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.

For b gt a gt 0, prove that 2/3+In a lt (b sqrtb In b -a sqrta In a)/(sqrtb-asqrta)lt 2/3 + Inb

Answer»
Discussion
2.

x = 1 is the radical axis of two rthognally intersecting circles . Ifx^(2) + y^(2) = 4is one of the circles then the othercircle

Answer»

`x^(2) + y^(2) - 4X + 4 = 0 `
`x^(2) + y^(2) - 8X + 4= 0 `
`x^(2) + y^(2) + 8x- 4= 0 `
none

Answer :B
Discussion
3.

Assertion (A) : coefficient x^(n) in log(1+x) is ((-1)^(n-1))/(n) when |x| lt 1. Reason (R ) : Coefficient of x^(n) in log(1-x) is-1//2 when |x| lt 1.

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A is true, R is true `R rArr A`
A is true, R is true, `R CANCEL rArrA`
A is true, R is FALSE
A is false R is true

ANSWER :C
Discussion
4.

cos[2"sin"^(-1)3/4+"cos"^(-1)3/4]=

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`3/5`
`-3/4`
Does not EXIST
`3/4`

ANSWER :B
Discussion
5.

By using the properties of definite integrals, evaluate the integrals int_(0)^(2pi)cos^(5)xdx

Answer»


ANSWER :`2(0)=0`
Discussion
6.

If the roots of the equation (4a - a^(2) - 5) x^(2)- (2a - 1) x + 3a = 0, a in R, are real and lie on opposite sides on unity, then the a liesin the interval :

Answer»

(1,5)
(1,4)
`(3 , INFTY)`
`(- infty, 4)`

ANSWER :B
Discussion
7.

Using the method of integration, find the area of the smaller region bounded by the ellipse x^(2)/9+y^(2)/4=1 and the line x/3+y/2=1.

Answer»


ANSWER :`3/2 (pi-2)`
Discussion
8.

Let D( R) denote the set of all differentiable functions defined on R. Define a relation ~ on D(R) as follows: f, g in D( r), f ~ g if f(x)g'(x) lt 0 AA x in R, Then

Answer»

~ is REFLEXIVE only
~ is TRANSITIVE but not SYMMETRIC
~ is not transitive
NONE of the above

ANSWER :D
Discussion
9.

Let a_1,a_2,a_3,a_4,a_5be a G.P. Of positive real numbers such that A.M.Of a_2 and a_4 is 117 and G.M. Of a_2 and a_4 is 108. Then A.M. Of a_1 and a_5 is :

Answer»

145.5
108
117
144.5

Answer :A
Discussion
10.

Evaluate the following integrals inte^(x)((xlogx+1)/(x))dx

Answer»


ANSWER :`E^(X) LOG x + C`
Discussion
11.

underset(k=1)overset(oo)Sigma (1)/(k!)(underset(n=1)overset(k)Sigma2^(n-1))=

Answer»

E
`e^(2)+e`
`e^(2)`
`e^(2)-e`

ANSWER :D
Discussion
12.

Two balls are drawn from a bag containing 5 white and 7 black balls. Find the probability od selecting 2 white balls if

Answer»

SOLUTION :TWO balls are DRAWN from a bag containing 5 white and 7 black balls.`THEREFORE absS=12`.
Discussion
13.

The roots of the equation x^5- 40x^4+ Px^3+ Qx^2+ Rx + 5 = 0 are in geometric progression. The sum of their reciprocals is 10. Then |S| is equal to :

Answer»


ANSWER :32
Discussion
14.

Probability of solving specific problem independently. If both try to solve the problem independently, find the probability that the problem is solved

Answer»

<P>

SOLUTION :P(A) = 1/2, P(A') = 1-1/2=1/2
P(B) = 1/3, P(B') = 1-1/3=2/3
P(PROBLEM solved)
=1-P(Problem not sloved)
=1-`P(A'nnB')`
=1-P(A') P(B')
=`1-1/2xx2/3=1-1/3=2/3`
Discussion
15.

Probability of solving specific problem independently. If both try to solve the problem independently, find the probability that exactly one of them solves the problem

Answer»

<P>

Solution :P(A) = 1/2, P(A') = 1-1/2=1/2
P(B) = 1/3, P(B') = 1-1/3=2/3
P(exaxtly one of them solves the problem)
=`P[(ANNB')UU(A'nnB)]`
=`P(AnnB')+P(A'nnB)`
=`P(A)P(B')+P(A')P(B)`
=`1/2xx2/3+1/2xx2/3=2/6+1/6`
=3/6=1/2
Discussion
16.

Let E and F be events with P(E) = 3/5,P(F) = 3/10 and P(EnnF)=1/5.Are E and F independent?

Answer»

Solution :P(E) P(F0=3/5xx3/10=9/50`NE P(ENNF)` THUS,E and F are not INDEPENDENT.
Discussion
17.

vec(a)=6hat(i)+7hat(j)+7hat(k),vec(b)=3hat(i)+2hat(j)-2hat(k),P(1,2,3) If A is the point with position vector vec(a) then area of the DeltaPLA in square units is equal to -

Answer»

`3sqrt(6)`
`7sqrt((17)/(2))`
`SQRT(17)`
`(7)/(2)`

ANSWER :B
Discussion
18.

