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.

Differentiate w.r.t.x the function in Exercises 1 to 11. (cos^(-1)""(x)/(2))/(sqrt(2x+7)), -7 lt x lt2.

Answer»


ANSWER :`-[(1)/(SQRT(4-X^2)sqrt(2x+7))+(cos^(-1)""(x)/(2))/((2x+7)^(3/2))]`
Discussion
2.

Consider the equation x^(5) + 5lambdax^(4) -x^(2) + (lambdaalpha-4)x^(2) - (8lambda +3) x +(lambdaalpha-2)=0, where lambda, alpha in R (i) Determine a such that the given equation has exactly one root independent of lambda. (ii) Determine a such that the given equation has exactly two roots independent of lambda .

Answer»


ANSWER :(i) `ALPHA =-64/5`
Discussion
3.

If therootsof 54x^3 -39x^2 - 26 x^2- 26 x+16 =0are in G.Pthenonerootis

Answer»

`-2/3`
`2/3`
`3/2`
`-3/2`

ANSWER :A
Discussion
4.

overset((pi)/(2))underset(0)int cos x*e^(sinx)dx=....

Answer»

`E+1`
`e-1`
e
`-e`

ANSWER :B
Discussion
5.

Evaluation of definite integrals by subsitiution and properties of its : int_(1)^(2)e^(-(1)/(x))(dx)/(x^(2))=............

Answer»

`(1)/(e)+(1)/(e^(2))`
`(1)/(e)+(1)/(SQRTE)`
`(1)/(sqrte)-(1)/(e)`
`(e+1)/(sqrte)`

ANSWER :C
Discussion
6.

The solution of (dy)/(dx) = tan^(2) (x+y) is

Answer»

`SIN (2X + 2Y) = 2x + 2y + C`
`sin (2x-2y) -2x -2y + c`
`sin (2x + 2y) = 2x -2y + c`
`sin (2x -2y) = 2x + 2y + c`

ANSWER :C
Discussion
7.

Evaluation of definite integrals by subsitiution and properties of its : int_(0)^(pi)sin2x.cos^(2)3xdx=............

Answer»

`-1`
`(1)/(2)`
`-(1)/(2)`
0

Answer :D
Discussion
8.

I: The equation whose roots are the squares of the roots of x^(3) - x^(2) + 8x - 6 = 0is x^(3) + 15x^(2) + 52x + 36 = 0. II: The equation whose roots are the cubes of the roots of x^(3) + 3x^(2) + 2 = 0is x^(3) + 33x^(2) + 12x + 8 = 0 .

Answer»

only I is TRUE
only II is true
both I and II are true
NEITHER I nor II true

Answer :2
Discussion
9.

If for any real x,(11x^(2)+12x+6)/(x^(2)+4x+2)= y is such that ylt a or y ge b, then a, b are

Answer»

3,5
`-5, 3`
`-4, 5`
`-6, 4`

ANSWER :B
Discussion
10.

If f(x)={:{((|x|)/(x)", for " x!=0),(1", for " x=0):}, then

Answer»

`underset(x rarr 1^(-))LIM F(x)=1`
`underset(x rarr 1^(+))lim f(x)=-1`
f is DISCONTINUOUS at origin
f is continuous at origin

Answer :C
Discussion
11.

Findthe areaof theregionenclosedby {(x,y):0 le y le x^2 +1,0 le y lex+1 ,0 le x le 2}.

Answer»


ANSWER :`23/6`
Discussion
12.

Let f (x) be a polynomial satisfying lim _(x to oo) (x ^(4) f (x))/( x ^(8) +1)=3 f (2) =5, f(3) =10, f (-1)=2, f (-6)=37The number of points of discontinuity of discontinuity of f (x)= (1)/(x ^(2)+1 -f (x))in [(-15)/(2), (5)/(2)] equals:

Answer»

4
3
1
0

Answer :B
Discussion
13.

If (""^(n)P_(r)-1)/(a)=(""^(n)P_(r))/(b)=(""^(n)P_(r)+1)/(c) ,then which of the following hold good?

Answer»

`C^(2)`=a(B+c)
`a^(2)=c(a+b)`
`b^(2)=a(b+C)`
`(1)/(a)+(1)/(b)+(1)/( c)=1`

ANSWER :C
Discussion
14.

{:abs((1,bc+ad,b^(2)c^(2)+a^(2)d^(2)),(1,ca+bd,c^(2)a^(2)+b^(2)d^(2)),(1,ab+cd,a^(2)b^(2)+c^(2)d^(2))):}=

Answer»

(a - B)(b - C) (c - d) (a - d) (a - c) (d - b)
(a - b) (a - c) (b - c) (b - d) (a - d) (c - d)
(a -b) (a -c) (a - d) (b - c) (b - d) (d - c)
(a - b)(b - c) (c - d)(b - d)

ANSWER :B
Discussion
15.

