Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\underset{x\to 0}{lim}(\left[\frac{50x}{{\tan }^{-1}x}\right]+\left[\frac{50x}{\tan x}\right])$ is

(where $[.]$ denotes greatest integer function )

If the $5^{th}$ term of a G.P. containing positive terms is $\frac{1}{3}$ and $9^{th}$ term is $\frac{16}{243}$, then the $4^{th}$ term will be

The number of solution(s) of ${\cos }^{5}x+{\cos }^5(x+\frac{2\pi }{3})+{\cos }^5(x+\frac{4\pi }{3})=0$ in $[0,2\pi ]$ is

The degree of polynomial ${(x^2+\sqrt{x^5-1})}^{2021}+{(x^2-\sqrt{x^5-1})}^{2021}$ is

Let vertices of a $△ABC$ are $A(-3,2,0),B(-2,0,2)$ and $C(1,-1,0).$ If $D$ is a point on $BC$ and $AD$ bisects the angle $\angle BAC,$ then point $D$ is

If $z=x+iy,|z|=1$ and $\omega =\frac{(1-z{)}^2}{1-z^2}$, then the locus of $\omega$ is equivalent to

What is the equation of the chord centered at (1, 2) in the circle $x^2+y^2-4x-6y-10=0$

The ordered triad $(x,y,z)$ which satisfies the system of linear equations is:

$x+y+z=6$

$x-y+z=2$

$3x+2y-4z=-5$

If the lines represented by the equation $a{x}^2-bxy-y^2=0$ make angles $\alpha$ and $\beta$ with the x - axis, then $\tan (\alpha +\beta )$ =

The centre of the circle $x=1+2\cos \theta ,y=-3+2\sin \theta ,$ is

For the expression $\sqrt{x^2+x}+\frac{1}{\sqrt{x^2+x}}>0,x\in$

The mean deviation about the median for the following data $3,7,8,9,4,6,8,13,12,10$ is:

In a team of 11, seven are batsmen, six are bowlers and one of them is a wicket keeper-batsman. How many of them are all-rounders (both batting and balling)?

$\text{The value of}\underset{x\to \infty }{lim}[\sqrt{x+\sqrt{x+\sqrt{x}}}-\sqrt{x}]\text{is}.$

$\overrightarrow{a}\ne \overrightarrow{0},\overrightarrow{b}\ne \overrightarrow{0},\overrightarrow{a}\times \overrightarrow{b}=\overrightarrow{0},\overrightarrow{c}\times \overrightarrow{b}=\overrightarrow{0}\Rightarrow \overrightarrow{a}\times \overrightarrow{c}=$

If $A=\left[\begin{array}{ccc}-1& 2& 3\\ 5& 7& 9\\ -2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-4& 1& -5\\ 1& 2& 0\\ 1& 3& 1\end{array}\right]$, then verify that
(ii)(A-B)'=A'-B'

Is the function, f(x) = min {x,x²} ᵿx ϵ R continuous?

1. undefined
2. undefined
3. undefined
4. undefined

Interval of k for which, $f\left(x\right)=\sin x-\cos x-kx+b$ is decreasing for all real values -

The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations in the set is increased by 2, then the median of the new set

Prove that:

$tan82{\frac{1}{2}}^{\circ }=(\sqrt{3}+\sqrt{2})(\sqrt{2}+1)=\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{6}$

Let a function $f:R\to R$ be defined as $f\left(x\right)=\{\begin{array}{cc}\sin x-e^x& \text{if}x\le 0\\ a+[-x]& \text{if}0<x<1\\ 2x-b& \text{if}x\ge 1\end{array}$



where $\left[x\right]$ is the greatest integer less than or equal to $x$. If $f$ is continuous on $R$, then $(a+b)$ is equal to

The solution of the partial differential equation $\frac{\partial u}{\partial t}=\alpha \frac{{\partial }^{2}u}{\partial x^2}$ is of the form

Prove that the coefficient of (r+1)th term in the expansion of $(1+x{)}^{n+1}$ is equal to the sum of the coefficients of rth and (r+1)th terms in the expansion of $(1+x{)}^n.$

The value of $\underset{n\to \infty }{lim}\prod _{r=1}^n{\left(\frac{n+r}{n}\right)}^{\frac{1}{n}}$ is

Let f(x)= {x^2 ; x>=0

{ax ; x<0

Find a for which f(x) is monotonically increasing function at x=0.

A = {1, 2, 3, 5} and B = {4, 6, 9}. Define a relation R from A to B by R = {(x, y) : the difference between x and y is odd : $xϵA,yϵB\}.$ Write R in roster form.

If ${\cos }^{-1}x-{\cos }^{-1}\frac{y}{2}=\alpha$ where $-1\le x\le 1,$ $-2\le y\le 2,x\le \frac{y}{2},$ then for all $x,y,4x^2-4xy\cos \alpha +y^2$ is equal to :

The least integral value of $k$ for which $f\left(x\right)=\frac{e^{-x}}{\sqrt{k+8x^2}}$ is monotonically decreasing for all $x\in R,$ is

Let $C_1$ and $C_2$ be two biased coins such that the probabilities of getting heed in a single toss are $\frac{2}{3}$ and $\frac{1}{3},$ respectively. Suppose $\alpha$ is the number of heads that appear when $C_1$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C_2$ is tossed twice, independently. Then the probability that the roots of the quadratic polynomial $x^2-\alpha x+\beta$ are real and equal, is

Three faces of a fair dye are yellow, two faces red and one blue. The die is tossed three times. The probability that the colours, yellow red and blue appear in first, second and the third tosses respectively is ............

Write the number of terms in the expansion of $(2+\sqrt{3}x{)}^{10}+(2-\sqrt{3}x{)}^{10}.$

The value of $\underset{0}{\overset{\pi /2}{\int }}\frac{{\tan }^{3}x}{{\tan }^{3}x+{\cot }^{3}x}dx$ is