Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\alpha$ for which $4\alpha \underset{-1}{\overset{2}{\int }}{e}^{-\alpha |x|}dx=5$ is

Find the angle between the planes

$2x+7y+11z-3=0\text{and}5x+3y+9z+1=0$

If f: $[1,\infty )\to [2,\infty )$ is given by $f\left(x\right)=x+\frac{1}{x}$ , then $f^{-1}\left(x\right)$ is equal to

A triangle is divided into 4 pieces and the area of the 4 regions are given inside the corresponding regions. The value of x is

For the curve corresponding to f(x) = x² - 8x + 12, find the point at which the tangent is parallel to the x axis

A fair die is rolled. consider events E = {1, 3,5} F = {2,3} and G = {2,3,4,5}. Find
$P\left(\frac{E}{G}\right)andP\left(\frac{G}{E}\right)$

If sinA - cos A = 1/2, then find the value of 1/(sinA+cosA)

Let two vectors are given by $\overrightarrow{a}=\hat{i}-2\hat{j}+3\hat{k},\overrightarrow{b}=-2\hat{i}+\hat{j}-\hat{k},$ then which of the following is a vector equation of line passing through point $(2\hat{i}+3\hat{j})$ and parallel to $(\overrightarrow{a}\times \overrightarrow{b})$

For any vector
$\overrightarrow{a},thevalueof(\overrightarrow{a}\times \hat{i}{)}^2+(\overrightarrow{a}\times \hat{j}{)}^2+(\overrightarrow{a}\times \hat{k}{)}^{2}is(a\left){\overrightarrow{a}}^2\right(b\left)3\overrightarrow{a}\right(c\left)4{\overrightarrow{a}}^2\right(d)2{\overrightarrow{a}}^2$

If $A=\{3,5\}$ and $A\times B=B\times A$, then the correct option(s) can be

The value of $x$ satisfying ${\log }_{16}x+{\log }_{x}16={\log }_{512}x+{\log }_{x}512$ is/are

The base
of an equilateral triangle with side 2a lies along they y-axis
such that the mid point of the base is at the origin. Find vertices
of the triangle.

The locus of the centres of the circles, which touch the circle, $x^2+y^2=1$ externally, also touch the $y-$axis and lie in the first quadrant, is:

Find the equation of a curve passing through the origin, given that the slope of the tangent to the curve at any point (x,y) is equal to the sum of the coordinates of the points.

Prove
that the function
is
continuous at x
= n, where
n is a
positive integer.

The coefficient of $x^k$ in $1+(1+x)+(1+x{)}^2+\cdots +(1+x{)}^n$, where $0\le k\le n$ is

In $\Delta ABC$, $a\le b\le c$, if $\frac{a^3+b^3+c^3}{si{n}^{3}A+si{n}^{3}B+si{n}^{3}C}=8$, then the maximum value of $a$ is

A plane which bisects the angle between the two given planes $2x–y+2z–4=0$ and $x+2y+2z–2=0,$ passes through the point :

If $x+y\sqrt{2}=2\sqrt{2}$ is a tangent to the ellipse $x^2+2y^2=4,$ then the eccentric angle of the point of contact is

Domain of the function $\frac{1}{{\log }_{10}(x+2)}+\sqrt{1-x}$ is

Solve the given inequality graphically in two-dimensional plane: x > –3

The function f(x) = e^x

$\int \frac{2x}{(1-x^2)\sqrt{x^4-1}}dx$ is equal to

Two vertices of an equilateral triangle are (–1, 0) and (1, 0) and its third vertex lies above the x-axis, the equation of the circumcircle is

The eccentricity of the ellipse $a{x}^2+b{y}^2+2fx+2gy+c=0$ if axis of ellipse parallel to x-axis is