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.

Select reaction in which correct products are given :

Answer»

`Ph-CH_(2)-overset(14)(C)"OO"H+NaHCO_(3) to CO_(2) uarr`
`Ph-OH + NaHoverset(14)(C)O_(3) to overset(14)(C)O_(2) uarr`

`MeCONa + H_(2)O to Me_(3)C - OH+NaOH`

Answer :A::C::D
Discussion
2.

Locate the position of the point P with respect to the circle S=0 when (i) P(1,2) and S=x^(2)+y^(2)+6x+8y-96 (ii) P(3,4) and S=x^(2)+y^(2)-4x-6y-12 (iii) P(2,-1) and S=x^(2)+y^(2)-2x-4y+3 (iv) P(1,5) andS=x^(2)+y^(2)-2x-4y+3

Answer»


ANSWER :(i) interior (II) Interior (III) EXTERIOR (iv) exterior
Discussion
3.

By using Gaussian elimination method, balance the chemical reaction equation: C_(2)H_(6)+O_(2)toH_(2)O+CO_(2).

Answer»


Answer :`2C_(2)H_(6)+7O_(2) to 6H_(2)O+4CO_(2)`.
Discussion
4.

A bag contains 5 red and 3 blue balls. If 3 balls are drawn at random without replacement the probability of getting exactly one red ball is ……..

Answer»

`(45)/(196)`
`(135)/(392)`
`(15)/(56)`
`(15)/(29)`

ANSWER :C
Discussion
5.

If r^(th) term is middleterm in (x^2 - (1)/(2x))^20 then (r+ 3)^(th) term is

Answer»

`(""^20C_7 X)/(2^13)`
`-( (""^20C_5x)/(4^13))`
`- ((""^20C_7x)/(2^13))`
`- ((""^20C_14x)/(4^13))`

ANSWER :C
Discussion
6.

Solve the following differential equations (1+x^(2))(dy)/(dx) + 2xy - 4x^(2) = 0

Answer»


Answer :`3Y(1+x^(2)) = 4X^(3) + 3C`
Discussion
7.

If the normal at any point P on ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 meets the auxiliary circle at Q and R such that /_QOR = 90^(@) where O is centre of ellipse, then

Answer»

`a^(4) +2b^(3) ge 3a^(2)b^(2)`
`a^(4) +2b^(4) ge 5a^(2)b^(2)+2a^(3)b`
`a^(4)+2b^(4) ge 3a^(2)b^(2)+AB`
NONE of these

Solution :Normal at `P(a cos THETA, b sin theta)` is
`ax sec theta - by cosec theta = a^(2) -b^(2)`
Homogenising with auxilliary circle
`x^(2) + y^(2) = a^(2)`
`x^(2) + y^(2) = (a)^(2) ((ax sec theta - by cosec theta)^(2))/((a^(2)-b^(2))^(2))`
`:.` For `/_QOR = 90^(@)`
Coefficient of `x^(2)+` Coefficient of `y^(2) =0`
`1- (a^(4)sec^(4)theta)/((a^(2)-b^(2))^(2)) + 1-(a^(2)b^(2)cosec^(2)theta)/((a^(2)-b^(2))^(2)) =0`
`a^(4) - 5a^(2)b^(2) + 2b^(4) = a^(4) TAN^(2) theta + a^(2)b^(2) cot^(2) theta`
`:. AM ge GM`
`a^(4) - 5a^(2)b^(2)+2b^(4) ge 2a^(3)b`
Discussion
8.

int e^(t) ((t)/(1+t^2))dt=

Answer»

`(e^t)/(1+t)`
`(e^t)/(1+t^2)`
`(-1)/(1+t^2)`
`(-e^t)/(1+t)`

ANSWER :A
Discussion
9.

An ellipse has its centre at origin, whose vertical major axis is 5 and the minor axis is 4. i. Write its equation. ii. What is its eccentricity?

Answer»


ANSWER :i.`(x^2)/(4) + (4y^2)/25 = 1`
II. `3/5`
Discussion
10.

Find the cartesian equation of the plane| through the intersection of the planes vecr.(2hati+6hatj)+12=0 and vecr.(3hati-hatj+4hatk)=0 which are at a unit distance from the origin.

Answer»


ANSWER :X - 2Y + 2z - 3 = 0
Discussion
11.

Which of the following pails constitute very similar radiations

Answer»

HARD ULTRAVIOLET RAYS and solft X-ray
Soil ultraviolet-rays and hard X-rays
Very hard X-ray and low-frequency y-rays
soft X-roys and y-rays

Answer :AC
Discussion
12.

