Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

If sin(x+y)sin(x−y)=a+ba−b, then tan xtan y=

Answer»

If sin(x+y)sin(x−y)=a+ba−b, then tan xtan y=

2.

If |a|<1 and |b|<1, then the sum of the series 1+(1+a)b+(1+a+a2)b2+(1+a+a2+a3)b3+⋯ is

Answer»

If |a|<1 and |b|<1, then the sum of the series
1+(1+a)b+(1+a+a2)b2+(1+a+a2+a3)b3+⋯ is

3.

Q. 26\quad Is \vert\vec a+\vec b\vert greater than \vert\vec a\vert+\vert\vec b\vert or less than ? Give reason.

Answer» Q. 26\quad Is \vert\vec a+\vec b\vert greater than \vert\vec a\vert+\vert\vec b\vert or less than ? Give reason.
4.

If A = [145326] then second element of second row of 3A = _____. ___

Answer»

If A = [145326] then second element of second row of 3A = _____.


___
5.

solve the inequality step-by-step.(x−1)^99(x−5)^100-------------------

Answer» solve the inequality step-by-step.
(x−1)^99(x−5)^100
------------------- <0
(x−3)^98(x−6)^97
6.

Let z=√32−i2. Then the smallest positive integer n such that (z95+i67)94=zn is

Answer»

Let z=√32−i2. Then the smallest positive integer n such that (z95+i67)94=zn is

7.

If the tangents from (1,1) to the circle x2+y2−4x+k = 0 are pendicular then k =

Answer»

If the tangents from (1,1) to the circle x2+y2−4x+k = 0 are pendicular then k =


8.

If →a and →b are two vectors with magnitude 1 and 3 respectively and (1−3→a.→b)2+|2→a+→b+3(→a×→b)|2=98. Then find the angle between →a and →b

Answer»

If →a and →b are two vectors with magnitude 1 and 3 respectively and (1−3→a.→b)2+|2→a+→b+3(→a×→b)|2=98.
Then find the angle between →a and →b

9.

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

Answer»

The sum of integers from 1 to 100 that are divisible by 2 or 5 is



10.

If , then what can be concluded about the vector ?

Answer» If , then what can be concluded about the vector ?
11.

Prove that the following function f(x) =x²-x+1 is neither strictly increasing nor strictly decreasing on (-1, 1)

Answer» Prove that the following function f(x) =x²-x+1 is neither strictly increasing nor strictly decreasing on (-1, 1)
12.

The general solution of the differential equation (ex+1) y dy=(y+1) ex dx is (where c is a constant of integration)

Answer»

The general solution of the differential equation (ex+1) y dy=(y+1) ex dx is (where c is a constant of integration)

13.

______________ matrix is both symmetric and skew-symmetric matrix.

Answer» ______________ matrix is both symmetric and skew-symmetric matrix.
14.

Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.

Answer»

Determine the number of 5 cards combinations out of a deck of 52 cards if there is exactly one ace in each combination.

15.

If A = {1, 3, 5, 7, 9} and B = {2, 4, 6, 8}, then the set builder representation of A U B is

Answer»

If A = {1, 3, 5, 7, 9} and B = {2, 4, 6, 8}, then the set builder representation of A U B is


16.

sin ax htlim sínar, ab * O14.

Answer» sin ax htlim sínar, ab * O14.
17.

If Cij is the cofactor of the element aij of the matrix A=2-3560415-7, then write the value of a32C32.

Answer» If Cij is the cofactor of the element aij of the matrix A=2-3560415-7, then write the value of a32C32.
18.

Let e1 and e2 are the eccentricities of 16x2+9y2=144 and 16x2−9y2=144 respectively, then which of the following is/are correct

Answer»

Let e1 and e2 are the eccentricities of 16x2+9y2=144 and 16x2−9y2=144 respectively, then which of the following is/are correct

19.

If the equation x² + px + p = 0, where p is an integer, has both roots integers, then how many integral values can (p² - 4p) attain?

Answer» If the equation x² + px + p = 0, where p is an integer, has both roots integers, then how many integral values can (p² - 4p) attain?
20.

If in a triangle ABC, (a+b+c)(b+c−a)=λbc, then :

Answer»

If in a triangle ABC, (a+b+c)(b+c−a)=λbc, then :

21.

