+y−1211
Answer» Find the solution for the given equation $\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$

41.

Find the solution for the given equation x+y−82 = x+2y−148 = 3x+y−1211

Answer»

Find the solution for the given equation

$\frac{x + y - 8}{2}$ = $\frac{x + 2 y - 14}{8}$ = $\frac{3 x + y - 12}{11}$

Discussion

42.	Directions:- Study the following information carefully to answer the question given below. Seven friends T, U, V, W, X, Y and Z are sitting in a straight line facing north. W sits fifth to the right of T. W does not sit at any of the extreme ends. Two people sit between Z and X. Y sits third to the left of U. Y sits exactly in the middle. Z is not an immediate neighbour of Y. What is is position with respect to W?
Answer» Directions:- Study the following information carefully to answer the question given below. Seven friends T, U, V, W, X, Y and Z are sitting in a straight line facing north. W sits fifth to the right of T. W does not sit at any of the extreme ends. Two people sit between Z and X. Y sits third to the left of U. Y sits exactly in the middle. Z is not an immediate neighbour of Y. What is is position with respect to W?

Discussion

43.	The bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is
Answer» The bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is

Discussion

44.	Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?
Answer» Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?

Discussion

45.	Question 8XY is a line parallel to side BC of a triangle ABC. If BE \|\| AC and CF \|\| AB meet XY at E and F respectively,show that ar(ΔABE)=ar(ΔACF).
Answer» Question 8 XY is a line parallel to side BC of a triangle ABC. If BE \|\| AC and CF \|\| AB meet XY at E and F respectively, show that $a r (Δ A B E) = a r (Δ A C F)$ .

Discussion

46.	(x-(a+2))(x-(a-1)) can't we further simplify it as (x-a-2)(x-a+1)?
Answer» (x-(a+2))(x-(a-1)) can't we further simplify it as (x-a-2)(x-a+1)?

Discussion

47.	If x=2α+1 and y=α−1 is a solution of the equation 2x−3y+5=0, find the value of α.
Answer» $I f x = 2 α + 1 a n d y = α - 1 is a solution of the equation 2 x - 3 y + 5 = 0, find the value of α .$

Discussion

48.	39. When (xcube-2xsq.+px-q) is divided by (xsquare-2x-3), the remainder is (x-6). Find the values of p&q.
Answer» 39. When (xcube-2xsq.+px-q) is divided by (xsquare-2x-3), the remainder is (x-6). Find the values of p&q.

Discussion

49.	Question 7 x=45(x+10)
Answer» Question 7 $x = \frac{4}{5} (x + 10)$

Discussion

50.	Question 47The two rational number lying between - 2 and - 5 with denominator as 1 are ___ and ___.
Answer» Question 47 The two rational number lying between - 2 and - 5 with denominator as 1 are ___ and ___.

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Four curves i.e.a) y=x3b) y=x7c) y=x2 andd) y=x6are depicted in the following graph. Which polynomial is represented by Graph 4?

24. A can hit a target four times in 5 shots ; B three times in 4 shots and C twice in 3 shots . They fire a volley ; what is the probability that 2 shots at least hit ? And if two hit , what is the probability that it is C who has missed ?

Which of the following rational numbers is a non-terminating and repeating decimal?

If the points (–2, 1) and (–1, – 2) are on the opposite sides of the line 2x + y + a = 0, then the set of values of a is _________.

A point Of is taken inside a quadrilateral ABCD such that it's distances from the angular points D and B are equal. Show that OA and OC are in one and same straight line.

In the given figure, PQRS and ABRS are parallelograms and X is any point on side BR. Show that(i) area (PQRS) = area (ABRS) (ii) area (AXS) =12 area (PQRS)

In triangle ABC, D is a point on BC such that BD:CD = 3:2. If area of triangle ABC=40cm^2. Then find the area of triangle ACD.

24xy2z26yz2=

If 2x+2f(x)=2, then the domain of the function f(x) is

In the following figure, ABCD is a parallelogram and BC is produced to a point Q such that AD = CQ. If AQ intersect DC at P, then show that area of(△BPC) = area of (△DPQ).

