Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\underset{x\to \infty }{lim}{x}^2\ln \left(x{\cot }^{-1}x\right)$ is

The real part of the multiplicative inverse of $\frac{1+2i}{5+6i}$ is

Let $A=\left[\begin{array}{ccc}1& sin\theta & 1\\ -sin\theta & 1& sin\theta \\ -1& -sin\theta & 1\end{array}\right]$, where $0\le \theta \le 2\pi$, then

a) det A=0
b) det $Aϵ(2,\infty )$
c) det $Aϵ(2,4)$
d) det $A\epsilon [2,4]$

$sin\left(ta{n}^{-1}x\right),|x|<1$, is equal to
a) $\frac{x}{\sqrt{1-x^2}}$
b) $\frac{1}{\sqrt{1-x^2}}$
c) $\frac{1}{\sqrt{1+x^2}}$
d) $\frac{x}{\sqrt{1+x^2}}$

One-hundred identical coins, each with probability, p, of showing up heads are tossed once. If 0 < p < 1 and the probability of heads showing on 50 coins is equal to that of heads showing on 51 coins, then the value of p is

Write the equation of the circle passing through (3,4) and touching y-axis at the origin.

The graph of $f\left(x\right)=e^{x^2}$, where $e>1$

The image of the point $(3,8)$ in the line $x+3y=7$ is

The sum of the series 1 + 2x + 3

$x^2$ + 4

$x^3$ + ..........upto n

terms is

All normals to the curve x = a cos t + at sin t, y = a sin t – at cos t

are at a distance a from the origin that is equal to….

If
(i) ,
then verify that

(ii)
,
then verify that

If the point $P(x_1+t(x_2-x_1),y_1+t(y_2-y_1\left)\right)$ divides the line segment joining the points $A(x_1,y_1)$ and $B(x_2,y_2)$ internally, then the range of $t$ is

If α, β, γ are the roots of the equation $x^3+4x+1=0$,then $(\alpha +\beta {)}^{-1}+(\beta +\gamma {)}^{-1}+(\gamma +\alpha {)}^{-1}=$

Given vector A bar = 2i^+3j^, the angle between A bar and Y-axis is?

Which of the following function is a monotonic function?

The following are some particulars of the distribution of weights of boys and girls in a class :

$\begin{array}{ccc}& \text{Boys}& \text{Girls}\\ \text{Number}& 100& 50\\ \text{Mean weight}& 60\text{kg}& 45\text{kg}\\ \text{Variance}& 9& 4\end{array}$

Which of the distributions is more variable ?

For any quadratic polynomial $f\left(x\right)=x^2+\frac{b}{a}x+\frac{c}{a};a\ne 0,$

if $\alpha ,\beta$ are the roots of $f\left(x\right)=0$ and

$k_1,k_2$ be two numbers such that $\alpha <k_1,k_2<\beta ,$ then select the correct statement.

To obtain the graph of y = - sinx from the graph of y = sinx, phase shift required is

The following model shows the growth of a specimen by 1 hr. The length of the microbe grown in 1 hr is .

If $\overrightarrow{a}=4\hat{i}+6\hat{j}$ and $\overrightarrow{b}=3\overrightarrow{j}+4\overrightarrow{k}$ then the vector form of component of $\overrightarrow{a}$ along $\overrightarrow{b}$ is

If the fifth term of the expansion $(a^{2/3}+a^{-1})$ does not contain 'a'. Then n is equal to

In an entrance test that is graded on the basis of two examination, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7 the probability of passing at least one of them is 0.95. What is the probability of passing both?

-1/2=cos x ,find x

If $f\left(x\right)=\frac{1}{x^2-17x+66},thenf\left(\frac{2}{x-2}\right)$ is discontinuous at x=

Given two events $A$ and $B$ such that odds against $A$ are $2$ to $1$ and odds in favour of $A\cup B$ are $3$ to $1,$ then

The range of the function $y=\frac{x-1}{(x^2-3x+3)}$ is [a, b] where a, b are respectively

Find all the points of discontinuity fo f where f(x)=$\{\begin{array}{c}\frac{sinx}{x},ifx<0\\ x+1,ifx\ge 0.\end{array}$

Assume
X,
Y,
Z,
W
and P
are matrices of order,
and
respectively.
If n
= p,
then the order of the matrix
is

A
p ×
2 B
2 ×
n C
n
×
3 D
p
×
n

A man walks a distance of $3$ units from the origin towards the north - east $\left(N{45}^{\circ }E\right)$ direction. From there, he walks a distance of $4$ units towards the north - west $\left(N{45}^{\circ }W\right)$ direction to reach a point $B$, then the position of $B$ in the Argand plane is

There are two urns$U_1$ and $U_2$. $U_1$ contains $2$ white and $8$ black balls and $U_2$ contains $4$ white and $6$ black balls. One urn is chosen at random and a ball is drawn and its colour noted and replaced. The process is repeated $3$ times and as a result one ball of white colour and $2$ of black are obtained. The probability that the urn chosen was $U_1$ is:

The value of the integral $\int \frac{e^{x^2+4\ln x}-x^3{e}^{x^2}}{x-1}dx$ equal to

(where $C$ is the constant of integration)