Evaluate the definite integrals int_(2)^(3)1/xdx

Answer»


ANSWER :`log3/2`
Discussion
13.

Express the following relationson A to B in each case in tabular form {1,2,3,4}, B = {1,2,3,4,5} f = {(x,y) : 2 divides 3x+y}

Answer»

SOLUTION :A = {1,2,3,4}, B = {12,3,4,5} `therefore` F = {(X,y) : 2 divides 3x + y }
= { (1,1), (1,3), (1,5), (2,2), (2,4), (3,1), (3,3),(3,5),(4,2),(4,4)}
Discussion
14.

Solve applying formula: 3x^(2)-(2-2i)x+10-4i=0.

Answer»


ANSWER :`(1)/(3)(2+5i),-2I`
Discussion
15.

int(1)/(cosxsin^(2)x)dx

Answer»


ANSWER :`-cosecx+log|secx+tanx|+c`
Discussion
16.

A word consists of 9 letters. 5 consonants and 4 vowels. Three letters are chosen at random. What is the probability that more than one vowel will be selected ?

Answer»


ANSWER :`(17)/(42) ~~ 0.4`
Discussion
17.

int_(0)^(pi//2) (dx)/(1+tan^3 x) is equal to

Answer»

`PI`
`pi/2`
`pi/4`
`3pi/2`

ANSWER :C
Discussion
18.

The vector of the plane passing through the intersection of the planes barr.(hati-hatj+2hatk)=3" and "barr.(3hati-hatj-hatk)=4 is

Answer»

`BARR.(hati-HATJ+2hatk)=3+4lambda`
`barr.(3hati-hatj+2hatk)=3+4lambda`
`barr.[(1+3lambda)hati-(1+lambda)hatj+(2-lambda)HATK)]=3+4lambda`
`barr.[(1+3lambda)hati-(1+lambda)hatj+(2-lambda)hatk)]=3-4lambda`

ANSWER :C
Discussion
19.

The lines : (x-2)/1=(y-3)/1=(z-4)/(-k) and (x-1)/k =(y-4)/2 =(z-5)/1 are co-planar if :

Answer»

`K=2`
K =0
K = 3
K = -1

Answer :B
Discussion
20.

Solve the differential equation x(dy)/(dx)+2y=xlogx.

Answer»


ANSWER :`y = (x^(2))/(16)(4 log|x| - 1) + CX^(-2)`
Discussion
21.

If x is small so that x^2 and higher powers can be neglected, then the approximately value for ((1-2x)^(-1) (1-3x)^(-2))/((1-4x)^(-3)) is

Answer»

1-2x
1-3x
1-4x
1-5x

Answer :C
Discussion
22.

Two coins are tossed once, where{:(" E "": ""tail appears on one coin"," F "": ""one coin shows head"):}Find P(E//F)

Answer»


ANSWER :(i) 1, (II) 0
Discussion
23.

If sides AB, BC and CA of a triangle ABC are represented byx + 2 = 0 , 3x + y = 0 " and " x = 3y + 2 = 0 respectively , then identify the correct statement.

Answer»

`Sigma TAN A = 4/3`
`II tan A = - 4/3`
`Sigma tan A tan B = - 41/9`
`SIN^(2) ( A + B) + cos^(2) C = 5/4`

ANSWER :B::C
Discussion
24.

Simplify sin^(-1) (sin 20)

Answer»


ANSWER :` :'" " 6PI - 20 in ( (-PI)/2 , pi/2 )`
Discussion
25.

Maximizez=6x+4y ,subjecttoxle2,x+yle3,- 2 x+y le1,xge 0 ,yge 0. Also , findmaximumvalue ofz.

Answer»

Solution :Firstwedraw the lines AB, CD and EF whoseequationsarex = 2,`x+y=3 and- 2x+y =1 `respectively.

