Explore topic-wise InterviewSolutions in Current Affairs.

${lim}_{x\to 0}{\left\{\frac{e^x+e^{-x}-2}{x^2}\right\}}^{\frac{1}{x^2}}$

If f(x) = $\alpha$x + $\beta$, and f = {(1,1), (2,3), (3,5), (4, 7)}, then $(\alpha ,\beta )$=

Prove that the radii of the circles
$x^2+y^2=1,x^2+y^2-2x-6y-6=0$
and $x^2+y^2-4x-12y-9=0$ are in A.P

Find the locus of a point which moves such that its distance from the origin is three times its distance from $x$-axis.

Write the value of $cos\frac{\pi }{7}cos\frac{2\pi }{7}cos\frac{4\pi }{7}$.

Let $\alpha \left(a\right)$ and $\beta \left(a\right)$ be the roots of the equation $(\sqrt[3]{31+a}-1)+(\sqrt{1+a}-1)x+(\sqrt[6]{61+a}-1)=0$ where $a>-1$. then ${lim}_{a\to 0^{+}}\alpha \left(a\right)$ and ${lim}_{a\to 0^{+}}\beta \left(a\right)$ are

The area (in sq. units) in the first quadrant bounded by the parabola, $y=x^2+1$, the tangent to it at the point $(2,5)$ and the coordinate axes is :

The asymptotes of the hyperbola $xy=hx+ky$ are

$cos\theta (tan\theta +2)(2tan\theta +1)=2sec\theta +5sin\theta$

The sum of non-integeral roots of the equation $x^4-3x^3-2x^2+3x+1=0$ is

If $\frac{3+i\sin \theta }{4-i\cos \theta },\theta \in [0,2\pi ]$, is a real number, then an argument of $\sin \theta +i\cos \theta$ is :

Equation of the circle of radius √2 containing the point (3, 1) and touching the line |x-1|=|y-1|, is

An investigator interviewed $100$ students to determine the performance of three drinks : milk, coffee and tea. The investigator reported that $10$ students take all three drink milk, coffee and tea ; $20$ students take milk and coffee; $25$ students take milk and tea ; $20$ students take coffee and tea; $12$ students take milk only; $5$ students take coffee only and $8$ students take tea only. Then the number of students who did not take any of three drinks is

if $\frac{z-i}{z+i}$(z ≠ -i) is a purely imaginary number, then z.$\overline{z}$ is equal to

If ${\sin }^{3}x+{\cos }^{3}x+\sin x\cos x=1$, then $x$ is equal to

The sum of first 'n' terms of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+....is$

If $\alpha$ is the $n^{th}$ root of unity, then $1+2\alpha +3{\alpha }^2+\dots$ to $n$ terms is equal to

$\int si{n}^{3}x.co{s}^{4}xdx$

If X = {$4^n$ - 3n - 1 : n ∈ N} and Y = { 9(n-1) : n ∈ N}, then X ∪ Y is equal to

Tangents are drawn from any point on the circle $x^2+y^2=41$ to the Ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ then the angle between the two tangents is

The slope of the tangent to the curve $x=t^2+3t-8,y=2t^2-2t-5$ at the point $(2,-1)$ is

A semicircular wire fo radius 'R' carries a current 'i'. What will be the magnetic field strength at its centre?

What is meant recruitment? How it is different from selection.

Let $f$ be a function which is continuous in $[0,1]$ and differentiable in $(0,1)$ such that $f\left(1\right)=0$, then there exists some $c\in (0,1)$ such that:

Find the intervals in which the function f given by $f\left(x\right)=2x^2-3x$ is

a) strictly increasing

b) strictly decreasing

If 'x' takes negative permissible value, then $si{n}^{-1}x$ is equal to

All the five digit numbers N = abcde having property a < b < c < d < e are arranged in the increasing order of their magnitude. Then the ${97}^{th}$number in the list contains the odd digit is

If the roots of the equation $q{x}^2+px+q=0$ where p, q are real, be complex, then the roots of the equation $x^2-4qx+p^2=0$ are

For which of the following value of $m$, is the area of the region bounded by the curve $y=x-x^2$ and the line $y=mx$ equals to $\frac{9}{2}$?

$\text{write the eccentricity of hyperbola}$

$9x^2-16y^2=144$

Determine whether each of the following relations are reflexive, symmetric and transitive:
(v) Relation R in the set A of human beings in a town at a particular time given by
(a) R = {(x, y): x and y work at the same place}
(b) R = {(x, y): x and y live in the same locality}
(c) R = {(x, y): x is exactly 7 cm taller than y}
(d) R = {(x, y): x is wife of y}
(e) R = {(x, y): x is father of y}

If $A$ is a symmetric matrix and $B$ is a skew- symmetrix matrix such that $A+B=\left[\begin{array}{cc}2& 3\\ 5& -1\end{array}\right],$ then $AB$ is equal to :

Which of the following statements must be true?

$\int x^2{e}^{x^3}dx=$

If $cosec\theta -sin\theta =a^3,sec\theta -cos\theta =b^3$, then prove that $a^2{b}^2(a^2+b^2)=1$

Let $n>1$ be a positive integer, then find the largest integer m such that ($n^m$ + 1) divides $1+n+n^2$ + ......+ $n^{127}$.

If in the expansion of $(1+x{)}^{15}$, the coefficient of $(2r+3{)}^{th}$ and $(r-1{)}^{th}$ terms are equal, then the value of r is

$\frac{3}{x-2}<1$