Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\left|\begin{array}{ccc}a-b-c& 2a& 2a\\ 2b& b-c-a& 2b\\ 2c& 2c& c-a-b\end{array}\right|$ is equal to

If leap year is selected at random, the probability that it will contain 53 Sundays is equal to:

$\text{The eccentricity of the hyperbola}{x}^2-4y^2=1is$

Water is dripping out from a conical funnel of semi-vertical angle π/4 at the uniform rate of 2 square cms /sec in the surface area, through a tiny hole at the vertex of the bottom. When the slant height of cone is 4 cm, then the rate of decrease of the slant height of water is

If $\alpha ,\beta$ be the roots of the equation $a{x}^2+bx+c=0$. Let $S_n={\alpha }^n+{\beta }^n,$ for $n\ge 1$
If $\Delta =\left|\begin{array}{ccc}3& 1+S_1& 1+S_2\\ 1+S_1& 1+S_2& 1+S_3\\ 1+S_2& 1+S_3& 1+S_4\end{array}\right|$, then $\Delta$ is equal to

The solution of the differential equation $\frac{dy}{dx}-2ytan2x=e^{2x}sec2x$ is

The integrating factor (IF) of the differential equation
$(1-y^2)\frac{dy}{dx}+yx=ay(-1<y<1)$ is
(a)$\frac{1}{y^2-1}$
(b)$\frac{1}{\sqrt{y^2-1}}$
(c)$\frac{1}{1-y^2}$
(d)$\frac{1}{\sqrt{1-y^2}}$

If $\frac{a+ib}{c+id}=x+iy$, then $\frac{a^2+b^2}{c^2+d^2}$ is equal to

A relation R on A = {1,2,3,4} is defined as x R y if x divides y. Then R is

1. 0.938

The general solution of $\cos x+\sin x=\cos 2x+\sin 2x$ is

The line y
= mx + 1 is a tangent to the curve y² = 4x
if the value of m is

(A) 1 (B) 2 (C) 3 (D)

The range of $f\left(x\right)=\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{(1-\cos x)\sqrt{...\infty }}}}$

In $\Delta ABC$, if $\frac{1}{b+c}+\frac{1}{c+a}=\frac{3}{a+b+c}$, then $\angle C$ is equal to

Two person A and B toss a die one after another. The person who throws 6 wins. If A starts the game,then the probability of his winning is

If $n\left(U\right)=60,n\left(A\right)=21,n\left(B\right)=43,$ then minimum and maximum value of $n(A\cup B)$ is

Let the foot of the perpendicular of $P(2,-3,1)$ on the line
$\frac{x+1}{2}=\frac{y-3}{3}=\frac{z-2}{-1}$ be $Q.$
If direction ratios of the line segment joining P and Q be $l,m,n$, then which of the following relations are correct ?

Let $A$ be a $3\times 3$ matrix such that $adjA=\left[\begin{array}{ccc}2& -1& 1\\ -1& 0& 2\\ 1& -2& -1\end{array}\right]$ and $B=adj\left(adjA\right)$.

If $\left|A\right|=\lambda$ and $\left|{\left(B^{-1}\right)}^T\right|=\mu$, then the ordered pair, $(\left|\lambda \right|,\mu )$ is equal to:

An A.P., a G.P., and a H.P. have a and b for their first two terms their $(n+2{)}^{th}$ terms will be in G.P. if $\frac{b^{2n+2}-a^{2n+2}}{ab(b^{2n}-a^{2n})}$

A coin is biased so that the head is 3 times as likely to occur as tail. If the coin is tossed twice, find the probability distribution of number of tails.

Solve
system of linear equations, using matrix method.

The equation of the curve whose parametric equations are $x=1+4\cos \theta ,y=2+3\sin \theta ,\theta \in R,$ is

The equation of the circle which passes through the points (2, 3) and (4, 5) and the centre lies on the straight line y – 4x + 3 = 0, is

If ${}^{n-1}{C}_r=(k^2-3{)}^n{C}_{r+1}$, then $kϵ$

Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation.

Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

a,b,c are positive integers such that a² + 2b² - 2bc = 100 and 2ab - c² = 100. Then is

If the sides of a triangle are in $A.P.$ and its area is $\frac{3}{5}$ of area of equilateral triangle of same perimeter, then ratio of sides is

Primitive of $f\left(x\right)=x{.2}^{In(x^2+1)}$ with respect to x is

A hyperbola having the transverse axis of length $\sqrt{2}$ has the same foci as that of the ellipse $3x^2+4y^2=12$, then this hyperbola does not pass through which of the following points

A team of $4$ students is to be selected from a total of $12$ students. The total number of ways in which the team can be selected such that two particular students refuse to be together and other two particular students wish to be together only is equal to

$\overrightarrow{AB}=3\hat{i}-\hat{j}+\hat{k}and\overrightarrow{CD}=-3\hat{i}+2\hat{j}+4\hat{k}$ are two vectors.The position vectors of the points A and C are $6\hat{i}+7\hat{j}+4\hat{k}and-9\hat{i}+2\hat{j}$,respectively. Find the position of vector of a point P on the line AB and a point Q on the line CD such that $\overrightarrow{PQ}$ is perpendicular to $\overrightarrow{AB}and\overrightarrow{CD}$ both.