Explore topic-wise InterviewSolutions in Current Affairs.

If the area of the auxiliary circle of the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b)$ is twice the area of the ellipse then eccentricity of the ellipse is

If $s=p+q+r$, then the value of $\left|\begin{array}{ccc}s+r& p& q\\ r& s+p& q\\ r& p& s+q\end{array}\right|$ is

In the interval $(0,1)$ maximum value of the function $f\left(x\right)=|x\ln x|$ is -

The derivative of the symmetric function drawn in given figure will look like

For a quadrilateral $ABCD$ , if $3,4,5$ and $6$ points are marked on the sides $AB,BC,CD$ and $DA$ respectively. Then number of triangles that can be formed with vertices on different sides, is

If $y^2+{\log }_e\left({\cos }^{2}x\right)=y,x\in (-\frac{\pi }{2},\frac{\pi }{2})$, then

A signal swhich can be green or red with probability $\frac{4}{5}$ and $\frac{1}{5}$ rexpectively, is received by station $A$ and then transmitted to station $B$. The probability of each staation receiving the signal correctly is $\frac{3}{4}$. If the signal received at station $B$ is green, then the probability that the origonal signal was green is

Let $f:R\to R$ be defined as $f(x+y)+f(x-y)=2f\left(x\right)f\left(y\right)$, $f\left(\frac{1}{2}\right)=-1$. Then the value of $\sum _{k=1}^{20}\frac{1}{\sin \left(k\right)\sin (k+f(k\left)\right)}$ is equal to

1. 0.5425

Equation of a line which is parallel to the line common to the pair of lines given by $6x^2-xy-12y^2-0$ and $15x^2+14xy-8y^2-0$ and at a distance 7 from it is

If a $5$ digit number is created using the digits $1,2,3,3,5$. If all possible numbers are arranged in ascending order, then the number situated at ${51}^{th}$ position is

1. -100

If $f\left(x\right)=\int (\cot \frac{x}{2}-\tan \frac{x}{2})dx,$ where $f\left(\frac{\pi }{2}\right)=0,$ then which of the following statements is (are) CORRECT ?

$($Note : $\text{sgn}\left(y\right)$ denotes the signum function of $y.)$

If $\alpha$, $\beta$ and $\gamma$ are in A.P., $\frac{\sin \alpha -\sin \gamma }{\cos \gamma -\cos \alpha }$ equals to

If $x\frac{dy}{dx}=y(logy-logx+1)$, then the solution of the equation is

Evaluate $2\sin \left(\frac{\pi }{12}\right)$

The sum of the solutions of the equation $|x^2-10x+21|=|x-3|$ is

If ax+by+c=0 and lx+my+n=0 are asymptotes of a hyperbola, then

The probability distribution of x is

$\begin{array}{ccccc}x& 0& 1& 2& 3\\ P\left(x\right)& 0.2& k& k& 2k\end{array}$

Find the value of k

Is slope of a line is defined as the tangent of the angle it makes with the positive x axis or simply the x- axis I.e. both positive and negative

Find points at which the tangent to the
curve y = x³ − 3x² −
9x + 7 is parallel to the x-axis.

1. 5

If 5 tan alpha =4, show that 5 sin alpha-3cos alpha/5sin alpha+2cos alpha=1/6.

The value of integral $\underset{0}{\overset{\pi }{\int }}\frac{x\tan x}{\sec x+\tan x}dx$ is equal to

The number of solutions of $\frac{{\sin }^3\frac{x}{2}-{\cos }^3\frac{x}{2}}{2+\sin x}=\frac{\cos x}{3}$ in the interval $[0,10\pi ]$ is

The value of ${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)$