Theverticesofthefeasibleregionare` O(0, 0 ), A (2, 0 ) ,P , QandF (0 , 1 ) `.Pisthe pointof intersectionof the lines.
`x+y=3andx=2 `
Substituting`x= 2`in `x+y=3 `,weget,
`2 +y=3`
`thereforey=1`
`thereforeP-=( 2,1) `
Qis the pointof INTERSECTION ofthe lines
`x+y=3""`... ( 1 )
and` -2x+y= 1 `
Onsubtracting, weget,
`3x= 2""therefore x=(2 ) /(3)`
`therefore`from(1) , ` ( 2) /(3)+y=3"" thereforey=(7) /(3) `
` thereforeQ -= (( 2) /(3),( 7 ) /(3)) `
Thevaluesoftheobjectivefunction `Z =6x+4y`attheseverticesare
`z (O ) =6 ( 0)+4(0) = 0 `
` z (A )=6 ( 2 )+4( 0 )= 12 `
`z (P )=6 ( 2 )+4( 1)= 12 + 4 = 16 `
`z (Q)=6 (( 2 ) /(3))+ 4 ( (7)/(3)) =(12) /(3) +(28) /(3)=(40 ) /(3) = 13.33 `
` z (F)=6(0) +4 ( 1 )=4`
` therefore` z has maximum value16,whenx =2 andy =1.
Discussion
26.

Evaluate : (i) int_(1)^(3)(cos(logx))/(x)dx (ii) int_(0)^(pi//2)sqrt(cos theta)sin^(3)theta d theta(iii) int_(0)^(pi//2)(cosx)/((1+sinx)(2+sinx))dx

Answer»

Solution :`(i)` Put `logx=t` so that `(1)/(x)dx=dt`.
Also, `(x=1impliest=log1=0)` and `(x=3impliest=LOG3)`.
`:. Int_(1)^(3)(COS(logx))/(x)dx=int_(0)^(log3)costdt=[sint]_(0)^(log3)=sin(log3)`.
`(II)` Put `cos theta=t` so that `sin theta d theta=-dt`.
Also, `(theta=0impliest=1)` and `(theta=(pi)/(2)impliest=0)`
`:.int_(0)^(pi//2)sqrt(costheta)sin^(3)d theta=int_(0)^(pi//2)sqrt(costheta)*(1-cos^(2)theta)sin theta d theta`
`=-int_(1)^(0)sqrt(t)(1-t^(2))dt=int_(0)^(1)(t^(1//2)-t^(5//2))dt`
`=[(2)/(3)t^(3//2)-(2)/(7)t^(7//2)]_(0)^(1)=((2)/(3)-(2)/(7))=(8)/(21)`.
`(iii)` Put `sinx=t` so that `cosx dx=dt`.
Also, `(x=0impliest=0)` and `(x=(pi)/(2)impliest=1)`.
`:.int_(0)^(pi//2)(cosx)/((1+sinx)(2+sinx))dx`
`=int_(0)^(1)(dt)/((1+t)(2+t))`
`=int_(0)^(1)[(1)/((1+t))-(1)/((2+t))]dt` [ by partial FRACTIONS]
`=int_(0)^(1)(dt)/((1+t))-int_(0)^(1)(dt)/((2+t))`
`=[log|1+t|]_(0)^(1)-[log|2+t|]_(0)^(1)`
`=[(log2-log1)-(log3-log2)]=(2log2)-(log3)`.
`(IV) int_(0)^(pi//2)(dx)/((1-2sinx))=int_(0)^(pi//2)(dx)/(1-2{(2tan(x//2))/(1+tan^(2)(x//2))})`
`=int_(0)^(pi//2)(sec^(2)(x//2))/([1+tan^(2)(x//2)-4tan(x//2)])dx`
`=2int_(0)^(1)(dt)/((1+t^(2)-4t))`, where `tan.(x)/(2)=t` `[{:(x=0impliest=0),(x=(pi)/(2)impliest=1):}]`
`=2int_(0)^(1)(dt)/((t-2)^(2)-(sqrt(3))^(2))=2*(1)/(2sqrt(3))[log|(t-2sqrt(3))/(t-2+sqrt(3))|]_(0)^(1)`
`=(1)/(sqrt(3))[log((sqrt(3)+1)/(sqrt(3)-1))-log((sqrt(3)+2)/(sqrt(3)-2))]`.
`(v) int_(0)^(pi//2)(dx)/((3+2cosx))=int_(0)^(pi//2)(dx)/(3+2*[(1-tan^(2)(x//2))/(1+tan^(2)(x//2))])`
`=int_(0)^(pi//2)(sec^(2)(x//2))/(tan^(2)(x//2)+5)dx`
`=2int_(0)^(1)(dt)/(t^(2)+(sqrt(5))^(2))`, where `tan.(x)/(2)=t` `[{:(x=0impliest=0),(x=(pi)/(2)impliest=1):}]`
`=2*(1)/(sqrt(5))[tan^(-1).(t)/(sqrt(5))]_(0)^(1)=(2)/(sqrt(5))tan^(-1).(1)/(sqrt(5))`.
`(vi) int_(0)^(pi//2)(dx)/((4sin^(2)x+5cos^(2)x))=int_(0)^(pi//2)(sec^(2)x)/((4tan^(2)x+5))dx`. [dividing num. and denom. by `cos^(2)x`]
`=int_(0)^(oo)(dt)/((4t^(2)+5))`, where `tanx=t` `[{:(x=0impliest=0),(x=(pi)/(2)impliest=oo):}]`
`=(1)/(4)int_(0)^(oo)(dt)/(t^(2)+((sqrt(5))/(2))^(2))=(1)/(4)*(2)/(sqrt(5))[tan^(-1).(2)/(sqrt(5))]_(0)^(oo)`
`=(1)/(2sqrt(5))[tan^(-1)(oo)-tan^(-1)(0)]`
`=(1)/(2sqrt(5))((pi)/(2)-0)=(pi)/(4sqrt(5))`.
Discussion
27.

