Explore topic-wise InterviewSolutions in Current Affairs.

A fair die is rolled. consider events E = {1, 3,5} F = {2,3} and G = {2,3,4,5}. Find
$P\left(\frac{E}{F}\right)andP\left(\frac{F}{E}\right)$

$P\left(\frac{E}{G}\right)andP\left(\frac{G}{E}\right)$

$P\left(\frac{E\cup F}{G}\right)andP\left(\frac{E\cap F}{G}\right)$

Let f: Q → Q be a function given by f(x) = x²,then f ^-1(9) =

If a class consists of $6$ periods, then the number of ways in which $5$ subjects can be taught such that each subject must be allotted at least one period and no period remains vacant is

Choose the
correct answer.

Let A
be a square matrix of order 3 ×
3, then
is
equal to

A.

B.

C.

D.

The integral $\int \frac{2x^3-1}{x^4+x}dx$ is equal to : (Here $C$ is a constant of integration)

The range of intergers that can be represented by n bit 2's complement number system is

The matrix A = $\left[\begin{array}{ccc}\frac{3}{2}& 0& \frac{1}{2}\\ 0& -1& 0\\ \frac{1}{2}& 0& \frac{3}{2}\end{array}\right]$ has three distinct eigen values and one of its eigen vectors is $\left[\begin{array}{c}1\\ 0\\ 1\end{array}\right]$



which one of the following can be anooter eigen vector of A?

Given quadratic equations $x^2+5x+p=0\&2x^2+qx+12=0$ have both roots common, then $p+q=$

${lim}_{x\to \frac{\pi }{4}}\frac{f\left(x\right)-f\left(\frac{\pi }{4}\right)}{x-\frac{\pi }{4}}$, where f(x) = sin 2x

If $f:R\to R$ is given by $f\left(x\right)=x+1,$ then the value of $\underset{n\to \infty }{lim}\frac{1}{n}\left[f\right(0)+f\left(\frac{5}{n}\right)+f\left(\frac{10}{n}\right)+...+f\left(\frac{5(n-1)}{n}\right)],$ is:

In a three dimensional co - ordinate system P, Q and R are images of a point A(a, b, c) in the xy the yz and the zx planes respectively. If G is the centroid of triangle PQR then area of triangle AOG is (O is the origin)

If Am (A suffix m) denotes m th term of an A.P, then Am is

The value of $\underset{0}{\overset{16\pi /3}{\int }}|\sin x|dx$ is equal to

Match the following. Graph of f(x) is given

If $tan\alpha ,tan\beta$ are the roots of the equation $x^2$ + ax + b = 0 then the value of $si{n}^2(\alpha +\beta )+asin(\alpha +\beta )cos(\alpha +\beta )+bco{s}^2(\alpha +\beta )=$

The value of $\underset{n\to \infty }{lim}\frac{1\cdot 2+2\cdot 3+3\cdot 4+\cdots +n(n+1)\left]\right[1-\cos \left(2/n\right)]}{n}$ is

The conjugate base of $HS{O}_3^{-}$ is

Prove that

[1/(sec²x-cos²x) + 1/(cosec²x-sin²x)] sin²x cos²x =

(1-sin²x cos²x)/(2+sin²x cos²x)

With initial conditions solve for y(t).

$y^{\prime \prime }\left(t\right)+5y^{\prime }\left(t\right)+6y\left(t\right)=x\left(t\right)$

$y\left(0^{-}\right)=2,y^{\prime }\left(0^{-}\right)=1andx\left(t\right)=e^{-t}u\left(t\right)$

If $\{\begin{array}{c}\frac{x^2-x}{2x},x\ne 0\\ k,x=0\end{array}$ and if f is continuous at x=0,then k=?

If $\omega$ is a complex number stisfying $|\omega +\frac{1}{\omega }|$=2,

then maximum distance of $\omega$ from origin is

If $S=\left[\begin{array}{cc}6& -8\\ 2& 10\end{array}\right]=P+Q$, where $P$ is a symmetric & $Q$ is a skew -symmetric matrix, then $Q$ is

Find the
maximum value of 2x³ − 24x + 107 in
the interval [1, 3]. Find the maximum value of the same function in
[−3, −1].

$\int \frac{dx}{x(logx-2)(logx-3)}=f\left(x\right)+cthenf\left(x\right)=$

If $y=\sqrt{x+\sqrt{y+\sqrt{x+\sqrt{y+\cdots \infty }}}},$ then $\frac{dy}{dx}=$

Taking
the set of natural numbers as the universal set, write down the
complements of the following sets:

(i) {x:
x
is an even natural number}

(ii) {x:
x
is an odd natural number}

(iii) {x:
x
is a positive multiple of 3}

(iv) {x:
x
is a prime number}

(v) {x:
x
is a natural number divisible by 3 and 5}

(vi) {x:
x
is a perfect square}

(vii) {x:
x
is perfect cube}

(viii) {x:
x
+ 5 = 8}

(ix) {x:
2x
+ 5 = 9}

(x) {x:
x
≥ 7}

(xi) {x:
x
∈
N and 2x
+ 1 > 10}

If matrix $A=\left[\begin{array}{ccc}0& 1& -1\\ 4& -3& 4\\ 3& -3& 4\end{array}\right]=B+C$, where $B$ is symmetric matrix and $C$ is skew-symmetric matrix.

Then the matrices $B$ and $C$ are:

Question 65

How many points are marked in the figure?

1. 2.645

Find the equation of circle which touches $2x-y+3=0$ and pass through the points of intersection of the line $x+2y-1=0$ and the circle $x^2+y^2-2x+1=0$

An intergrating factor of the equation $(1+y+x^{2}y)dx+(x+x^3)dy=0$ is