43030 + Interview Questions in Mathematics

1.	Check whether the following are quadratic equation:(x−3)(2x+1)=x(x+5)
Answer» Check whether the following are quadratic equation: $(x - 3) (2 x + 1) = x (x + 5)$

Discussion

2.	2. Let f(x)= tan x, x (-/2,/2) & g(x)= (3-x.x).find gof
Answer» 2. Let f(x)= tan x, x (-/2,/2) & g(x)= (3-x.x).find gof

Discussion

3.	Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.
Answer» Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.

Discussion

4.	If sin x=-2425, then the value of tan x is __________ .
Answer» If $\sin x = \frac{- 24}{25},$ then the value of tan x is __________ .

Discussion

5.	Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.
Answer» Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Discussion

6.	An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is
Answer» An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

Discussion

7.	If z=a+ib satisfy (4+2i)z+(8−2i)z′=−2+10i, where z′ is the complex conjugate of z, then the value of \|a+2b\| is
Answer» If $z = a + i b$ satisfy $(4 + 2 i) z + (8 - 2 i) z^{'} = - 2 + 10 i,$ where $z^{'}$ is the complex conjugate of $z$ , then the value of $\| a + 2 b \|$ is

Discussion

8.	A function f(x) is designed asFor f(x) to be a valid probability densityfunction the value of A must bef(x)=⎧⎪⎪⎨⎪⎪⎩01A(3x+5)0;x<33<x<6x>6
Answer» $A f u n c t i o n f (x) i s d e s i g n e d a s F o r f (x) t o b e a v a l i d p r o b a b i l i t y d e n s i t y f u n c t i o n t h e v a l u e o f A m u s t b e f (x) = ⎧ ⎪⎪ ⎨ ⎪⎪ ⎩ \begin{matrix} 0 \frac{1}{A} (3 x + 5) 0 \end{matrix}; \begin{matrix} x < 3 3 < x < 6 x > 6 \end{matrix}$

Discussion

9.	Consider a region R={(x,y)∈R2:x2≤y≤2x}. If a line y=α divides the area of region R into two equal parts, then which of the following is true
Answer» Consider a region $R = {(x, y) \in R^{2} : x^{2} \leq y \leq 2 x}$ . If a line $y = α$ divides the area of region $R$ into two equal parts, then which of the following is true

Discussion

10.	Find the range of f(x) = 2-\vert x+2\vert
Answer» Find the range of f(x) = 2-\vert x+2\vert

Discussion

11.	Find the equation of the straight line which makes a triangle of area 96 √3 with the axes and perpendicular from the origin to it makes an angle of 30∘ with y-axis.
Answer» Find the equation of the straight line which makes a triangle of area $96 \sqrt{3}$ with the axes and perpendicular from the origin to it makes an angle of $30^{\circ}$ with y-axis.

Discussion

12.	If α,β are the roots of ax2+bx+c=0 and α+k, β+k are the roots of px2+qx+r=0, then b2−4aca2−4pr is equal to
Answer» If $α, β$ are the roots of $a x^{2} + b x + c = 0 a n d α + k, β + k$ are the roots of $p x^{2} + q x + r = 0$ , then $\frac{b^{2} - 4 a c}{a^{2} - 4 p r}$ is equal to

Discussion

13.	In a football tournament, a team T has to play with each of the 6 other teams once. Each match can result in a win, draw or loss. Then the number of ways in which the team T finishes with more wins than losses, is
Answer» In a football tournament, a team $T$ has to play with each of the $6$ other teams once. Each match can result in a win, draw or loss. Then the number of ways in which the team $T$ finishes with more wins than losses, is

Discussion

14.	What would be the mean proportion of 25 and 400 ?
Answer» What would be the mean proportion of 25 and 400 ?

Discussion

15.	If the shortest distance between the straight lines 3(x−1)=6(y−2)=2(z−1) and 4(x−2)=2(y−λ)=(z−3), λ∈R is 1√38, then the integral value of λ is equal to:
Answer» If the shortest distance between the straight lines $3 (x - 1) = 6 (y - 2) = 2 (z - 1)$ and $4 (x - 2) = 2 (y - λ) = (z - 3), λ \in R$ is $\frac{1}{\sqrt{38}},$ then the integral value of $λ$ is equal to:

Discussion

16.	The value of sin π4+θ-cos π4-θ is(a) 2 cosθ(b) 2 sinθ(c) 1(d) 0
Answer» The value of $\sin (\frac{π}{4} + θ) - \cos (\frac{π}{4} - θ)$ is (a) 2 cosθ (b) 2 sinθ (c) 1 (d) 0

Discussion

17.	Two coins are tossed once, where E is the event of tail appearing on one coin, F is the event of one coin shows head. Then the value of P(E/F) is:
Answer» Two coins are tossed once, where $E$ is the event of tail appearing on one coin, $F$ is the event of one coin shows head. Then the value of $P (E / F)$ is:

Discussion

18.	The equation of a circle of radius 1 touching the circles x2+y2−2\|x\|=0 is
Answer» The equation of a circle of radius 1 touching the circles $x^{2} + y^{2} - 2 \| x \| = 0$ is

Discussion

19.	Which of the following cannot be the possible value of any probability?
Answer» Which of the following cannot be the possible value of any probability?

Discussion

20.	Equation of the ellipse with vertices (-4,3), (8,3) and e=56 is
Answer» Equation of the ellipse with vertices (-4,3), (8,3) and e= $\frac{5}{6}$ is

Discussion

21.	If f(x) = x2 -2 and g(x) = 2x. Find f/g.
Answer» If f(x) = x² -2 and g(x) = 2x. Find f/g.

21.

If f(x) = x2 -2 and g(x) = 2x. Find f/g.

Answer»

If f(x) = x² -2 and g(x) = 2x. Find f/g.

Discussion

22.	The equation of 2x2+3y2−8x−18y+35=k represents
Answer» The equation of $2 x^{2} + 3 y^{2} - 8 x - 18 y + 35 = k$ represents

Discussion

23.	∫1−1 x−[x] dx Equals
Answer» $\int_{- 1}^{1} x - [x] d x$ Equals

Discussion

24.	If x=2 sin x1+cos x+sin x, then prove that 1-cos x+sin x1+sin x is also equal to a.
Answer» If $x = \frac{2 \sin x}{1 + \cos x + \sin x}$ , then prove that $\frac{1 - \cos x + \sin x}{1 + \sin x}$ is also equal to a.

Discussion

25.	If the two lines →r=2^i−2^k+λ(^j−^k) and →r=^j+^k+μ(^i+2^j−α^k) intersect at a point, then the value of α=
Answer» If the two lines $\to r = 2^i - 2^k + λ (^j -^k)$ and $\to r =^j +^k + μ (^i + 2^j - α^k)$ intersect at a point, then the value of $α =$

Discussion

26.	∫-12x+1+x+x-1dx
Answer» $\int_{- 1}^{2} (\|x + 1\| + \|x\| + \|x - 1\|) d x$

Discussion

27.	Let →a=6→i−3→j−6→k and →d=→i+→j+→k. Suppose that →a=→b+→c where →b is parallel to →d and →c is perpendicular to →d. Then →c is
Answer» Let $\to a = 6 \to i - 3 \to j - 6 \to k$ and $\to d = \to i + \to j + \to k .$ Suppose that $\to a = \to b + \to c$ where $\to b is parallel to \to d and \to c is perpendicular to \to d .$ Then $\to c$ is

Discussion

28.	A function f:(R−A)→R is defined as f(x)=x+2x2−3x+4, where R is one set of real numbers and A is a finite set of points where f(x) is not defined. Then n(A)=___.
Answer» A function $f : (R - A) \to R$ is defined as $f (x) = \frac{x + 2}{x^{2} - 3 x + 4},$ where R is one set of real numbers and A is a finite set of points where f(x) is not defined. Then n(A)=___.