Let f: {2, 3, 4, 5} rarr{3, 4, 5, 9} and g : {3, 4, 5, 9} rarr {7, 11, 15}be functions defined as f (2) = 3, f(3) = 4, f(4) = f(5) = 5 and g(3) = g(4) = 7 and g(5) = g(9) = 11. Find gof.

Answer»


SOLUTION :N/A
Discussion
16.

Let the vectors vec(PQ),vec(QR),vec(RS),vec(ST),vec(TU) and vec(UP) represent the sides of a regular hexagon. Statement 1: vec(PQ)xx(vec(RS)+vec(ST))!=vec0 Statement 2: vec(PQ)xxvec(RS)=vec0 and vec(PQ)xxvec(ST)!=vec0

Answer»

1
2
3
4

Solution :Clearly, `vec(RS)+vec(ST)=vec(RT)` which is not parallel to `vec(PQ)`
`:.vec(PQ)XX(vec(RS)+vec(ST))!=vec0`
So STATEMENT-1 is TRUE.
Also, `vec(PQ)` is not parallel to `vec(RS)`

`:.PQxxvec(RS)!=vec0`
So, statement -2 is not true.
Discussion
17.

Equation of pair of lines passing through (2, 1) and perpendicular to the lines 16x^(2) + 17 xy + 12 y^(2) = 0 is

Answer»

`12X^(2) - 17 xy + 6 y^(2) - 31x - 22y + 64 = 0`
`12x^(2) - 17 xy + 6 y^(2) + 31x + 22y - 104 = 0`
`12x^(2) - 17 xy + 6 y^(2) - 31x + 22y + 20 = 0`
None of these

Answer :C
Discussion
18.

There are 21 points in a plane no three of which are collinear. The number of triangles formed by joining them is

Answer»

1330
210
1850
180

Answer :A
Discussion
19.

OABC is a tetrahedron in which O is the origin and position vector ot points A, B, C are hati+2hatj+3hatk,2hati+alpha hatj+hatk and hati+3hatj+2hatk respectively. An integral value of alpha for which shortest distance between OA and BC is sqrt((3)/(2)).

Answer»


ANSWER :3
Discussion
20.

Tickets to the annual Follies Show at Littleton High School are $4 for adults and $2.50 for students. There is a cost of $750 to produce the show. If the x-axis represents the number of adult tickets sold and the y-axis represents the number of student tickets sold, which graph represents all the possible combinations of ticket sales that allow the junior class to at least cover the cost of the show ?

Answer»




ANSWER :C
Discussion
21.

Iff : R to R be given by f (x) = (3 -x ^(3)) ^(1/3), then fof (x) is

Answer»


ANSWER :`=X`
Discussion
22.

A tennis ball receives a top spin when struck by a racket and describes a curved trajectory. The top spin implies that the rotatory motion of the top surface of tha ball is in the direction of the translatory motion of the ball. Which one of the following statement is the best description of the trajectory ?

Answer»

PRESSURE on the top surface is LOWER, trajectory RISES
Pressure on the top surface is lower, trajectory dips
Pressure on the top surface is higher, trajectory rises
Pressure on the top surface is higher, trajectory dips

Solution :D
In ball's frame `v_("air")=v+wr`
`v_("air")=v-wr`
APPLYING Benoulli's
`P_("above") GT P_("below")`
`:.` trajectory dipes
Discussion
23.

Find graphically the minimum value of Z = 100x + 50y, subject to the constraints x + y le 300, 3x + y le 600, y le x + 200, x ge 0, y ge 0.

Answer»


ANSWER :Minimum value of Z = 10,000; when X = 0 and y = 200
Discussion
24.

If y =tan^(-1)((5x)/(1-6x^(2))),where (-1)/(sqrt6)ltxlt(1)/(sqrt6)"then prove that"(dy)/(dx)=((2)/((1+4x^(2)))+(3)/((1+9x^(2)))).

Answer»
Discussion
25.

Evalute the following integrals int (1)/(3x^(2) + x + 1) dx

Answer»


ANSWER :`(2)/(SQRT(11))tan^(-1)((6x+1)/(sqrt(11)))+c`
Discussion
26.

If p=cos2 alpha+isin2 alpha,q=cos2beta+isin2beta then sqrt(p//q)-sqrt(q//p)=

Answer»

`2isin(alpha+beta)`
`2isin(alpha-beta)`
`2I COS(alpha-beta)`
`2icos(alpha+beta)`

ANSWER :B
Discussion
27.