Evaluate the following : (i) 2x3+2x2−7x+72, when x=3−5i2(ii) x4−4x3+4x2+8x+44, when x=3+2i(iii) x4+4x3+6x2+4x+9, when x=−1+i√2(iv) x6+x4+x2+1, when x=1+i√2(v) 2x4+5x3+7x2−x+41, when x=−2−√3i

Answer»

Evaluate the following :

(i) 2x3+2x2−7x+72, when x=3−5i2(ii) x4−4x3+4x2+8x+44, when x=3+2i(iii) x4+4x3+6x2+4x+9, when x=−1+i√2(iv) x6+x4+x2+1, when x=1+i√2(v) 2x4+5x3+7x2−x+41, when x=−2−√3i

22.

Which one of the images are symmetrical?

Answer»

Which one of the images are symmetrical?

23.

limx→01−cosxx2is−−−−−−−−−−−−−

Answer»

limx→01−cosxx2is−−−−−−−−−−−−−



24.

For the following, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b. xa+yb=1

Answer»

For the following, form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.

xa+yb=1

25.

Show that the points (2,3),(3,1) and (1,5) are collinear.

Answer» Show that the points (2,3),(3,1) and (1,5) are collinear.
26.

if f(x) = root (x+root 2x-1) - root (x-root 2x-1), then find {f(2020) + f(2021) + f(2022)}^2

Answer» if f(x) = root (x+root 2x-1) - root (x-root 2x-1), then find {f(2020) + f(2021) + f(2022)}^2
27.

Which of the following is an indeterminate form (where [.] denotes greatest integer function)

Answer»

Which of the following is an indeterminate form (where [.] denotes greatest integer function)

28.

The differential equation representing the family of circles with their centres on x−axis and whose radius is equal to the distance from from (−1,2) to the line 3x+4y−15=0, is given by y2[(dydx)2+k]=4, then k2+5 is equal to

Answer» The differential equation representing the family of circles with their centres on x−axis and whose radius is equal to the distance from from (−1,2) to the line 3x+4y−15=0, is given by y2[(dydx)2+k]=4, then k2+5 is equal to
29.

The value of the expression tan 12cos-125 is ​(a) 2+5 (b) 5-2 (c) 5+22 (d) 5+2

Answer» The value of the expression tan 12cos-125 is

​(a) 2+5 (b) 5-2 (c) 5+22 (d) 5+2
30.

If k ϵ N and Ik=∫2kπ−2kπ|sin x|[sinx]dx, (where [.] denotes greatest integer function), then

Answer»

If k ϵ N and Ik=∫2kπ−2kπ|sin x|[sinx]dx, (where [.] denotes greatest integer function), then

31.

Evaluate: ∣∣∣∣∣0xy2xz2x2y0yz2x2zzy20∣∣∣∣∣

Answer»

Evaluate:
∣∣
∣
∣
∣
0xy2xz2x2y0yz2x2zzy20∣∣
∣
∣
∣

32.

A curve y=f(x),x∈R satisfying the differential equation e−axy′+x(ax+2)=a2(1+a2+ax) is increasing only in the interval [−2,1]. If the curve intersects at the positive x and y axes at A(p,0) and B(0,q) such that p+q&lt;4, then [pq] is , where [.] represents the greatest integer function.

Answer» A curve y=f(x),x∈R satisfying the differential equation e−axy′+x(ax+2)=a2(1+a2+ax) is increasing only in the interval [−2,1]. If the curve intersects at the positive x and y axes at A(p,0) and B(0,q) such that p+q<4, then [pq] is ,
where [.] represents the greatest integer function.
33.

If a= -1, b=1/2, then find the value of(2a3 b​​​​​​2)3

Answer» If a= -1, b=1/2, then find the value of(2a3 b​​​​​​2)3
34.

If for a complex number z1 and z2, arg(z1)−arg(z2)=0, then |z1−z2| is equal to

Answer»

If for a complex number z1 and z2, arg(z1)−arg(z2)=0, then |z1−z2| is equal to

35.

