43030 + Interview Questions in Mathematics

1.	The value of 2 cosπ13 cos 9π13+cos 3π13+cos 5π13 is ________________.
Answer» The value of $2 \cos \frac{π}{13} \cos \frac{9 π}{13} + \cos \frac{3 π}{13} + \cos \frac{5 π}{13}$ is ________________.

Discussion

2.	If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2, then y/x is -1.25
Answer» If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2, then y/x is -1.25

Discussion

3.	Evaluate the following limits:limx→0sinα+βx+sinα-βx+sin2αxcos2βx-cos2αx
Answer» Evaluate the following limits: $\lim_{x \to 0} \frac{\sin (α + β) x + \sin (α - β) x + \sin 2 α x}{\cos^{2} β x - \cos^{2} α x}$

Discussion

4.	If y=xtany, then dydx is equal to
Answer» If $y = x tan y,$ then $\frac{d y}{d x}$ is equal to

Discussion

5.	8. tan1 cosx-sinxcosx+sinx/'44
Answer» 8. tan1 cosx-sinxcosx+sinx/'44

Discussion

6.	If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane r.(3^i+4^j−12^k)+13=0, then find value of p.
Answer» If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane $r . (3^i + 4^j - 12^k) + 13 = 0$ , then find value of p.

Discussion

7.	The possible number of extremum point(s) for f(x)=x2+2cosx+2 on (0,π2) is:
Answer» The possible number of extremum point(s) for $f (x) = x^{2} + 2 cos x + 2$ on $(0, \frac{π}{2})$ is:

Discussion

8.	What is general and principal solution? And how to find them
Answer» What is general and principal solution? And how to find them

Discussion

9.	Choose the function rule that matches the given system input with its output.
Answer» Choose the function rule that matches the given system input with its output.

Discussion

10.	What is sin theta
Answer» What is sin theta

Discussion

11.	In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did hit a boundary.
Answer» In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did hit a boundary.

Discussion

12.	The value of the integral ∫3x−1(x+2)2dx is(where C is an arbitrary constant)
Answer» The value of the integral $\int \frac{3 x - 1}{(x + 2)^{2}} d x$ is (where $C$ is an arbitrary constant)

Discussion

13.	Given that the events A and B are such that and P (B) = p . Find p if they are (i) mutually exclusive (ii) independent.
Answer» Given that the events A and B are such that and P (B) = p . Find p if they are (i) mutually exclusive (ii) independent.

Discussion

14.	If R = {(x, y) : where x ∈ R and −5 ≤ x ≤ 5} is a relation, then range (R) = _______ .
Answer» If R = {(x, y) : where x ∈ R and −5 ≤ x ≤ 5} is a relation, then range (R) = _______ .

Discussion

15.	The negation of A→(A∨∼B)
Answer» The negation of $A \to (A \lor \sim B)$

Discussion

16.	If parabola y=(x−2)2 is shifted by 3 units toward right, then will be the equation of new parabola obtained.
Answer» If parabola y=(x−2)2 is shifted by 3 units toward right, then will be the equation of new parabola obtained.

Discussion

17.	The general term of the sequence 7,12,17,22,27,…is
Answer» The general term of the sequence $7, 12, 17, 22, 27, \dots$ is

Discussion

18.	Which of the following is/are simple event?
Answer» Which of the following is/are simple event?

Discussion

19.	let n be an odd natural number such that the variance of 1,2,3,4,…,n is 14. Then n is equal to
Answer» let $n$ be an odd natural number such that the variance of $1, 2, 3, 4, \dots, n$ is $14.$ Then $n$ is equal to

Discussion

20.	If cosec θ=10 then sec θ=?(a) 110(b) 210(c) 310(d) 103
Answer» If $cosec θ = \sqrt{10} then \sec θ = ?$ (a) $\frac{1}{\sqrt{1} 0}$ (b) $\frac{2}{\sqrt{10}}$ (c) $\frac{3}{\sqrt{10}}$ (d) $\frac{\sqrt{10}}{3}$

Discussion

21.	∫π20log tan x dx= [MP PET 1999; RPET 2001, 02; Karnataka CET 1999, 2000, 01, 02]
Answer» $\int_{0}^{\frac{π}{2}} l o g t a n x d x =$ [MP PET 1999; RPET 2001, 02; Karnataka CET 1999, 2000, 01, 02]

Discussion

22.	If n+1C3=2 nC2, then the value of n is
Answer» If $^{n + 1} C_{3} = 2^{n} C_{2}$ , then the value of $n$ is

Discussion

23.	Find the value of a + b2 + c3 + d4.Given that a, b, c and d are the x co-ordinates of the points which are reflections of (4, 3), (3, 2), (2, 1) and (1, 0) in x-axis.
Answer» Find the value of $a$ + $b^{2}$ + $c^{3}$ + $d^{4}$ . Given that $a$ , $b$ , $c$ and $d$ are the x co-ordinates of the points which are reflections of (4, 3), (3, 2), (2, 1) and (1, 0) in x-axis.