Question 1Visualize 3.765 on the number line using successive magnification.

(3pq+3qr)2−18pq2r = .

Observe the construction given below. To construct triangle ABC, the given components are

Question 1(ii)Represent these numbers on the number line:−56

Abcd is square the bisector of angle DBC cut ac and CD at e and f respectively prove that bf*CE=be*df

Proof of Theorem ( Two distinct lines cannot have more than one point in common )

How to rationalize -: (a) 2−√3/2+√3 (b) 2√5+3√2/2√5−3√2

8a3 − b3 − 4ax + 2bx

The decimal form of 78 is _.

The marks obtained by 40 students in class X of a certain school in a math paper of 100 marks total are presented in the table. Find the mean using direct method.Class Interval0−1010−2020−3030−4040−50Number of students341315528.75

What is the approximate value of √2 +√3 ?

How many parts should be shaded in figure B to make it represent the same fraction as the unshaded part of figure A?

Simplify:15 - (6 + 6 × 6) ÷ (9 + 5)

the length of a focal chord of the parabola y^2 =4ax at a dis†an ce b from the vertex is c. Then 1. a^2=bc 2. a^3=b^2c 3. b^2=ac 3. b^2c=4a^{}

If one of the factors of the polynomial (3x3+25x2+36x−36) is (x+3), then find the other factors using synthetic division.

ABCD is a rhombus in which altitude from D to side AB bisects AB. Find the angles of the rhombus.

In figure, AX bisects ∠BAC as well as ∠BDC. State the three facts needed to ensure that △ACD ≅ △ABD

In ΔABC,∠B=90∘. Find the sides of the triangle, if AB = (x + 2) cm, BC = (x + 4) cm and AC = (x + 6) cm.

The distance of the point in (1,-2,3) from the plane x-y+z=5 measured parallel to the line x/2=y/3=(z-1)/6is

What is walli's theoram

Find the value of 5√16×5√2.

Two chords AB, CD of lengths 5 cm, 11 cm respectively of a circle are parallel, If the distance between AB and CD is 3 cm, find the radius of the circle.

Factorize: a4−2a3−4a+8

In each of the following, using the remainder theorem, find the remainder when f(x) is divided by g(x) and verify the result by actual division: (1−8)1. f(x) = x3 + 4x2 − 3x + 10, g(x) = x + 4

In a right angled triangle, one acute angle is double the other. Prove that the hypotenuse is double the smallest side. [4 MARKS]

You have been asked to plot graphs of the following equations: Equation 1: 3x+2y=1 Equation 2: y−2x=2 Fill the following tables (find p, q, r, s) which you will use to plot the graphs: Equation 1: x05ypq Equation 2: xrsy05

In the given figure, ABCD is a quadrilateral in which diagonals AC and BD intersect at a point E then,

The diagonals of a rectangle ABCD intersect at O. If ∠BOC=68∘, then ∠ODA is

Find the solution for the given equation x+y−82 = x+2y−148 = 3x+y−1211

The bisectors of the acute angles of a right triangle meet at O, then the angle at O between the two bisectors is

Working at the same constant rate, 7 identical machines can produce a total of 490 toys per minute.At this rate, how many toys could 10 such machines produce in 5 minutes?

Question 8XY is a line parallel to side BC of a triangle ABC. If BE || AC and CF || AB meet XY at E and F respectively,show that ar(ΔABE)=ar(ΔACF).

(x-(a+2))(x-(a-1)) can't we further simplify it as (x-a-2)(x-a+1)?

If x=2α+1 and y=α−1 is a solution of the equation 2x−3y+5=0, find the value of α.

39. When (xcube-2xsq.+px-q) is divided by (xsquare-2x-3), the remainder is (x-6). Find the values of p&q.

Question 7 x=45(x+10)

Question 47The two rational number lying between - 2 and - 5 with denominator as 1 are ___ and ___.

Abcd is square the bisector of angle DBC cut ac and CD at e and f respectively prove that bfCE=bedf

Question 47The two rational number lying between - 2 and - 5 with denominator as 1 are _ and _.