If tan (x+y) = e^(x+y), then (dy)/(dx):

Answer»

is always equal to -1
may or may not be equal to -1
`(dy)/(DX) `cannot be obtained
None of these

Solution :`TAN (X + y) = e^(x+y)`
` RARR sec^2 (x+y) [1+(dy)/(dx)]=e^(x+y)[1+(dy)/(dx)]`
` therefore (dy)/(dx) = -1 "or " 1+e^(2(x+y)) = e^(x+y)` (not possible)
` 1+t^2 -t = 0 rArr (t - 1/t)^2 +3/4 =0 therefore (dy)/(dx) = -1 AA x,y`
Discussion
19.

intsinx/(cos^2x)dx

Answer»

SOLUTION :`intsinx/(cos^2x)DX=intsinx/(COSX)XX1/(cosx)dx
=`intsecx xxtanxdx=secx+C`
Discussion
20.

If A+B+C=2S then cos^(2)S+cos^(2)(S-A)+cos^(2)(S-B)+cos^(2)(S-C)=

Answer»

`2sinA+cosBsinC`
`4 COS A//2 cos B//2 cos C//2`
`2+2cos A cos B cos C`
`SINA sinB`

Answer :C
Discussion
21.

If int_(n)^(n+1) f(x) dx = n^(2) +n, AA n in I then the value of int_(-3)^(3) f(x) dx is equal to

Answer»

6
10
16
12

Answer :C
Discussion
22.

Let x represent the difference between the number of heads and thenumbers of tails obtained when a coin is tossed 6 times. Then possible values of X is

Answer»

{6,4,2,0}
{1,2,4,}
{3,4,6}
{1,6,9}

ANSWER :A
Discussion
23.

Number of points lying on the line 7x+4y+2=0 which is equidistant from the lines 15x^(2) + 56xy+ 48y^(2)=0 is

Answer»

2
0
1
None of these

Answer :A
Discussion
24.

5-digit number are formed using 2,3,5,7,9 with out repeating the digits. If p is the number of such numbers that exceeds 20000 and q be the number of those that lie between 30000 and 90000, then p:q is

Answer»

`6 : 5 `
`3 : 2 `
`4 : 3 `
`5 : 3`

ANSWER :D
Discussion
25.

If ""^(n-1)C_(3)+""^(n-1)C_(4)gt""^(n)C_(3), then

Answer»

`ngt5`
`ngt6`
`ngt7`
`ngt8`

ANSWER :C
Discussion
26.

Evaluate the definite integrals in exercise. overset((pi)/(2)) underset(0)int (cos^(2)xdx)/(cos^(2)x+4 sin^(2)x)

Answer»


ANSWER :`(PI)/(6)`
Discussion
27.

An equation of the curve satisfying xdy - ydx = sqrt(x^(2) - y^(2))dx and y(1) = 0 is

Answer»

`y = x^(2)log|SIN x|`
`y = x sin(log|x|)`
`y^(2) = x(x-1)^(2)`
`y = 2X^(2)(x-1)`

ANSWER :B
Discussion
28.

Write the number of solution of the following system of equation. a_1x+b_1y+c_1z=0 a_2x+b_2y+c_2z=0 a_3x+b_3y+c_3z=0 and[[a_1,b_1,c_1],[a_2,b_2,c_2],[a_3,b_3,c_3]] =0

Answer»

SOLUTION :INFINITE solution as
`Delta=Delta_1=Delta_2=Delta_3=0`
Discussion
29.

Let S = {1, 2, 3,…., 50} and A_(k) be the set of multiples of k in S for k in N. IF x_(k) is a number chosen from A_(k), then match the items of List-I with the items of List-II. The correct match is

Answer»

A B C D
VI I IV V
A B C D
III I VI V
A B C D
II V I IV
A B C D
VI I III V

Answer :D
Discussion
30.

For real x, the greatest value of (x^(2)+2x+4)/(2x^(2)+4x+9) is

Answer»

1
`-1 `
`(1)/(2)`
`(1)/(4)`

ANSWER :C
Discussion
31.

I: The modulus of (sqrt3 + i)/((1 + i) (1 + sqrt3i)) is (1)/(sqrt2) II : The least positive value of n for which ((1 - i)/(1 + i))^(n)= 1 is 2 Which of the statements are true

Answer»

only I
only II
Both I & II
NEITHER I nor II

Answer :C
Discussion
32.

If the ordered pairs (x_(1), y_(1)) and (x_(2), y_(2)) satisfying the system of equations log_(10)y-log_(10)|x|=log_(100)4 and log_(100)|x+y|=1/2, find the value of (x_(1)+x_(2)+y_(1)+y_(2))

Answer»


ANSWER :`003`
Discussion
33.

{:(" "Lt),(n rarr oo):} [(sqrt(n^(2)-1^(2)))/(n^(2))+(sqrt(n^(2)-2^(2)))/(n^(2))+(sqrt(n^(2)-3^(2)))/(n^(2)).+....n "terms"]=

Answer»

`pi/4`
`pi/2`
`pi/3`
`pi/6`

ANSWER :A
Discussion
34.

