Explore topic-wise InterviewSolutions in Current Affairs.

The value of ${\int }_2^3\frac{\sqrt{x}}{\sqrt{5-x}+\sqrt{x}}.dx$ is equal to

If the line $ax+by+c=0;a\ne 0,b\ne 0$ is perpendicular to line $3y+4x+5=0$, then the value of $\frac{3}{a}+\frac{4}{b}$ is

Number of solution(s) of the equation $x^2-5x\text{sgn}(x^2-9)+6=0$ is

(Here, $\text{sgn}$ denotes the signum function)

Find the sum of the following series:

${\tan }^{-1}\frac{1}{3}+{\tan }^{-1}\frac{2}{9}+{\tan }^{-1}\frac{4}{33}+....+{\tan }^{-1}\frac{2^{n-1}}{1+2^{2n-1}}$

Show that each of the relation R in the set $A=\{x\in Z:0\le x\le 12\}$, given by
(i) R = {(a, b) : |a - b| is a multiple of 4}

(ii) R = {(a, b) : a = b} is an equivalence relation. Find the set of all elements related to 1 in each case.

A straight line drawn through the point A (2, 1) making an angle $\pi /4$ with positive x-axis intersects another line x + 2y + 1 = 0 in the point B. Find length AB.

Find the area of the triangle with coordinates A(-2, 1), B(3, 3) and C(1, -2).

If $A$ and $B$ are two independent events then the value of $P(A^{\prime }\cap B^{\prime })-P(A\cap B)$ is same as:

The vertices of a triangle are $A(0,-6),$ $B(-6,0)$ and $C(1,1)$ respectively. Then coordinates of the excentre opposite to vertex $A$ are

If $\int f\left(x\right)dx=\Psi \left(x\right)$, then $\int x^{5}f\left(x^3\right)dx$ is equal to

Find the 9^th term in the following sequence whose n^th term is

The letters of the word ${}^{\prime }LOGARITH{M}^{\prime }$ are arranged in all possible ways. The number of arrangements in which the relative positions of the vowels and consonants are not changed is

If $z_1,z_2$ are complex numbers such that $Re\left(z_1\right)=|z_1-1|$, $Re\left(z_2\right)=|z_2-1|$ and $arg(z_1-z_2)=\frac{\pi }{6}$, then $Im(z_1+z_2)$ is equal to:

The area of the triangle formed by the coordinate axes and tangent to the curve $y={\log }_{e}x$ at $(1,0)$ is

Let $P$ be a plane passing through the points $(2,1,0),(4,1,1)$ and $(5,0,1)$ and $R$ be any point $(2,1,6)$. Then the image of $R$ in the plane $P$ is:

Find the number of solutions of the equation, $sin=x^2+x+1$

The coefficient of x in the equation $x^2$ + px +q =0 was taken as 17 in place of 13, its roots were found to be -2 and -15, the roots of the original equation are

If f(x) = sin[π^2]x+sin[-π^2]x, where [x]denotes greatest Integer less than or equal to x, then

Let $Z$ be the set of integers. If $A=\{x\in Z:|x-3{|}^{x^2-5x+6}=1\}$ and $B=\{x\in Z:10<3x+1<22\},$ then the number of subsets of the set $A\times B$ is

The number of all possible positive integral values of $\alpha$ for which the roots of the quadratic equation, $6x^2-11x+\alpha =0$ are rational numbers is :

If $\frac{x}{a}+\frac{y}{b}=\sqrt{2}$ touches the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,$ then its eccentric angle $\theta$ is equal to

The greatest possible perimeter of the triangle is

If f(x) = $\frac{sin2x+Asinx+Bcosx}{x^3}$ = is continuous at x = 0 then B – 2A = _____________

The value of $\int \frac{(a^x+b^x{)}^2}{a^x\cdot b^x}dx$ is, where $a>1,b>1$ & $a\ne b$

​​​​​​​(where $C$ is constant of integration)