Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\left|\begin{array}{cc}x& x+1\\ x-1& x\end{array}\right|$ is

Suppose A is a non-singular matrix such that $A^3-3A^2+6A-I=0.Then,A^{-1}$=___

The local maxima of the funtion $f\left(x\right)=\sin x+\cos x\forall x\in [0,\frac{\pi }{2}]$ is

The range of $f\left(x\right)=\frac{1}{5\sin x-6}$ is

Let $p$ and $q$ be real numbers such that $p\ne 0,p^3\ne q$ and $p^3\ne –q$. If $\alpha$ and $\beta$ are non-zero complex numbers satisfying $\alpha +\beta =–p$ and ${\alpha }^3+{\beta }^3=q$, then a quadratic equation having $\frac{\alpha }{\beta }$ and $\frac{\beta }{\alpha }$as its roots is

${lim}_{x\to 2}\frac{x^3-8}{x^2-4}$

If the normal to the parabola $y^2=4ax$ at the point $(a{t}^2,2at)$ cuts the parabola again at $(a{T}^2,2aT)$, then the range of $T$ is

If the points of intersection of the circle $x^2+y^2=16$ with $x-\text{axis}$ are foci of an ellipse and points of intersection of circle $x^2+y^2=16$ with $y-\text{axis}$ are end points of minor axis of the same ellipse, then eccentricity of the ellipse is

If a ray is incident on a parabolic mirror $y^2=4x$ along a line $y=6$ as shown, then what is the equation of the line along which the reflected ray travels?

The value of $\underset{0}{\overset{1}{\int }}\left|x^2\right(x-3)+3(x-1\left)\right|dx$ is

If the vectors $\overrightarrow{a}=\hat{i}+2\hat{j}+3\hat{k},\overrightarrow{b}=3\hat{i}+6\hat{j}+7\hat{k},\overrightarrow{c}=x\hat{i}+2\hat{j}+3\hat{k}$ form a right handed system, then

The graph of $y=1+{\log }_{4}x$ is

For the equation $3x^2$+ px + 3 =0, p > 0 is one of the root is square of the other, then p is equal to

The sum of the series of ${\cot }^{-1}\frac{5}{\sqrt{3}}+{\cot }^{-1}\frac{9}{\sqrt{3}}+{\cot }^{-1}\frac{15}{\sqrt{3}}+{\cot }^{-1}\frac{23}{\sqrt{3}}+\cdots \infty$ is equal to

If $\alpha$ and $\beta$ are the eccentric angles of the extremities of a focal chord of an ellipse, then the eccentricity of the ellipse is

The combined equation of bisectors of angles between coordinate axes, is

Direction ratios of the line bisecting the acute angle between lines whose direction ratios are $(1,2,-1)$ and $(2,-1,-1),$ is

The probabilities of these mutually exclusive events A, B and C are given by $\frac{2}{3},\frac{1}{4}$ and $\frac{1}{6}$ resoectively. The statement

Sum of the series $3,9,27,...$ upto $6$ terms

Area of the triangle formed by the points $\left(\right(a+3\left)\right(a+4)a+3),\left(\right(a+2\left)\right(a+3),(a+2\left)\right)$ and $\left(\right(a+1\left)\right(a+2\left)\right(a+1\left)\right)$

If $\alpha ,\beta$ are the roots of quadratic equation $x^2+7x+10=0$. Then the quadratic equation with roots as $\alpha +2$ and $\beta +2$ is

Let $f\left(x\right)=(1+x{)}^{201}and{f}^i(0)=\frac{d^{i}f\left(x\right)}{d{x}^i}{|}_{x=0}$. Then $f\left(0\right)+{\sum }_{i=1}^{201}\frac{f^{\left(i\right)}\left(0\right)}{i!}$ equals

Solve $x^2\frac{dy}{dx}=x^2+xy+y^2.$

At an election, a voter may vote for any number of candidates, not greater than the number to be elected. There are 10 candidates and 4 are to be elected. If a voter votes for at least one candidate, then the number of ways in which he can vote is

If $y=f\left(x\right),$ where $f:A\to B$ is a function in $x,$ then which of the following statements is true?



(i) Every element of $A$ needs to have an image.



(ii) $x\in A$ must be related to one and only one value of $y$ of $B.$

If $(p+q)x^4+p{x}^2+6x+1$ is a quadratic polynomial, then the value of $p,q$ can be:

Fundamental period of the function $f\left(x\right)=\frac{(1+\sin x)(1+\sec x)}{(1+\cos x)(1+\text{cosec}x)},x\in R-\left\{\right(2n+1)\pi ,\frac{(4m-1)\pi }{2},n,m\in Z\}$ is

The locus of the mid points of the chords of the circle $x^2+y^2-ax-by=0$ which subtend a right angle at $(\frac{a}{2},\frac{b}{2})$ is :

Evaluate $\int \left(x\right(\tan x)+\ln (\sec x\left)\right)dx$

(where $C$ is constant of integration)