Find the area of the region bounded by the curve y^(2)=4x and the line x=3.

Answer»


ANSWER :`8sqrt3`
Discussion
28.

A line makes 90^@, 135^@, 45^@ with x, y and z axes respectively than its direction cosines are

Answer»

`lt 1, 0, 2 gt`
`LT0,(-1)/sqrt2,1/sqrt2gt`
`lt1/sqrt2,1/sqrt2,(-1)/sqrt2gt`
`lt1/sqrt2,1/sqrt2,0gt`

ANSWER :B
Discussion
29.

If the forcus of a parabola divides a focal chord of the parabola into segments of lengths 5, 3 units, then the length of the latusrectum of that parabola is

Answer»

`15/4`
20
`25/2`
`15/2`

ANSWER :D
Discussion
30.

For adiabatic free expansion of a real gas, the correct relation are :

Answer»

W=0
q=0
`DeltaU=0`
`DeltaT=0`

SOLUTION :(A),(B),( C)
For A diabatic free EXPANSION `to`
`q=0,W=0,DeltaU=0`
`DeltaU=f(T,V)` for a real GAS .
hence `DeltaT ne0`
Discussion
31.

int(x^(5)+x^(4)+4x^(3)+4x^(2)+4x+4)/((x^(2)+2)^(5)) is equal to

Answer»

`(4x-3)/((x^(2)+1)^(2))+(3)/(8)(x)/(x^(2)+2)+(1)/(SQRT(2))TAN^(-1)""(x)/(sqrt(2))+C`
`(1)/(12)(2x-3)/((x^(2)+2)^(2))+(3)/(16)(x)/(x^(2)+2)+(3)/(16sqrt(2))tan^(-1)""(x)/(sqrt(2))+C`
`(2x-3)/((x^(2)+2)^(2))+(3)/(8)(x)/(x^(2)+2)+(1)/(2sqrt(2))tan^(-1)""(x)/(sqrt(2))+C`
NONE of these

Answer :D
Discussion
32.

If therootsofax^(3)+ bx^2 + cx+ d=0are inG.Pthen therootsofdx^3- cx^2+ bx-a=0 are in

Answer»

A.P
G.P
H.P
A.G.P

Answer :B
Discussion
33.

Find the square of (a+40i)+sqrt(9-40sqrt(-i))

Answer»

SOLUTION :`=(a+40i+sqrt(9-40i))^2`
`=a^2+1600i^2+9-40i+80"AI " +80isqrt(9-40i)+2asqrt(9-40i)`
`=a^2-1600+9-40i+80 "ai" +2sqrt(9-40i)(a+40i)`
`=a^2-1591-40i+80"ai" +2sqrt(9-40i)(a+40i)`
Discussion
34.

If A is a symmetric matrix , then A^(3) is a ….. Matrix .

Answer»


ANSWER :`n=3`
Discussion
35.

The proposition p ~(p ^^ ~q)is a

Answer»

contradiction
tautology.
contingency
none of these

Answer :C
Discussion
36.

Prove the A uu B = U"and "A nn B = phi impliesB =A'

Answer»

SOLUTION :Let `A UU B =U` and `A nn B = phi`
`:. Let x in B ``:.B=A.(.: A nn B = phi )`
Discussion
37.

Find outthe quartile deviation of the income of a certain person given in rupees for 12 months in a year. 139, 150 , 151, 151, 157 , 158 , 160 , 161 , 162, 162, 173, 175

Answer»


ANSWER :5.5
Discussion
38.