If g(x) = lim_( n to oo)(x^(m)f(x) + h(x)+1)/(2x^(m) + 3x +3) is continuousat x =1 and g(1) = lim_(x to 1) (log{e^(x)})^(2/(log_(e)x)) ,such thatA g(1) + B f(1) + C h(1)= 1, and(A + B + C)^(n) = 243then n is

Answer»


ANSWER :` 5 XX 2^(10)`
Discussion
28.

Differentiate cos^(-1) ((sin x + cos x)/(sqrt2)), - (pi)/(4) lt x lt (pi)/(4)

Answer»


ANSWER :`-1`
Discussion
29.

Resolve (1)/((x+1)^(6)(x+2)) into partial fractions.

Answer»


ANSWER :`(1)/(x+2)-(1)/(x+1)+(1)/(x+1)^(2)-(1)/((x+1)^(3))+...+(1)/((x+1)^(6))`
Discussion
30.

{:(" "Lt),(n rarr oo):}1/n { f(1/n)+f(2/n)+...+f(2)}=

Answer»

`int_(0)^(1) F(1/X)dx`
`int_(0)^(1) f(x)dx`
`int_(0)^(1) f(2x)dx`
`int_(0)^(2)f(x)dx`

Answer :D
Discussion
31.

Solve the equation:2 x^2- 6x + 4 = 0

Answer»


ANSWER :X = 13.78 ; y= 2.88
Discussion
32.

An ellipse drawn by taking a diameter of the circle (x-1)^(2)+y^(2)=1 as its semiminor axis and a diameter of the circle x^(2)+(y-2)^(2)=4 as its semi-major axis. If the centre of the ellipse is at the origin and its axes are the coordinate axes, then the equation of the ellipse is

Answer»

`4x^(2) +y^(2) =4`
`X^(2) +4y^(2) =8`
` 4x^(2) +y^(2) =8`
` x^(2) +4y^(2) =16`

ANSWER :D
Discussion
33.

If A and B are any two events such that P(overset(_)A)=0.4, P(overset(_)B)=0.9 then what is the value of P(overset(_)A cup overset(_)B) equal to

Answer»

0.2
0.5
0.6
0.7

Solution :We have `P(overset(_)A CUP overset(_)B)=P(overset(_)A)+P(overset(_)B)-P(overset(_)A cap overset(_)B)`
`P(overset(_)A )=P(overset(_)B)-P(overset(_)A cup overset(_)B)"By(De-Morgan's LAW")`
`P(overset(_)A )=P(overset(_)B)-(1-P(overset(_)A cup overset(_)B))=4+3-(1-9)=6`
Discussion
34.

Discuss the monotonicity and local extrema of the function f(x)=log (1+x)-(x)/(1+x), x gt -1 and hence find the domain where, log (1+x) gt (x)/(1+x)

Answer»


Answer :`LOG (1+X) GT (x)/(1+x) on (0, infty)`
Discussion
35.

What do the{z:|z-a|-|z+a|=c} represent?

Answer»

SOLUTION :Here`{Z:|z-a|-|z+a|=c}`
implies that , the difference of the DISTANCES of the point (x,y) from TWO fixed points'-a'and'a" is a CONSTANT i.e.c. So the locus is a hyperbola.
Discussion
36.

Write the vector equation of a line through the point (1,2,3) and parallel to the vector 3overset^i+2overset^j-2overset^k

Answer»

Solution :The parameric EQUATION of the LINE through `(1,-1,2) and parallel to the VECTOR `(3overset^i+overset^j-overset^k)` are x=1+3lambda,y=-1+lambda,z=2-lambda`
Discussion
37.

If n positive integers are taken at random and multiplied together, the probability that the last digit of the product is 2,4,6, or 8 is

Answer»

`(5^n -3^n)/(5^n)`
`(4^n - 2^n)/(5^n)`
`(3^n -2^n)/(5^n)`
`(3^n -2^n)/(4^n)`

ANSWER :A
Discussion
38.

Consider a curved mirror y = f(x) passing through (8, 6) having the property that all light rays emerging from origin, after reflected from the mirror becomes parallel to x-axis. The equation of the mirror is y^(a) = b(c-x^(d)) where a, b, c, d are constants, then

Answer»

B=4
b = 36
C= 9
c = 1

Answer :B::C
Discussion
39.

"Sec" (tan sqrt(x)).

Answer»


ANSWER :`(SEC(tansqrt(x)).TAN(tansqrt(x)).sec^(2)sqrt(x))/(2sqrt(x))`
Discussion
40.