Discussion

24.	If g(x)=x2+x−1 and (g∘f)(x)=4x2−10x+5, then f(54) is equal to
Answer» If $g (x) = x^{2} + x - 1$ and $(g \circ f) (x) = 4 x^{2} - 10 x + 5,$ then $f (\frac{5}{4})$ is equal to

Discussion

25.	6. x2 log x
Answer» 6. x2 log x

Discussion

26.	If 5∑n=15∑m=1tan−1mn=kπ,k∈R, then [k]=where ([.] denotes greatest integer function)
Answer» If $5 \sum n = 1 5 \sum m = 1 {tan}^{- 1} \frac{m}{n} = k π, k \in R,$ then $[k] =$ where ( $[.]$ denotes greatest integer function)

Discussion

27.	If an open box with a square base is to be made of a given quantity of cardboard of area c2, then show that the maximum volume of the box is c36√3 cu units.
Answer» If an open box with a square base is to be made of a given quantity of cardboard of area $c^{2},$ then show that the maximum volume of the box is $\frac{c^{3}}{6 \sqrt{3}}$ cu units.

Discussion

28.	Let n(A–B)=25+X,n(B–A)=2X and n(A∩B)=2X. If n(A)=2(n(B)), then X is
Answer» Let $n (A - B) = 25 + X, n (B - A) = 2 X$ and $n (A \cap B) = 2 X .$ If $n (A) = 2 (n (B)),$ then $X$ is

Discussion

29.	The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observations, is
Answer» The variance of $20$ observations is $5$ . If each observation is multiplied by $2,$ then the new variance of the resulting observations, is

Discussion

30.	Find the image of the point (3, 8) with respect to the line x + 3 y = 7 assuming the line to be a plane mirror.
Answer» Find the image of the point (3, 8) with respect to the line x + 3 y = 7 assuming the line to be a plane mirror.

Discussion

31.	Let f(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩e−x22−cosxxln(1+x)sinx(ex−1), x≠0 k , x=0. If f(x) is continuous at x=0, then k equals
Answer» Let $f (x) = ⎧ ⎪⎪⎪⎪ ⎨ ⎪⎪⎪⎪ ⎩ \begin{matrix} \frac{e^{\frac{- x^{2}}{2}} - cos x}{x ln (1 + x) sin x (e^{x} - 1)}, & x \neq 0 k, & x = 0 \end{matrix} .$ If $f (x)$ is continuous at $x = 0$ , then $k$ equals

Discussion

32.	The value of k for which the Planes x-y+z+1=0, Kx+3y+2z-3=0 and 3x+ky+z-2=0 form a triangular prism must be equal to
Answer» The value of k for which the Planes x-y+z+1=0, Kx+3y+2z-3=0 and 3x+ky+z-2=0 form a triangular prism must be equal to

Discussion

33.	The equation of the auxiliary circle of the hyperbola x264−y236=1 is
Answer» The equation of the auxiliary circle of the hyperbola $\frac{x^{2}}{64} - \frac{y^{2}}{36} = 1$ is

Discussion

34.	The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5, is
Answer» The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5, is

Discussion

35.	what is the nth term of the sequence 2, 5, 8, 11?
Answer» what is the nth term of the sequence 2, 5, 8, 11?

Discussion

36.	If limx→0f(x)x=10 and limx→0f(sin x)g(x) cos2 x=5 with g(0)=0, then the value of limx→0g(1−cos x)x2is
Answer» If $lim x \to 0 \frac{f (x)}{x} = 10 and lim x \to 0 \frac{f (sin x)}{g (x) {cos}^{2} x} = 5$ with $g (0) = 0$ , then the value of $lim x \to 0 \frac{g (1 - cos x)}{x^{2}}$ is

Discussion

37.	∫(1x−3−1x2−3x) dx= ____ +C, x>3
Answer» $\int (\begin{matrix} \frac{1}{x - 3} - \frac{1}{x^{2} - 3 x} \end{matrix}) d x =$ ____ $+ C, x > 3$

Discussion

38.	25. If x=a(Δ +sinΔ ) , y=(1-cosΔ ) Find second order derivative at Δ =÷ 2
Answer» 25. If x=a(Δ +sinΔ ) , y=(1-cosΔ ) Find second order derivative at Δ =÷ 2

