Explore topic-wise InterviewSolutions in Current Affairs.

The equation of a line touching the curve $y={\mathrm{be}}^{-\frac{x}{a}}$ at a point where it crosses the y-axis is .

If $|z_1|=1,|z_2|=2,|z_3|=3$ and $|9z_1{z}_2+4z_1{z}_3+z_2{z}_3|=12,$ then the value of $|z_1+z_2+z_3|$ is equal to

If a focal chord of the parabola $y^2=bx$ is $2x-y-8=0$, then the equation of the directrix is

Based on the given arrangement, how is A related to D?

A box has 4 dice in it. 4 of them are fair and one of them is marked with 5 on all its faces. A dice chosen at random and rolled thrice shows 5 on all the occasions. The probability that the die chosen was a biased one is?

If $A=\{x:x\in R,0<x<2\}$, $B=\{x:x\in R,1<x\le 3\}$, then $A-B=$

The domain of the function $f\left(x\right)={[9^x+{27}^{\frac{2}{3}(x-2)}-219-3^{2(x-1)}]}^{\frac{1}{4}}$

A function $f:R\to [1,\infty )$ satisfies the equation $f\left(xy\right)=f\left(x\right)f\left(y\right)-f\left(x\right)-f\left(y\right)+2$. If f is differentiable on $R-0andf\left(2\right)=5,f^{\prime }\left(x\right)=\frac{f\left(x\right)-1}{x}.\lambda then\lambda$ =________

If one of the slopes of the pair of lines $a{x}^2+2hxy+b{y}^2=0$ is n times the another, then

${lim}_{x\to 0}\frac{5xcosx+3sinx}{3x^2+tanx}$

$\text{Write the number of values of}\theta in[\theta ,2\pi ]thatsatisfytheequationsi{n}^2\theta -cos\theta =\frac{1}{4}.$

Using binomial theorem determine which number is larger $(1.2{)}^{4000}$ or 800?

Write the element $a_{12}$ of the matrix $A=[a_{ij}{]}_{2\times 2}$, whose elements $a_{ij}$ are given by $a_{ij}=e^{2ix}$ sin jx.

Let $E=\frac{1}{1^2}+\frac{1}{2^2}+\frac{1}{3^2}+....$ then,

If $(p^2-4p+5,2)=(2p-3,|p-2|)$, then the number of values of $p$ is

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

A bag contains 4-balls, two balls are drawn from the bag and are found to be white then probability that all balls in the bag are white is

Which of the following sets are finite and which are infinite ?

(i) Set of concentric circles in a plane.

(ii) Set of letter of the English Alphabets.

(iii) {$xϵN;x>5$}

(iv) {$xϵN;x>200$ }

(v) {$xϵZ;x<5$ }

(vi) {$xϵR;0<x<1$ }.

If $\tan \left(\cot x\right)=\cot \left(\tan x\right)$, then the least positive value of $\cot x+\tan x$ is

Let $y=min\{x,x^2,x^3\}$. At how many points in the interval $(-1,1]$, $y$ is not differentiable?

If ${lim}_{x\to 0}kxcosecx={lim}_{x\to 0}xcoseckx$,find k.

The number of distinct terms in the expansion of ${(x+\frac{1}{x}+x^2+\frac{1}{x^2})}^{15}$ is
(Different power of $x$ means different terms)

Prove that:
(i)$sin({60}^{\circ }-\theta )cos({30}^{\circ }+\theta )+cos({60}^{\circ }-\theta )sin({30}^{\circ }+\theta )=1$
(ii) $sin(\frac{4\pi }{7}+7)cos(\frac{\pi }{9}+7)-cos(\frac{4\pi }{9}+7)sin(\frac{\pi }{9}+7)=\frac{\sqrt{3}}{2}$
(iii)$sin(\frac{3\pi }{8}-5)cos(\frac{\pi }{8}+5)+cos(\frac{3\pi }{8}-5)sin(\frac{\pi }{8}+5)=1$

If $\int \frac{2x+5}{\sqrt{7-6x-x^2}}dx=A\sqrt{7-6x-x^2}+B{\sin }^{-1}\left(\frac{x+3}{4}\right)+C$ (where $C$ is a constant of integration), then the orderd pair $(A,B)$ is equal to :

If the polynomial $P\left(x\right)=24x^4+{\lambda }_1{x}^3+{\lambda }_2{x}^2+{\lambda }_{3}x+1$, where ${\lambda }_1,{\lambda }_2,{\lambda }_3\in R$ has four positive real roots $\alpha ,\beta ,\gamma ,\delta$ such that $\alpha +2\beta +3\gamma +4\delta =4$, then

Number of $4$ digit numbers of the form
$N=abcd,$ which satisfy following conditions :
$\left(i\right)4000\le N<6000$
$\left(ii\right)N$ is a multiple of $5$
$\left(iii\right)3\le b<c\le 6$ is equal to

A parabola has the origin as its focus and the line $x=4$ as the directrix. Then the vertex of the parabola is at

Find the length of the perpendicular from the origin to the straight line joining the two points whose coordinates are $(acos\alpha ,asin\alpha )$ and $(acos\beta ,asin\beta )$

Given two independent events A and B such that P(A) = 0.3, P(B) = 0.6 Find
P(A and B)

P(A and not B)

P(A and B)

P (neither A nor B)

Find the shortest distance between the lines whose vector equtions are
$r=(1-t)\hat{i}+(t-2)\hat{j}+(2-2t)\hat{k}andr=(s+1)\hat{i}+(2s-1)\hat{j}-(2s+1)\hat{k}$

Rural and urban students are equally likely to get admission in a college. If $100$ students get admission, then the probability that more rural students get admission than urban students is

The integrating factor of the differential equation $\frac{dy}{dx}+(3x^2{\tan }^{-1}y-x^3)(1+y^2)=0$ is

In a $\Delta$ ABC, a, c, A are given and $b_1,b_2$ are two values of the third side b such that $b_2,2b_1$ , then sin A is equal to

The area of the region bounded by the curves $f\left(x\right)=\sin \pi x$ and x-axis for $x\in [-1,2]$ is

Determine the value of 'k' for which the following function is continuous at x=3 :

$f\left(x\right)=\{\begin{array}{cc}\frac{(x+3{)}^2-36}{x-3},& x\ne 3\\ k,x=3& \end{array}$

If $X=\{4^n-3n-1:n\in N\}$ and $Y=\left\{9\right(n-1):n\in N\},$ then show that $X\cap Y=X.$

The number of solution of the equation $ta{n}^{-1}\left(\frac{x}{1-x^2}\right)+ta{n}^{-1}\left(\frac{1}{x^3}\right)=\frac{3\pi }{4}$ belonging to the interval (0, 1) is

A normal to the hyperbola, $4x^2-9y^2=36$ meets the co-ordinate axes $x$ and $y$ at $A$ and $B$, respectively. If the parallelogram $OAPB$ ($O$ being the origin) is formed, then the locus of $P$ is :

Sketch the graph of the following functions on the same scale :
$y=cos2x,y=cos(2x-\frac{\pi }{3})$

Give a specimen of an account.

If $z=(1+i)(1-i\sqrt{3})(-2-2i)\left(i\right)\left(3\right),$ then