The value of int_(0)^(100)[tan^(-1)x]dx is ([.]G.I.G)

Answer»

100
`100-TAN^(-1)1`
`100-tan1`
`100+(PI)/4`

Solution :We have
`int_(0)^(100)[tan^(-1)x]dx=int_(0)^(tan1)[tan^(-1)x]dx+int_(tan1)^(100)[tan^(-1)x]dx`
`impliesint_(0)^(100)[tan^(-1)x]dx=int_(0)^(tan1) 0 dx+int_(tan1)^(100) dx=100-tan1`
Discussion
39.

Evaluate the following integrals int(2x-3)/(sqrt(2x^(2)+5x+6))dx

Answer»


ANSWER :`sqrt(2X^(2)+5x+6)-(11)/(2sqrt(2))SINH^(-1)((4x+5)/(sqrt(23)))+C`
Discussion
40.

By using elementary operations, Find the inverse of the matrix A= [[2,3],[5,7]]

Answer»


ANSWER :`A^(-1)= [[1,(1)/(2)],[2,(3)/(2)]]`
Discussion
41.

bar(x),bar(y),bar(z) are zero vectors. If …………… then bar(x).bar(y)=bar(x).bar(z).(bar(x),bar(y)ne0).

Answer»

`BAR(X)` is PERPENDICULAR to `bar(y)`.
`bar(x)` is perpendicular to `bar(Z)`.
`bar(x)` is perpendicular to `bar(y)+bar(z)`.
`bar(x)` is perpendicular to `bar(y)=bar(z)`.

ANSWER :D
Discussion
42.

Consider equation (x - sin alpha) (x-cos alpha) - 2 = 0 . Which of the followingis /are true?

Answer»

If `0lt alpha LT (pi)/(4)`, then the equationhas both ROOTS in `(sin alpha, cos alpha)`
If `(pi)/(4) lt alpha (pi)/(2)`, then theequations has both rootsin `(sin alpha, cos alpha OO)`
If `0lt alpha lt (pi)/(4)`, theone roots lies in `(-oo, sin alpha)` and theotherin `(sin alpha,oo)`
If `(pi)/(4) lt alpha lt (pi)/(2)` thenone rootliesin `(-oo, cos alpha )` and the otheris `(sin alpha, oo)`

Solution :Let , `f(x) = (x - sin alpha ) (x - cos alpha) - 2 `
Then. ` f(sin alpha) = - 2 lt 0 ` and
` f(cos alpha) = - 2 lt 0 ` and
` f(cos alpha ) = - 2 lt 0 `
So, sin ` ALPHAAND cos alpha ` lie between the
roots
Discussion
43.

Mother father and son line up at random for a family picture{:(" E "": ""son on one end"," F "": ""father in middle"):}Find P(E//F)

Answer»


ANSWER :1
Discussion
44.

If a (b +c), b (c+a) , c (a +b) are in A.P. , prove that (1)/(a), (a)/(b), (1)/(c ) are also ln A.P.

Answer»


ANSWER :`1/a, 1/b, 1/c` are in A.P.
Discussion
45.

If the normals at the point t_(1) and t_(2) on y^(2)=4axintersect at the point t_(3) on the parabola then t_(1)t_(2) =

Answer»

1
2
`t_(3)`
`2t_(3)`

ANSWER :B
Discussion
46.

Determine the area of the figure bounded by two branches of the curve (y-x)^(2) = x^(3) and the straight line x=1

Answer»


ANSWER :`(4)/(5)`
Discussion
47.

If ABCDEF is a regular hexagon and bar(AB) = bara thenbar(AD) + bar(EB) + bar(FC) =

Answer»

`4bara`
`1/4bara`
`2bara`
`1/2bara`

ANSWER :A
Discussion
48.

Let F denote the set of all onto functions from A = {a_(1), a_(2), …, a_(10)} to B = {x, y}. A function f is chosen at random from F. Find the probabiltiy that the function f is such that f(a_(1)) = x.

Answer»


ANSWER :`(1)/(2)`
Discussion
49.

int (3)/(2x^(2) - x- 1)dx =

Answer»

`log |(x- 1)/(x + 1)| + C `
`log |(x+ 1)/(2X - 1)| + c `
`log |(x- 1)/(2x - 1)| + c `
`log |(2x- 2)/(2x + 1)| + c `

ANSWER :D
Discussion
50.

How many 4 letter words can be formed using the letters of the word ARTICLEsuch that each word must contain atieast one vowel

Answer»


ANSWER :816
Discussion