Discussion

39.	Write the set builder form A = {−1, 1}
Answer» Write the set builder form $A = {- 1, 1}$

Discussion

40.	If sin θ : a = cos α : 1 and tan θ : b = cot α : 1, then the value of (a sin α) : b equals
Answer» If sin θ : a = cos α : 1 and tan θ : b = cot α : 1, then the value of (a sin α) : b equals

Discussion

41.	If a≠0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2=4ax and x2=4ay , then
Answer» If $a \neq 0$ and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas $y^{2} = 4 a x$ and $x^{2} = 4 a y$ , then

Discussion

42.	A circle is inscribed in an isosceles trapezium ABCD in which AB = 10 and DC = 30. Find the area of the circle. (1) 45 pi(2) 50 pi(3) 60 pi(4) 75 pi
Answer» A circle is inscribed in an isosceles trapezium ABCD in which AB = 10 and DC = 30. Find the area of the circle. (1) 45 pi (2) 50 pi (3) 60 pi (4) 75 pi

Discussion

43.	2, 2x2 + x + 1 = 0
Answer» 2, 2x2 + x + 1 = 0

Discussion

44.	Mark the correct alternative in each of the following:If x is a real number and x<5, then(a) x≥5(b) -5<x<5(c) x≤-5(d) -5≤x≤5
Answer» Mark the correct alternative in each of the following: If x is a real number and $\|x\|$ $<$ 5, then (a) x $\geq$ 5 (b) $-$ 5 $<$ x $<$ 5 (c) x $\leq$ $-$ 5 (d) $-$ 5 $\leq$ x $\leq$ 5

Discussion

45.	Find the transpose of the following matrix. [1−123]
Answer» Find the transpose of the following matrix. $[\begin{matrix} 1 & - 1 2 & 3 \end{matrix}]$

Discussion

46.	If f(x)=∣∣∣∣0x−ax−bx+a0x−cx+bx+c0∣∣∣∣, which of the following is true? (a) f(a) = 0 (b) f(b) = 0 (c) f(0) = 0 (d) f(1) = 0
Answer» If $f (x) = ∣ ∣∣ ∣ \begin{matrix} 0 & x - a & x - b x + a & 0 & x - c x + b & x + c & 0 \end{matrix} ∣ ∣∣ ∣$ , which of the following is true? (a) f(a) = 0 (b) f(b) = 0 (c) f(0) = 0 (d) f(1) = 0

46.

If f(x)=∣∣∣∣0x−ax−bx+a0x−cx+bx+c0∣∣∣∣, which of the following is true? (a) f(a) = 0 (b) f(b) = 0 (c) f(0) = 0 (d) f(1) = 0

Answer»

If $f (x) = ∣ ∣∣ ∣ \begin{matrix} 0 & x - a & x - b x + a & 0 & x - c x + b & x + c & 0 \end{matrix} ∣ ∣∣ ∣$ ,

which of the following is true?

(a) f(a) = 0
(b) f(b) = 0
(c) f(0) = 0
(d) f(1) = 0

Discussion

47.	The graph of the function y=f(x) is symmetrical about line x=2, then
Answer» The graph of the function $y = f (x)$ is symmetrical about line $x = 2,$ then

Discussion

48.	The value of cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65 is
Answer» The value of $c o s \frac{π}{65} c o s \frac{2 π}{65} c o s \frac{4 π}{65} c o s \frac{8 π}{65} c o s \frac{16 π}{65} c o s \frac{32 π}{65}$ is

Discussion

49.	By using properties of definite integrals, evaluate the integrals Let ∫π2−π2sin2xdx.
Answer» By using properties of definite integrals, evaluate the integrals Let $\int_{- \frac{π}{2}}^{\frac{π}{2}} s i n^{2} x d x .$

Discussion

50.	Let the equation of a curve be x=a(theta+sintheta),y=a(1-costheta). If theta changes at a constant rate k then the rate of change of the slope of the tangent to the curve at theta=/3 is
Answer» Let the equation of a curve be x=a(theta+sintheta),y=a(1-costheta). If theta changes at a constant rate k then the rate of change of the slope of the tangent to the curve at theta=/3 is

Discussion

Explore topic-wise InterviewSolutions in Current Affairs.

The value of 2 cosπ13 cos 9π13+cos 3π13+cos 5π13 is ________________.

If Point P (-4,6) divides the line segment AB with A(-6,10) and B(x,y) in the ratio 3:2, then y/x is -1.25

Evaluate the following limits:limx→0sinα+βx+sinα-βx+sin2αxcos2βx-cos2αx

If y=xtany, then dydx is equal to

8. tan1 cosx-sinxcosx+sinx/'44

If the points (1, 1, p) and (-3, 0, 1) be equidistant from the plane r.(3^i+4^j−12^k)+13=0, then find value of p.

