Explore topic-wise InterviewSolutions in Current Affairs.

Let $A$ and $B$ be two independent events such that $P\left(A\right)=m$ and $P\left(B\right)=2m.$ If $\alpha ,\beta$ are the values of $m$ for which $P(\text{exactly one of}A,B\text{occurs})=\frac{5}{9},$ then the value of ${\alpha }^2+{\beta }^2$ is equal to

Evaluate $\int \frac{cos2x+2si{n}^{2}x}{co{s}^{2}x}dx$

The solution of the differential equation $\frac{dy}{dx}=-\left(\frac{x-2y+5}{2x-y+4}\right)$ is

(where $C$ is integration constant)

If $\sum _{r=0}^n\left(\frac{r+2}{r+1}\right)C_r=\frac{2^8-1}{6}$, where $C_r={}^n{C}_r$, then the value of $n$ is

Solution of the equation $(1+x^2)dy=(1+y^2)dx$ is-

Find the next term in the sequence below.

65, 80, 95, 110, 125, 140,_____

Which of the following expression(s) represent a polynomial

Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,(a>b)$ be given ellipse, length of whose latus rectum is $10.$ If its eccentricity is the maximum value of the function, $\varphi \left(t\right)=\frac{5}{12}+t-t^2,\text{then}{a}^2+b^2$ is equal to

Consider a parabola $S:y^2=4x$. Let points A(–1, 0) and B(0, 1) and F be the focus of parabola S.

Let Q(13, 9) be a given fixed point and $P(\alpha ,\beta )$ be a point on the parabola 'S' such that PQ + PF is least, then

Let $S=\frac{1}{6}+\frac{1}{24}+\frac{1}{60}+\frac{1}{120}+\cdots \text{upto}\infty$. Then the value of $2S$ is

The angle between the planes 4x + 2y - 5z = 11 and 3x - 5y - 6z = 2 is:

If e^{(sin x)} - e^{(-sin x)} = 4 then find number of real solutions

^​

The value of $\int \frac{2^x+1}{2^{2x}+2^x}dx$ is

(where $C$ is constant of integration)

If $P(\alpha ,\beta )$ is a point on the ellipse $4x^2+9y^2=1$, at which the tangent is parallel to the line $y=\frac{8x}{9}+200,$ then the value of $|\alpha +\beta |$ is

Let $f:R\to R$ be a function defined by

$f\left(x\right)=\{\begin{array}{cc}\frac{1-\cos ax}{x^2}& \text{if}x<0\\ b& \text{if}x=0\\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}& \text{if}x>0\end{array}$



If $f$ is continuous in $R,$ then $b-a$ can be

Two students while solving a quadratic equation in $x$, one copied the constant term incorrectly and got the roots as $3$ and $2$. The other copied coefficient of $x$ incorrectly and got roots as $-6$ and $1$ respectively. The correct root(s) is/are (Assume the leading coefficient of the quadratic equation as $1$)

Let $\overrightarrow{a}$ and $\overrightarrow{b}$ be two unit vectors inclined at an angle $\theta ,$ then $\sin \left(\frac{\theta }{2}\right)$ is equal to

Which word will be represented by [5] [10] [5]?

(A) MIN (B) TOR (C) MOP

The sum of the series $\sum _{n=1}^{\infty }\frac{n^2+6n+10}{(2n+1)!}$ is equal to :

If equation $si{n}^{4}x=1+ta{n}^{8}x$ then x is

Let $n$ denote the number of solutions of the equation $z^2+3\overline{z}=0,$ where $z$ is a complex number. Then the value of $\sum _{k=0}^{\infty }\frac{1}{n^k}$ is equal to

If the line $(x-y+1)+k(y-2x+4)=0$ makes equal intercept on the axes then the value of $k$ is

The area bounded by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $[0,\frac{\pi }{2}]$ is

Ram rolls a fair die. Which of the following can be the outcome?

Let $f\left(x\right)=\frac{\sqrt{x-1+2\sqrt{x-2}}}{\sqrt{x-2}-1}x$. Then

If the line $y=\sqrt{3}x$ cuts the curve $x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0$ at points $A,B,C$ then $\left(\text{where O is origin}\right)$

For a function $f\left(x\right)=\cos x\forall x\in [\pi ,5\pi ],$ select the regions for which $\cos x\ge \mathrm{0.5.}$

If E and F are events such that P(E) =, P(F) = and P(E and F) =, find:(i) P(E or F), (ii) P(not E and not F).