Prove that sin15^@ = (sqrt3-1)/(2sqrt2)

Answer»

Solution :`sin15^@=sin(45^@-30^@)=SIN45^@cos30^@-COS45^@SIN30^@=1/(sqrt2).sqrt3/2-1/sqrt2.(1)/2=(sqrt3-1)/(2sqrt2)`
Discussion
41.

LetA={:[( 1,sin theta , 1),( -sin theta , 1, sin theta ),( -1 ,-sin theta , 1 )]:} ,"where" 0 letheta le 2pi ,Then

Answer»

`DET(A) =0`
` Det(A) in (2, INFTY ) `
`Det (A) in (2,4) `
`Det(A) in [2,4]`

ANSWER :D
Discussion
42.

Find the range of the following functions f(x) = log_e (2 sin x + tan x -3x +1) where pi/6 lt x lt pi/3

Answer»


Answer :Range of f(x) is `[log_e(2+1/sqrt3)-PI/2), log(1 + 2SQRT3- pi)]`
Discussion
43.

{:(,"Column - I", "Column - II"),("(A)" ,"The area bounded by curve","(P)"2 ),(, x = 3y^(2) – 9" and the", ),(,"lines x = 0, y = 0 and y = 1 ",),(,"in square units is equal to",),("(B)", "If a curve "f(x) = a sqrt(x) + bx, (Q)4 ),(,(f(x)ge0AAx in [0,9]),),(,"passes through the point",),(,"(1, 2) and the area bounded ",),(,"by the curve, line x = 4 ",),(,"and x-axis is 8 square unit,",),(,"then 2a + b is equal to",),("(C)", "The area enclosed between", (R)8 ),(,"the curves " y = sin^(2)x and,),(,y = cos^(2)x" in the interval",),(,0 le x le pi " in square units is",),(,"equal to ",),("(D)","The area bounded by the", (S)5 ),(,"curve " y^(2) = 16 x" and line",),(,y=mx " is " 2/3 "square units, ",),(,"then m is equal to",):}

Answer»


ANSWER :A::B::C::D
Discussion
44.

The roots of the equation x^(3)-3x-2=0 are

Answer»

`-1, -1,2`
`-1, 1, -2`
`-1, 2, -3`
`-1, -1, -2`

ANSWER :A
Discussion
45.

Consider ax ^(4) +(7a -2b) x ^(3) + (12a-14b-c ) x^(2) - (2ab +7c) x+1-12c =0, has no real roots and f _(1)(x)=sqrt(log _((pi+e))(ax ^(4) + (7a-2b) x ^(3) + (12a-14b-c) x ^(2) -(24 b +7c) x+1 -12c))/(sqrta sqrt(- sgn (1+ ac+ b^(2)))) f _(2) (x) = -2+ 2log _(sqrt2) cos (tan ^(-1) (sin (pi(cos (pi ( x+ (7 )/(2))))))).Then match the following :

Answer»

<P>

ANSWER :`A toS; Bto P; C to Q; D to R`
Discussion
46.

Find which of the operations given above has identity. a"*"b=ab^2

Answer»


SOLUTION :N/A
Discussion
47.

Differentiate the functions with respect to x in cos (sqrtx)

Answer»


ANSWER :`(-SIN (SQRTX))/(2sqrtx)`
Discussion
48.

4^(n+1) + 15n + 14 is divisible by 9 for every natural number n ge 0.

Answer»

Solution :Let`P_n = 4^(n+1) + 15n + 14`
When n = 1, `4^2 + 15 + 14 = 45` is divisible by 9.
`therefore P_1` is true. Let `P_k` be true.
i.e , `4^(k+1) + 15k + 14` is divisible by 9. Now `4^(k+1+1) + 15(k+1) + 14`
= `4^(k+2) + 15k + 29`
`4(k+1).4 + 60k + 56 - 45k - 27`
= `4(4^(k+1) + 15k + 14) - 9(5k+3)` Which is divisible by 9.
`therefore P_(k+1)` is true.
`therefore P_n` is true for all VALUES of `n ge 0`.
Discussion
49.

If I_n = int_(pi//2)^(oo) e^(-x) x dx], then(I_(2018) )/(I_(2016)) =

Answer»

`(2018 XX 2019)/((2017)^2 + 1)`
`(2018 xx 2017)/((2018)^2 + 1)`
`( (2018)(2016) )/(2017)^2+ 1) `
`((2018)(2017) )/((2019)^2+ 1)`

ANSWER :B
Discussion
50.

Using the method of integration find the area bounded by the curve |x| + |y| = 1.

Answer»


ANSWER :2
Discussion