Explore topic-wise InterviewSolutions in Current Affairs.

$If2si{n}^2\theta =3cos\theta ,where0\le \theta \le 2\pi ,thenfindthevalueof\theta .$

If $I_m={\int }_1^e(\ln x{)}^{m}dx$ and $\frac{I_m}{K}+\frac{I_{m-2}}{L}=e,(m>1,m\in N)$ then the values of $K$ and $L$ are

In a community it is found that $52\%$ people like prime video and $73\%$ like Netflix and $x\%$ like both, then

If the number of terms in the expansion of ${(1-\frac{2}{x}+\frac{4}{x^2})}^n$, $x\ne 0$ is 28, then the sum of the coefficients of all the terms in this expansion, is :

The number of solutions of the equation $|5\tan 2\theta \tan \theta -12\tan \theta |+|3{\sin }^2\theta -\sin 2\theta |=0$ in the interval $[0,2\pi ]$ is

Write the value of ${lim}_{x\to 0^{-}}\frac{\sin x}{\sqrt{x}}$

Find the equation of normal to the parabola $y^2=8x$ at (8, 8) using parametric form.

For every real number c$\ge 0$, find all the complex number z which satisfy the equation

$|z{|}^2$ - 2iz + 2c(1 + i) = 0

If Show that A + A′ is a symmetric matrix

A line passes through a point A (1, 2) and makes an makes an angle of ${60}^{\circ }$ with the x-axis and intersects the line x + y = 6 at the point P. Find AP.

Write the coordinates of the orthocentre of the triangle formed by the lines $x^2-y^2=0$ and $x+6y=18$.

The general solution of the differential equation $\frac{dy}{dx}=\frac{(x+y)+(x+y-1)\ln (x+y)}{\ln (x+y)}$ is (where $C$ is a constant of integration)

Find
the inverse of each of the matrices, if it exists.

Find the local maxima and local minima, if any of the following function. Also, find the local maximum and the local minimum values, as the case may be as follows.

$f\left(x\right)=x\sqrt{1-x},x>0$

In a lottery, a person chooses six different numbrs at random from I to 20, and if these six numbers match with six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game?

$\underset{0}{\overset{\frac{\pi }{4}}{\int }}log\left(\frac{sinx+cosx}{cosx}\right)dx$

Let $f\left(x\right)=|x-1|$. Then,

Consider the set of eight vectors
V={ai+bj+ck}:a,b,c $ϵ\{-1,1\}$. Three non - coplanar vectors can be chosen from V in $2^p$ ways, Then $p$ is ___

If a function $f\left(x\right)$ defined by

$f\left(x\right)=\{\begin{array}{cc}a{e}^x+b{e}^{-x},& -1\le x<1\\ c{x}^2,& 1\le x\le 3\\ a{x}^2+2cx& 3<x\le 4\end{array}$

be continuous for some $a,b,c\in R$ and $f^{\prime }\left(0\right)+f^{\prime }\left(2\right)=e,$ then the value of $a$ is :

Tangents $PA$ and $PB$ are drawn to the circle $(x-4{)}^2+(y-5{)}^2=4$ from the point $P$ on the curve $y=\sin x$, where $A$ and $B$ lie on the circle. Consider the function y = $f\left(x\right)$ represented by the locus of the centre of the circumcircle of triangle $PAB$, then

Range of $y=f\left(x\right)$ is

Let $P(a{t}^2,2at),Q,R(a{r}^2,2ar)$ be three points on a parabola $y^2=4ax.$ If $PQ$ is the focal chord and $PK,QR$ are parallel where the co-ordinates of $K$ is $(2a,0),$ then the value of $r$ is

Find the equation of the normal to curve $y^2=4x$ at the point (1, 2).

The value of $\theta$ for which the system of equations $\left(\sin 3\theta \right)x-2y+3z=0,\left(\cos 2\theta \right)x+8y-7z=0$ and $2x+14y-11z=0$ has a non-trivial solution, is
($n\in Z)$

If $y=ta{n}^{-1}\left(\frac{4x}{1+5x^2}\right)+ta{n}^{-1}\left(\frac{2+3x}{3-2x}\right)$ then $\frac{dy}{dx}atx=\frac{1}{5}is$

If the reflection of the parabola $y^2=4(x-1)$ in the line x + y = 2 is the curve $Ax+By=x^2$, then the value of (A+B) is

Determine if the points $(1,5),(2,3),and(-2,-11)$ are collinear.

If $f\left(x\right)=0$ is a quadratic equation such that $f(-\pi )=f\left(\pi \right)=0$ and $f\left(\frac{\pi }{2}\right)=-\frac{3{\pi }^2}{4},$ then $\underset{x\to -\pi }{lim}\frac{f\left(x\right)}{\sin \left(\sin x\right)}$ is

The equation of the plane, which is equidistant from lines $\frac{x-1}{1}=\frac{y-2}{2}=\frac{z-2}{3}$ and $\frac{x-2}{2}=\frac{y-2}{1}=\frac{z-1}{2}$ is