The possible number of extremum point(s) for f(x)=x2+2cosx+2 on (0,π2) is:

What is general and principal solution? And how to find them

Choose the function rule that matches the given system input with its output.

What is sin theta

In a cricket match, a batswoman hits a boundary 6 times out of 30 balls she plays. Find the probability that she did hit a boundary.

The value of the integral ∫3x−1(x+2)2dx is(where C is an arbitrary constant)

Given that the events A and B are such that and P (B) = p . Find p if they are (i) mutually exclusive (ii) independent.

If R = {(x, y) : where x ∈ R and −5 ≤ x ≤ 5} is a relation, then range (R) = _______ .

The negation of A→(A∨∼B)

If parabola y=(x−2)2 is shifted by 3 units toward right, then will be the equation of new parabola obtained.

The general term of the sequence 7,12,17,22,27,…is

Which of the following is/are simple event?

let n be an odd natural number such that the variance of 1,2,3,4,…,n is 14. Then n is equal to

If cosec θ=10 then sec θ=?(a) 110(b) 210(c) 310(d) 103

∫π20log tan x dx= [MP PET 1999; RPET 2001, 02; Karnataka CET 1999, 2000, 01, 02]

If n+1C3=2 nC2, then the value of n is

Find the value of a + b2 + c3 + d4.Given that a, b, c and d are the x co-ordinates of the points which are reflections of (4, 3), (3, 2), (2, 1) and (1, 0) in x-axis.

If g(x)=x2+x−1 and (g∘f)(x)=4x2−10x+5, then f(54) is equal to

6. x2 log x

If 5∑n=15∑m=1tan−1mn=kπ,k∈R, then [k]=where ([.] denotes greatest integer function)

If an open box with a square base is to be made of a given quantity of cardboard of area c2, then show that the maximum volume of the box is c36√3 cu units.

Let n(A–B)=25+X,n(B–A)=2X and n(A∩B)=2X. If n(A)=2(n(B)), then X is

The variance of 20 observations is 5. If each observation is multiplied by 2, then the new variance of the resulting observations, is

Find the image of the point (3, 8) with respect to the line x + 3 y = 7 assuming the line to be a plane mirror.

Let f(x)=⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩e−x22−cosxxln(1+x)sinx(ex−1), x≠0 k , x=0. If f(x) is continuous at x=0, then k equals

The value of k for which the Planes x-y+z+1=0, Kx+3y+2z-3=0 and 3x+ky+z-2=0 form a triangular prism must be equal to

The equation of the auxiliary circle of the hyperbola x264−y236=1 is

The sum of all natural numbers less than 200, that are divisible neither by 3 nor by 5, is

what is the nth term of the sequence 2, 5, 8, 11?

If limx→0f(x)x=10 and limx→0f(sin x)g(x) cos2 x=5 with g(0)=0, then the value of limx→0g(1−cos x)x2is

∫(1x−3−1x2−3x) dx= ____ +C, x&gt;3

25. If x=a(Δ +sinΔ ) , y=(1-cosΔ ) Find second order derivative at Δ =÷ 2

Write the set builder form A = {−1, 1}

If sin θ : a = cos α : 1 and tan θ : b = cot α : 1, then the value of (a sin α) : b equals

If a≠0 and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2=4ax and x2=4ay , then

A circle is inscribed in an isosceles trapezium ABCD in which AB = 10 and DC = 30. Find the area of the circle. (1) 45 pi(2) 50 pi(3) 60 pi(4) 75 pi

2, 2x2 + x + 1 = 0

Mark the correct alternative in each of the following:If x is a real number and x&lt;5, then(a) x≥5(b) -5&lt;x&lt;5(c) x≤-5(d) -5≤x≤5

Find the transpose of the following matrix. [1−123]

If f(x)=∣∣∣∣0x−ax−bx+a0x−cx+bx+c0∣∣∣∣, which of the following is true? (a) f(a) = 0 (b) f(b) = 0 (c) f(0) = 0 (d) f(1) = 0

The graph of the function y=f(x) is symmetrical about line x=2, then

The value of cos π65 cos 2π65 cos 4π65 cos 8π65 cos 16π65 cos 32π65 is

By using properties of definite integrals, evaluate the integrals Let ∫π2−π2sin2xdx.

Let the equation of a curve be x=a(theta+sintheta),y=a(1-costheta). If theta changes at a constant rate k then the rate of change of the slope of the tangent to the curve at theta=/3 is

∫(1x−3−1x2−3x) dx= ____ +C, x>3

Mark the correct alternative in each of the following:If x is a real number and x<5, then(a) x≥5(b) -5<x<5(c) x≤-5(d) -5≤x≤5