Discussion

29.	If the roots of the equation (a2−bc)x2+2(b2−ac)x+c2−ab=0 are equal, then
Answer» If the roots of the equation $(a^{2} - b c) x^{2} + 2 (b^{2} - a c) x + c^{2} - a b = 0$ are equal, then

Discussion

30.	Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is:
Answer» Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is:

Discussion

31.	The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is
Answer» The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is

Discussion

32.	15+4h=13 Then h=1/ ___
Answer» $\frac{1}{5} + 4 h = \frac{1}{3}$ Then $h = 1 /$ ___

Discussion

33.	Differentiate the equation. y=20/(x²-4
Answer» Differentiate the equation. y=20/(x²-4

Discussion

34.	The ratio of the coefficient of x2 to the coefficient of x10 in the expansion of (x5+4⋅3−log√3√x3)10 is
Answer» The ratio of the coefficient of $x^{2}$ to the coefficient of $x^{10}$ in the expansion of ${(x^{5} + 4 \cdot 3^{- {log}_{\sqrt{3}} \sqrt{x^{3}}})}^{10}$ is

Discussion

35.	∫ 1sin(x-a) sin (x-b)dx is equal to (a) sin b-a logsin(x-a)sin(x-b)+C (b) cosec b-a logsin(x-a)sin(x-b)+C(c) cosec b-a logsin(x-b)sin(x-a)+C (d) sin b-a logsin(x-a)sin(x-b)+C
Answer» $\int \frac{1}{\sin (x - a) \sin (x - b)} d x i s e q u a l t o (a) \sin (b - a) \log \|\frac{\sin (x - a)}{\sin (x - b)}\| + C (b) \cos e c (b - a) \log \|\frac{\sin (x - a)}{\sin (x - b)}\| + C (c) \cos e c (b - a) \log \|\frac{\sin (x - b)}{\sin (x - a)}\| + C (d) \sin (b - a) \log \|\frac{\sin (x - a)}{\sin (x - b)}\| + C$

Discussion

36.	∫π0 xf(sin x)dx=
Answer» $\int_{0}^{π} x f (s i n x) d x =$

Discussion

37.	The coefficient of x203 in the expression (x−1)(x2−2)(x3−3)⋯(x20−20) is
Answer» The coefficient of $x^{203}$ in the expression $(x - 1) (x^{2} - 2) (x^{3} - 3) \dots (x^{20} - 20)$ is

Discussion

38.	sin 3θ1+2 cos 2θ is equal to
Answer» $\frac{s i n 3 θ}{1 + 2 c o s 2 θ}$ is equal to

Discussion

39.	If the trace of two matrices A=[2a2539−6b] and B=[−b2538a−8] are equal,where a,b∈R, then 2a−b equals to
Answer» If the trace of two matrices $A = [\begin{matrix} 2 a^{2} & 5 3 & 9 - 6 b \end{matrix}]$ and $B = [\begin{matrix} - b^{2} & 5 3 & 8 a - 8 \end{matrix}]$ are equal,where $a, b \in R,$ then $2 a - b$ equals to

Discussion

40.	The solution set of 1−√1−4x2x<3 is
Answer» The solution set of $\frac{1 - \sqrt{1 - 4 x^{2}}}{x} < 3$ is

Discussion

41.	What is the meaning or definition of domain , range and co domain.
Answer» What is the meaning or definition of domain , range and co domain.

Discussion

42.	On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h–1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h–1. For an observer on a stationary platform outside, what is the(a) speed of the child running in the direction of motion of the belt ?.(b) speed of the child running opposite to the direction of motion of the belt ?(c) time taken by the child in (a) and (b) ?Which of the answers alter if motion is viewed by one of the parents?(Fig: 3.26)
Answer» On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h^–1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h^–1. For an observer on a stationary platform outside, what is the (a) speed of the child running in the direction of motion of the belt ?. (b) speed of the child running opposite to the direction of motion of the belt ? (c) time taken by the child in (a) and (b) ? Which of the answers alter if motion is viewed by one of the parents? (Fig: 3.26)

42.

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h–1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h–1. For an observer on a stationary platform outside, what is the(a) speed of the child running in the direction of motion of the belt ?.(b) speed of the child running opposite to the direction of motion of the belt ?(c) time taken by the child in (a) and (b) ?Which of the answers alter if motion is viewed by one of the parents?(Fig: 3.26)

Answer»

On a long horizontally moving belt (Fig. 3.26), a child runs to and fro with a speed 9 km h^–1 (with respect to the belt) between his father and mother located 50 m apart on the moving belt. The belt moves with a speed of 4 km h^–1. For an observer on a stationary platform outside, what is the

(a) speed of the child running in the direction of motion of the belt ?.