If alphaandbeta are not the multiple of (pi)/(2)and [{:(cos^(2)alpha,cosalphasinalpha),(cosalphasinalpha,sin^(2)alpha):}]xx[{:(cos^(2)beta,sinbetacosbeta),(sinbetacosbeta,sin^(2)beta):}]=[{:(0,0),(0,0):}]then alpha-beta is ......

Answer»

any MULTIPLE of `PI`
odd multiple of `(pi)/(2)`
0
odd multiple of `pi`

ANSWER :B
Discussion
35.

If three successive coefficients in (1+x)^n are 6,15,20 then n =

Answer»

5
7
6
9

Answer :C
Discussion
36.

The remainder when 2^(2000) is divided by 17 is

Answer»

1
2
8
12

Answer :A
Discussion
37.

Find the direction cosines of the vector joining the points A(1,2,-3) and B(-1,-2,1) directed fromA to B.

Answer»


ANSWER :`-(1)/(3),-(2)/(3),(2)/(3)`
Discussion
38.

The sum of 1^(st) n terms of the series (1^(2))/(1) + (1^(2) + 2^(2))/(1 + 2) + (1^(2) + 2^(2) + 3^(2))/(1 + 2 + 3) +..

Answer»

1)`(n+2)/(3)`
2)`(n(n+2))/(3)`
3)(n(n-2))/(3)`
4)`(n(n-2))/(6)`

Answer :B
Discussion
39.

Applying the method of chords , find the positive root of the equation f(x) =x^(3) +1.1 x^(2) +0.9 x - 1.4 = 0 with an accuracy of 0.005 .

Answer»


ANSWER :`0.6705`
Discussion
40.

Identify the quantifier in the statement and write the negation of the statement.Everyone who lives in India is an indian.

Answer»

Solution :There EXISTS a PERSON who lives in INDIA but not an Indian.
Discussion
41.

LetA and B be skew - symmetricmetrices of order n . Then :

Answer»

AB is a symmetric MATRIX
AB is a skew - symmetric matrix
AB is symmetricmatrix if A an B commute
None of these

Answer :C
Discussion
42.

If B - 45^(@) in DeltaABC, then :

Answer»

`(1 - COTA)(1 - COTC) = 2`
`(1 + cotA)(1 + cotC) = 2`
`cotA cotB cotC + cotA cotB + cotC = 1`
`cotA + cotB + cotC = cotA cotB cotC.`

Answer :B
Discussion
43.

int(1+x)/(sinx(x+logx))dx=

Answer»

`log|(tan(x+logx))/(2)|+C`
`(1)/(2)log|(tan(x+logx))/(2)|+c`
`log|tan((x+logx)/(2))|+c`
`(1)/(2)log|tan((x+logx)/(2))|+c`

Answer :C
Discussion
44.

Evaluate : int (1-x) sqrt(x) .dx

Answer»


ANSWER :`=2/3x^(3//2) -2/5 X^(5//2) +C`
Discussion
45.

If int_(0)^(pi)xf(sinx)dx=Aint_(0)^(pi//2)(sinx)dx, then A is

Answer»

0
`2PI`
`PI//4`
`pi`

ANSWER :D
Discussion
46.

Ifsqrt(3) +1is arootof theequation3x^3 + ax^2 + bx +12 =0wherea and barerationalnumbersthen(a,b)=

Answer»

`12,-6`
`-12,6`
`-12,-6`
`6,12`

ANSWER :B
Discussion
47.

Find the domains and ranges of the functions. (1)/(sqrt(2x+3))

Answer»


ANSWER :`(-(3)/(2),OO),(0,oo)`
Discussion
48.

Statement-1 :When we dip our hands in a beaker filled partially with water, the force on bottom of beaker increases. Statement-2: The liquid level increases.

Answer»

Statement-1 is TRUE, statement-2 is true and statement-2 is corretct explanation for statement-1
Statement-1 is true, statement-2 is true and statement-2 is NOT correct explanation for statement-1
Statement-1 is true, statement-2 is false
Statement-1 is false, statement-2 is true

Solution :A
When we DIP our hand in a beaker filled partially with water, the LIQUID leveld increases. HENCE pressure at base increases.
Discussion
49.

Select the correct statement(s) about FCC (ABCAB...) structure.

Answer»

DISTANCE between nearest octahedral void and tetrahedral void is `(SQRT(3)a)/(4)`
Distance between two nearest octahedral void is `(a)/(sqrt(2))`
Distance between two nearest tetrahedral void is `(sqrt(3)a)/(2)`
Distance between layer A and B is 2R `sqrt((2)/(3))`

ANSWER :A::B::D
Discussion
50.

If the origin is the centroid of the triangle PQR with vertices P(2a,2,6),Q(-4,3b,-10) and R(8,14,2c), then find the values of a, b and c.

Answer»


ANSWER :a=-2, h=`(-16)/(3), C= 2`
Discussion