Let A,B,C be finite sets. Suppose that n(A)=10,n(B)=15,n(C)=20,n(A∩B)=8 and n(B∩C)=9. Then the maximum possible value of n(A∪B∪C) is

Answer» Let A,B,C be finite sets. Suppose that n(A)=10,n(B)=15,n(C)=20,n(A∩B)=8 and n(B∩C)=9. Then the maximum possible value of n(A∪B∪C) is
36.

Let f:R→R be a differentiable function such that f(0)=0, f(π2)=3 and f′(0)=1. If g(x)=π2∫x[f′(t)cosec t−cott cosec t f(t)]dtfor x∈(0,π2], then limx→0g(x)=

Answer» Let f:R→R be a differentiable function such that f(0)=0, f(π2)=3 and f′(0)=1. If g(x)=π2∫x[f′(t)cosec t−cott cosec t f(t)]dtfor x∈(0,π2], then limx→0g(x)=
37.

39. n~1xdr--10

Answer» 39. n~1xdr--10
38.

If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is

Answer»

If circle x2+y2−6x−10y+c=0 does not touch (or) intersect the coordinates axes and the point (1,4) is inside the circle, then the range of c is

39.

46. Integral (cosx - sinx)÷ (1 - sin2x)

Answer» 46. Integral (cosx - sinx)÷ (1 - sin2x)
40.

With usual notation in a △ABC, if (1r1+1r2)(1r2+1r3)(1r3+1r1)=KR3a2b2c2, then K has the value equal to

Answer» With usual notation in a △ABC, if (1r1+1r2)(1r2+1r3)(1r3+1r1)=KR3a2b2c2, then K has the value equal to
41.

Let f:R→Z be a continuous function such that f(4)=4. Then the value of f(5) is

Answer» Let f:R→Z be a continuous function such that f(4)=4. Then the value of f(5) is
42.

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4 Find P(AB).

Answer»

Let A and B be independent events with P(A) = 0.3 and P(B) = 0.4 Find
P(AB).

43.

If (a+√2bcosx)(a−√2bcosy)=a2−b2, where a&gt;b&gt;0, then dxdy at (π4,π4) is

Answer»

If (a+√2bcosx)(a−√2bcosy)=a2−b2, where a>b>0, then dxdy at (π4,π4) is

44.

Integrate the following functions. ∫sinx1+cosxdx.

Answer»

Integrate the following functions.
∫sinx1+cosxdx.

45.

The coefficient of the middle term in the binomial expansion in powers of x of (1+αx)4 and of (1−αx)6 is the same, if α equals

Answer»

The coefficient of the middle term in the binomial expansion in powers of x of (1+αx)4 and of (1−αx)6 is the same, if α equals

46.

The ninth term of an A.P is -32, and the sum ofeleventh and thirteenth terms is -94.find the commondifference of the A.P

Answer» The ninth term of an A.P is -32, and the sum of
eleventh and thirteenth terms is -94.find the common
difference of the A.P
47.

The value of limx→∞⎡⎢⎢⎣(8(xn/ex)−27(xn/ex))ex(4(xn/ex)+6(xn/ex)+9(xn/ex))xn⎤⎥⎥⎦, where n∈N is

Answer»

The value of limx→∞⎡⎢
⎢
⎣
(8(xn/ex)−27(xn/ex))ex(4(xn/ex)+6(xn/ex)+9(xn/ex))xn⎤⎥
⎥
⎦
,
where n∈N is

48.

Findthe inverse of each of the matrices, if it exists.

Answer»

Find
the inverse of each of the matrices, if it exists
.



49.

If f(x)=sin4x+cos4x−12sin2x, then the range of f(x) is

Answer»

If f(x)=sin4x+cos4x−12sin2x, then the range of f(x) is

50.

Let the point B be the reflection of the point A(2,3) with respect to the line 8x−6y−23=0. Let ΓA and ΓB be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles ΓA and ΓB such that both the circles are on the same side of T. If C is the point of intersection of T and line passing through A and B, then the length of the line segment AC is

Answer» Let the point B be the reflection of the point A(2,3) with respect to the line 8x−6y−23=0. Let ΓA and ΓB be circles of radii 2 and 1 with centres A and B respectively. Let T be a common tangent to the circles ΓA and ΓB such that both the circles are on the same side of T. If C is the point of intersection of T and line passing through A and B, then the length of the line segment AC is