(b) speed of the child running opposite to the direction of motion of the belt ?

(c) time taken by the child in (a) and (b) ?

Which of the answers alter if motion is viewed by one of the parents?

(Fig: 3.26)

Discussion

43.	Find theabsolute maximum value and the absolute minimum value of thefollowing functions in the given intervals:(i) (ii) (iii) (iv)
Answer» Find the absolute maximum value and the absolute minimum value of the following functions in the given intervals: (i) (ii) (iii) (iv)

43.

Find theabsolute maximum value and the absolute minimum value of thefollowing functions in the given intervals:(i) (ii) (iii) (iv)

Answer»

Find the
absolute maximum value and the absolute minimum value of the
following functions in the given intervals:

(i) (ii)

(iii)

(iv)

Discussion

44.	How to solve inequalities involving modulus sign
Answer» How to solve inequalities involving modulus sign

Discussion

45.	25. If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2 then k is equal to
Answer» 25. If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2 then k is equal to

Discussion

46.	If X={1,2,3,4,5} and Y={1,3,5,7,9}, then which of the following relation(s) is/are not a function from X→Y?
Answer» If $X = {1, 2, 3, 4, 5}$ and $Y = {1, 3, 5, 7, 9}$ , then which of the following relation(s) is/are not a function from $X \to Y$ ?

Discussion

47.	Given ab+bc-ca = 3 and a2+b2+c2 = 31 Then find the value of (a-b+c)
Answer» Given ab+bc-ca = 3 and a²+b²+c² = 31 Then find the value of (a-b+c)

Discussion

48.	Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x (iv) cosec x (v) 3 cot x + 5 cosec x (vi) 5 sin x - 6 cos x + 7 (vii) 2 tan x - 7 sec x
Answer» Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x (iv) cosec x (v) 3 cot x + 5 cosec x (vi) 5 sin x - 6 cos x + 7 (vii) 2 tan x - 7 sec x

Discussion

49.	Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below:2x + 4y ≤ 83x + y ≤ 6x + y ≤ 4 x ≥ 0, y ≥ 0 [CBSE 2015]
Answer» Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below: 2x + 4y ≤ 8 3x + y ≤ 6 x + y ≤ 4 x ≥ 0, y ≥ 0 [CBSE 2015]

Discussion

50.	If cos α+cos β=0=sin α+sin β, then prove that cos 2α+cos 2β=−2 cos (α+β)
Answer» If $c o s α + c o s β = 0 = s i n α + s i n β$ , then prove that $c o s 2 α + c o s 2 β = - 2 c o s (α + β)$

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

Check whether the following are quadratic equation:(x−3)(2x+1)=x(x+5)

2. Let f(x)= tan x, x (-/2,/2) & g(x)= (3-x.x).find gof

Find an infinite G.P. whose first term is 1 and each term is the sum of all the terms which follow it.

If sin x=-2425, then the value of tan x is __________ .

Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

An urn contains 9 balls two of which are red, three blue and four black. Three balls are drawn at random. The probability that they are of the same colour is

If z=a+ib satisfy (4+2i)z+(8−2i)z′=−2+10i, where z′ is the complex conjugate of z, then the value of |a+2b| is

A function f(x) is designed asFor f(x) to be a valid probability densityfunction the value of A must bef(x)=⎧⎪⎪⎨⎪⎪⎩01A(3x+5)0;x&lt;33&lt;x&lt;6x&gt;6

Consider a region R={(x,y)∈R2:x2≤y≤2x}. If a line y=α divides the area of region R into two equal parts, then which of the following is true

Find the range of f(x) = 2-\vert x+2\vert

Find the equation of the straight line which makes a triangle of area 96 √3 with the axes and perpendicular from the origin to it makes an angle of 30∘ with y-axis.

If α,β are the roots of ax2+bx+c=0 and α+k, β+k are the roots of px2+qx+r=0, then b2−4aca2−4pr is equal to

In a football tournament, a team T has to play with each of the 6 other teams once. Each match can result in a win, draw or loss. Then the number of ways in which the team T finishes with more wins than losses, is

What would be the mean proportion of 25 and 400 ?

