Explore topic-wise InterviewSolutions in Current Affairs.

Find the middle term(s)in the expansion of:

$\left(i\right){(x-\frac{1}{x})}^{10}$

$\left(ii\right)(1-2x+x^2{)}^n$

$\left(iii\right)(1+3x+3x^2+x^3{)}^{2n}$

$\left(iv\right){(2x-\frac{x^2}{4})}^9$

$\left(v\right){(x-\frac{1}{x})}^{2n+1}$

$\left(vi\right){(\frac{x}{3}+9y)}^{10}$

$\left(vii\right){(3-\frac{x^3}{6})}^7$

$\left(viii\right){(2ax-\frac{b}{x^2})}^{12}$

$\left(ix\right){(\frac{p}{x}+\frac{x}{p})}^9$

$\left(x\right){(\frac{x}{a}-\frac{a}{x})}^{10}$

The mean and the variance of a binomial distribution are 4 and 2 respectively. Then the probability of 2 successes is

Find X and Y if

$\left(ii\right)2X+3Y=\left[\begin{array}{cc}2& 3\\ 4& 0\end{array}\right]and3X+2Y=\left[\begin{array}{cc}2& -2\\ -1& 5\end{array}\right]$

Which of the following definite integrals reduces to $\frac{\pi }{2}$?

If $f(x+f(y\left)\right)=f\left(x\right)+y\forall x,y\in R$ and $f\left(0\right)=1$, then the value of $f\left(7\right)$ is

We can't find the inverse of a singular matrix because |A|=0.But there should be an inverse for singular matrix as well, right?Is there any way to find the increase ofa singular matrix?

If the line's $(1+t)x-2ty+3t^2=0$ and $t^{2}x-(3-t)y+6=0,t\ne 0$ are perpendicular to each other, then the number of possible value(s) of $t$ is

Find the values of y for which the equation y$x^2+yx+1=0$ has real roots.

The set of solutions of $2^{|x|}-|2^{x-1}-1|=2^{x-1}+1$ is

Which of the following are not the direction ratios of the sides of the triangle whose vertices are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2)

Identify the graph above.

If $w=\cos \left(\frac{\pi }{n}\right)+i\sin \left(\frac{\pi }{n}\right)$, then value of $1+w+w^2+\cdots +w^{n-1}$ is

If four persons are chosen at random from a group of 3 men, 2 women and 4

children. Then the probability that exactly two of them are children, is

[Kurukshetra CEE 1996; DCE 1999]

The angle between asymptotes of the standard hyperbola (centered at origin and $x$-axis as transverse axis) is $\frac{\pi }{3}$. If the radius of the director circle of the hyperbola is $4$ then the equation of the hyperbola is

The value of $\underset{-\pi /4}{\overset{\pi /4}{\int }}{\sin }^{103}x.{\cos }^{101}xdx$ is

The acute angle between two lines whose direction cosines are given by the relation between $l+m+n=0and{l}^2+m^2-n^2=0$

The equations of the sides AB, BC and CA of $\Delta ABC$ are $y-x=2,x+2y=1$ and $3x+y+5=0$ respectively. The equation of the altitude through B is

Let A, B, C be any three events in a sample space of a random experiment. Let the events $E_1=$ exactly one of A, B occurs, $E_2=$ exactly one of B, C occurs, $E_3=$ exactly one of C, A occurs, $E_4$ = all of A, B, C occurs, $E_5=$ atleast one of A, B, C occurs. $P\left(E_1\right)=P\left(E_2\right)=P\left(E_3\right)=\frac{1}{3},P\left(E_4\right)=\frac{1}{9}\text{then}P\left(E_5\right)=$

Differentiate the following functions with respect to x :

$\frac{x+e^x}{1+logx}$

How can I solve the eqn

4a=3b &

4b=5c

If $x=sec\theta -cos\theta ,y=se{c}^{10}\theta -co{s}^{10}\theta$ and $(x^2+4)=k(y^2+4)$, then k is equal to

Choose the most appropriate option to replace (?).
620 632 608 644 596 ?

Let $A=\{a,e,i,o,u\}$ and $B=\{m,y,g,h,n,s\}$. If $f:A\to B$ is a function, then the maximum number of such functions possible are

The value of the sum $\sum _{n=1}^{13}(i^n+i^{n+1})$ , where i = $\sqrt{-1}$ equals

Can MPS or MPC ever be negative? Give reasons in support of your answer.

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal to half of the distance between its foci, is___ .

Minimum value of (x + 1) (x + 2) (x + 3) (x + 4) + 2 is ___

The angle between the lines $2x-y+3=0$ and $x+2y+3=0$ is

If f : R $\to$ R be a function given by f (x) = $(3-x^3{)}^{\frac{1}{3}}$ ,then f $\circ$ f(x) =

$\text{The equation,}\frac{x^2}{10-a}+\frac{y^2}{4-a}=1\text{represents ellipse if}$

f(x) = $\{\begin{array}{c}2x,ifx<0\\ 0,if0\le x\le 1\\ 4x,ifx>1\end{array}$

For the matrix, $A=\left[\begin{array}{cc}1& 5\\ 6& 7\end{array}\right]$, verify that

(i) (A+A') is a symmetric matrix.

(ii) (A-A') is a skew-symmetric matrix.

Match the following :
$\begin{array}{cccc}& Column-I& & Column-II\\ \left(A\right)& arg\frac{z+1}{z-1}=\frac{\pi }{4}& \left(P\right)& Parabola\\ \left(B\right)& |z-2|=4& \left(Q\right)& Partofacircle\\ \left(C\right)& argz=\frac{\pi }{4}& \left(R\right)& Fullcircle\\ \left(D\right)& z=t+i{t}^2(t\in R)& \left(S\right)& StraightLine\end{array}$

General solution of the equation ${\sin }^{2}x+{\text{cosec}}^{2}x-2(\sin x+\text{cosec}x)+2=0$ is

A player $X$ has a biased coin whose probability of showing heads is $p$ and a player $Y$ has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If $X$ starts the game, and the probability of winning the game by both the players is equal, then the value of ${}^{\prime }{p}^{\prime }$ is :

A 10.0 cm gas column is trapped by a column of Hg 4 cm long in capillary tube of uniform bore. The tube is held horizontally in a room at 1 atm. Length of the air column when the tube is held vertically with the open end up is

Differentiate the following functions with respect to x :

$cos(x+a)$

$2(3-x)\ge \frac{x}{5}+4$

If $\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|$

$=(a+b+c)(x+a+b+c{)}^2,x\ne 0$ and $a+b+c\ne 0$, then $x$ is equal to :