Explore topic-wise InterviewSolutions in Current Affairs.

State whether the given table is not the probability distributions of a random variable. Give reasons for your answer.
$$\begin{array}{cccc}X& 0& 1& 2\\ P\left(X\right)& 0.4& 0.4& 0.2\end{array}$$

$$\begin{array}{cccccc}x& 0& 1& 2& 3& 4\\ P\left(X\right)& 0.1& 0.5& 0.2& -0.1& 0.3\end{array}$$

$$\begin{array}{cccc}Y& -1& 0& 1\\ P\left(Y\right)& 0.6& 0.1& 0.2\end{array}$$

$$\begin{array}{cccccc}Z& 3& 2& 1& 0& -1\\ P\left(Z\right)& 0.3& 0.2& 0.4& 0.1& 0.05\end{array}$$

If $y=a\cos \left(\ln x\right)+b\sin \left(\ln x\right),$ then $x^2\frac{d^{2}y}{d{x}^2}+x\frac{dy}{dx}=$

If y(x) satisfies the differential equation $\frac{dy}{dx}=sin2x+3ycotx$ and $y\left(\frac{\pi }{2}\right)=2,$ then which of the following statement(s) is/are correct?

Find the equation of the circle passing :trough the origin and the points where the line 3x +4y = 12 meets the axes of coordinates.

Nonzero vectors $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ satisfy $\overrightarrow{a}.\overrightarrow{b}=0,(\overrightarrow{b}-\overrightarrow{a}).(\overrightarrow{b}+\overrightarrow{c})=0and2|\overrightarrow{b}+\overrightarrow{c}|=|\overrightarrow{b}-\overrightarrow{a}|$. If $\overrightarrow{a}=\mu \overrightarrow{b}+4\overrightarrow{c}then\mu =$ ___

Let $P$ be a plane, which contains the line of intersection of the planes, $x+y+z-6=0$ and $2x+3y+z+5=0$ and it is perpendicular to the $xy$-plane. Then the distance of the point $(0,0,256)$ from $P$ is equal to :

A person draws a card from a pack, replaces it shuffles the pack, again draws a card, replace it and draws again. This process he does until he draw a heart card. The probability that he will have to make at least four draws is

If the point $(a,a^2)$ lies inside the triangle formed by the lines $2x+3y-1=0,x+2y-1=0$ and $-8x+8y+2=0$ then

The real value of $\lambda$ for which the image of the point $(\lambda ,\lambda -1)$ with respect to the line $3x+y=6\lambda$ is the point $({\lambda }^2+1,\lambda )$ is

Using binomial theorem, prove that $3^{3n+2}-8b-9$ is divisible by $64,n\in N.$

If $f\left(\frac{x}{y}\right)=\frac{f\left(x\right)}{f\left(y\right)}$ for all $x,y\in R,y\ne 0$ and $f^{\prime }\left(x\right)$ exists for all $x,f\left(2\right)=4.$ Then the value of $f\left(5\right)$ is

If 'Mukesh Kumar' is written by a graphite pencil, it weighs $3.0\times {10}^{-10}gm.$ How many carbon atoms are present in it? $N_A=6\times {10}^{23}$

${\int }_{\pi /3}^{\pi /2}\frac{\sqrt{1+cosx}}{(1-cosx{)}^{5/2}}dx$

The line OA makes an angle of $\theta ={30}^o$ with negative x-axis as shown in the figure. Which of the following could be the measure of the angle made by OA with respect to positive x-axis?

Find the coefficient of x⁵
in the product (1 + 2x)⁶
(1 – x)⁷
using binomial theorem.

Equation of the ellipse with vertices (-4,3), (8,3) and e=$\frac{5}{6}$ is

If the complex number $z$ satisfies $z+\sqrt{2}|z+1|+i=0$, then $z$ is :

If $y=mx+c$ is a common tangent to the curves $y=x^2+8$ and $y=-x^2,$ then which of the following(s) is/are correct

The mean deviation about the mean for the following data :
$5,6,7,8,6,9,13,12,15$ is :

The area (in sq. units) bounded by the parabola $y=x^2-1$, the tangent at the point $(2,3)$ to it and the $y$-axis is:

1. 1

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c},\overrightarrow{d}$ are non-zero vectors satisfying $\overrightarrow{a}=\overrightarrow{b}+\overrightarrow{c}$,$\overrightarrow{b}\times \overrightarrow{d}=\overrightarrow{0}$ and $\overrightarrow{c}\cdot \overrightarrow{d}=0$ , then $\frac{\overrightarrow{d}\times (\overrightarrow{a}\times \overrightarrow{d})}{|\overrightarrow{d}{|}^2}$ is always equal to

The equation of line passing through points $(1,0,-2)$ and $(2,3,-4)$ in vector form is(are)

(where ${\lambda }_1,{\lambda }_2\in R$)

Four persons independently solve a certain problem correctly with probabilities $\frac{1}{2},\frac{3}{4},\frac{1}{4},\frac{1}{8}.$ Then, the probability that the problem is solved correctly by atleast one of them, is ?

From which of the following the distance of the point (1, 2, 3) is $\sqrt{10}$

If $f\left(x\right)=\{\begin{array}{cc}\frac{sin\left[x\right]}{\left[x\right]},& \left[x\right]\ne 0\\ 0,& \left[x\right]=0\end{array},$ where [.]
denotes the greatest integer function, then ${lim}_{x\to 0}f\left(x\right)$ is equal to

If G(x) = - $\sqrt{25-x^2}$ then $\underset{x\to 1}{lim}\frac{G\left(x\right)-G\left(1\right)}{x-1}$ has the value