If the shortest distance between the straight lines 3(x−1)=6(y−2)=2(z−1) and 4(x−2)=2(y−λ)=(z−3), λ∈R is 1√38, then the integral value of λ is equal to:

The value of sin π4+θ-cos π4-θ is(a) 2 cosθ(b) 2 sinθ(c) 1(d) 0

Two coins are tossed once, where E is the event of tail appearing on one coin, F is the event of one coin shows head. Then the value of P(E/F) is:

The equation of a circle of radius 1 touching the circles x2+y2−2|x|=0 is

Which of the following cannot be the possible value of any probability?

Equation of the ellipse with vertices (-4,3), (8,3) and e=56 is

If f(x) = x2 -2 and g(x) = 2x. Find f/g.

The equation of 2x2+3y2−8x−18y+35=k represents

∫1−1 x−[x] dx Equals

If x=2 sin x1+cos x+sin x, then prove that 1-cos x+sin x1+sin x is also equal to a.

If the two lines →r=2^i−2^k+λ(^j−^k) and →r=^j+^k+μ(^i+2^j−α^k) intersect at a point, then the value of α=

∫-12x+1+x+x-1dx

Let →a=6→i−3→j−6→k and →d=→i+→j+→k. Suppose that →a=→b+→c where →b is parallel to →d and →c is perpendicular to →d. Then →c is

A function f:(R−A)→R is defined as f(x)=x+2x2−3x+4, where R is one set of real numbers and A is a finite set of points where f(x) is not defined. Then n(A)=___.

If the roots of the equation (a2−bc)x2+2(b2−ac)x+c2−ab=0 are equal, then

Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. Then the common ratio of the G.P. is:

The equation of the circle of radius 5 and touching the coordinate axes in third quadrant is

15+4h=13 Then h=1/ ___

Differentiate the equation. y=20/(x²-4

The ratio of the coefficient of x2 to the coefficient of x10 in the expansion of (x5+4⋅3−log√3√x3)10 is

∫ 1sin(x-a) sin (x-b)dx is equal to (a) sin b-a logsin(x-a)sin(x-b)+C (b) cosec b-a logsin(x-a)sin(x-b)+C(c) cosec b-a logsin(x-b)sin(x-a)+C (d) sin b-a logsin(x-a)sin(x-b)+C

∫π0 xf(sin x)dx=

The coefficient of x203 in the expression (x−1)(x2−2)(x3−3)⋯(x20−20) is

sin 3θ1+2 cos 2θ is equal to

If the trace of two matrices A=[2a2539−6b] and B=[−b2538a−8] are equal,where a,b∈R, then 2a−b equals to

The solution set of 1−√1−4x2x&lt;3 is

What is the meaning or definition of domain , range and co domain.

Find theabsolute maximum value and the absolute minimum value of thefollowing functions in the given intervals:(i) (ii) (iii) (iv)

How to solve inequalities involving modulus sign

25. If the line 2x+y=k passes through the point which divides the line segment joining the points (1,1) and (2,4) in the ratio 3:2 then k is equal to

If X={1,2,3,4,5} and Y={1,3,5,7,9}, then which of the following relation(s) is/are not a function from X→Y?

Given ab+bc-ca = 3 and a​​​​​​2+b​​​​​​2+c​​​​​​2 = 31 Then find the value of (a-b+c)

Find the derivative of the following functions: (i) sin x cos x (ii) sec x (iii) 5 sec x + 4 cos x (iv) cosec x (v) 3 cot x + 5 cosec x (vi) 5 sin x - 6 cos x + 7 (vii) 2 tan x - 7 sec x

Find graphically, the maximum value of Z = 2x + 5y, subject to constraints given below:2x + 4y ≤ 83x + y ≤ 6x + y ≤ 4 x ≥ 0, y ≥ 0 [CBSE 2015]

If cos α+cos β=0=sin α+sin β, then prove that cos 2α+cos 2β=−2 cos (α+β)

A function f(x) is designed asFor f(x) to be a valid probability densityfunction the value of A must bef(x)=⎧⎪⎪⎨⎪⎪⎩01A(3x+5)0;x<33<x<6x>6

The solution set of 1−√1−4x2x<3 is

Given ab+bc-ca = 3 and a2+b2+c2 = 31 Then find the value of (a-b+c)