Explore topic-wise InterviewSolutions in Current Affairs.

Find the value of $m$ for which
$5^m÷5^{-3}=5^5$

The value of $\underset{x\to 0}{lim}\frac{1-4^x-5^x+{20}^x}{\sqrt{2\cos x+7}-3}$ is

Compute the indicated product
$$\left[\begin{array}{cc}2& 1\\ 3& 2\\ -1& 1\end{array}\right]$$$$\left[\begin{array}{ccc}1& 0& 1\\ -1& 2& 1\end{array}\right]$$

Given an example of a relation. Which is
(i) Symmetric but neither reflexive nor transitive.

(ii) Transitive but neither reflexive nor symmetric.

(iii) Reflexive and symmetric but not transitive.

(iv) Reflexive and transitive but not symmetric.

(v) Symmetric and transitive but not reflexive.

Integrate the function.
$\int e^x(sinx+cosx)dx.$

The area of the triangle formed by three points $P\{a{t}_1{t}_2,a(t_1+t_2\left)\right\},Q\{a{t}_2{t}_3,a(t_2+t_3\left)\right\},R\{a{t}_3{t}_1,a(t_3+t_1\left)\right\}$ is _____.

If $x\in [-3,2]$, then $2x+7$ lies in

Solution set of $2x–1>7$ and $3x–2\le 16$ is

The coordinates of the corner points of the bounded feasible region are $(10,0),(2,4),(1,5)$ and $(0,8)$. The maximum of objective function $z=60x+10y$ is

If $\frac{\sqrt{1+cosx}+\sqrt{1-cosx}}{\sqrt{1+cosx}=\sqrt{1-cosx}}=cot(a+\frac{x}{2}),xϵ(\pi ,2\pi )$ then a___

The value of $\theta$ which satisfy the equation $3{\tan }^2\theta +3\tan \theta -\cot \theta =1$ (where $n\in Z$) can be

If the lines $\frac{x-2}{1}=\frac{y-3}{1}=\frac{z-4}{-k}$ and$\frac{x-1}{k}=\frac{y-4}{2}=\frac{z-5}{1}$ are coplanar, then k can have

In acute angled triangle $ABC,r+r_1=r_2+r_3$ and $\angle B>\frac{\pi }{3}$ then

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

If $y={[x+\sqrt{x^2+a^2}]}^n,then\frac{dy}{dx}$ is equal to

If a, b, c are in G.P. and x, y are AM's between a, b and b, c respectively, then

Let f(x) be a real valued function defined on: $R\to R$ such that $f\left(x\right)=[x{]}^2+[x+1]-3$, where [x] denotes greatest integer less than or equal to x, then which of the following option(s) is/are correct?

3.Cards marked with numbers 13,14,15,.....,60 are placed in a box and mixed throughly.One card is drawn at random from the box.Find the probability that number on the drawn card is

(i)divisible by 5,(ii)a number which is a perfect square. (Ans. (i)5/24 (ii)1/12.)

The set of all those points, where the function

$f\left(x\right)=\frac{x}{1+|x|}$

is differentiable, is

Solve for x and y : $12sinx+5cosx=2y^2-8y+21$.

A straight line $L$ through the point $(3,-2)$ is inclined at an angle ${60}^{\circ }$ to the line $\sqrt{3}x+y=1.$ If $L$ also intersects the $x$-axis, then the equation of line $L$ is

The value of $\underset{0}{\overset{\frac{\pi }{4}}{\int }}2{\tan }^{3}xdx$ is

$Ifthefocioftheellipse\frac{x^2}{16}+\frac{y^2}{b^2}=1andthehyperbola\frac{x^2}{144}-\frac{y^2}{81}=\frac{1}{25}coincide,writethevalueof{b}^2$

If $\alpha ,\beta$ are the roots of the equation $a{x}^2+bx+c=0$, then the value of determinant $\left|\begin{array}{ccc}1& cos(\alpha -\beta )& cos\alpha \\ cos(\alpha -\beta )& 1& cos\beta \\ cos\alpha & cos\beta & 1\end{array}\right|$ is equal to

If $\int \frac{2x^{2}se{c}^{2}xdx}{(xse{c}^{2}x-tanx{)}^2}=f\left(x\right)+cosx+x+c$, where C is constant of integration, then value of $f\left(\frac{\pi }{4}\right)-f(-\frac{\pi }{4})$ is equal to

The number of solution of ${\sec }^2\theta {\text{cosec}}^2\theta +2{\text{cosec}}^2\theta =8$ for $x\in [0,2\pi ]$ is

The coefficient of $x$ in the equation $x^2+px+q=0$, was wrongly written as $17$ in place of $13$ and the roots thus found to be $-2$ and $-15$. The roots of the correct equation is/are

Equation of the hyperbola with length of the latusrectum $\frac{9}{2}$ and e = $\frac{5}{4}$ is

Let $f\left(x\right)=cosx(sinx+\sqrt{si{n}^{2}x+si{n}^2\theta }),\theta$ is a given const, then max of f(x)is

If$A=\left[\begin{array}{ccc}2& 0& 1\\ 1& 1& 0\\ 2& 1& 1\end{array}\right]$ and $adjA=\left[\begin{array}{ccc}1& 2& -1\\ x& y& z\\ -1& -2& 2\end{array}\right]$ then $(x,y,z)$

If $Z_1,Z_2,Z_3$ are complex numbers such that

$|Z_1|=|Z_2|=|Z_3|=|\frac{1}{Z_1}+\frac{1}{Z_2}+\frac{1}{Z_3}|=1$ then $|Z_1+|Z_2+Z_3|$ is

Find equivalent capacitance between A and B.

The mean deviation about the median for the following data

$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of students}& 6& 8& 14& 16& 4& 2\end{array}$

is