Explore topic-wise InterviewSolutions in Current Affairs.

Find the point on x-axis which is equidistant from the points A(3, 2, 2) and B(5, 5, 4).

For a positive integer $n,$ let $a\left(n\right)=1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}\dots +\frac{1}{2^n-1}$ then

$If{\int }_2^{4}f\left(x\right)dx=\frac{1}{2}andf(6-x)=f\left(x\right),then{\int }_2^{4}xf\left(x\right)dx=$

${lim}_{x\to \frac{\pi }{2}}(1-sinx)tanx$ will be equal to _____

The derivative of $\frac{2}{(x+1)}$ with respect to x will be

A rifle man is firing at a distant target and has only 10% chance of hitting it. The minimum number of rounds he must fire in order to have 50% chance of hitting it at least once is

[Kurukshetra CEE 1998]

Which of the following cannot be valid assignment of probability for elementary events or outcomes of sample space

$S=\{w_1,w_2,w_3,w_4,w_5,w_6,w_7\}$:
Elementary events :

(i) $\begin{array}{ccccccc}{w}_1& w_2& w_3& w_4& w_5& w_6& w_7\\ 0.1& 0.01& 0.05& 0.03& 0.01& 0.2& 0.6\end{array}$

(ii) $\begin{array}{ccccccc}\frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}& \frac{1}{7}\end{array}$

(iii) $\begin{array}{ccccccc}0.7& 0.6& 0.5& 0.4& 0.3& 0.2& 0.1\end{array}$

(iv) $\begin{array}{ccccccc}\frac{1}{14}& \frac{1}{14}& \frac{1}{14}& \frac{1}{14}& \frac{1}{14}& \frac{1}{14}& \frac{1}{14}\end{array}$

The coefficient of $x^5$ in the expansion of $(1+x{)}^{21}+(1+x{)}^{22}+(1+x{)}^{23}+\cdots +(1+x{)}^{30}$

PSQ is a focal chord of the parabola $y^2=8x$.If SP=6,then write SQ.

The equation of the parabola whose vertex is (a,0) and the directrix has the equation x+y=3a,is

Find S when $\overline{\text{C}}=200,\text{MPC}=0.4$ and $\text{Y}=1,000$.

Solve the following linear in equations in R.

Solve:-4x >30, when

(i) $xϵR$ (ii) $xϵZ$ (iii) $xϵN$

Let $A=(\sin \theta +1,\cos \theta )$ and $B=(1-\cos \theta ,-\sin \theta )$. Then the maximum value of $AB$ is

A tangent drawn through the point $(2,-1)$ to a circle meets it at $(2,3)$. If radius of the circle is $3$ units, then equation of the circle can be

Find the coordinates of all letters in the graph given below.

Let $A(2,-3)$ and $B(-2,1)$ be vertices of a triangle $ABC.$ If the centroid of this triangle moves on the line $2x+3y=1,$ then the locus of vertex $C$ is

The number of solution(s) of $y=x^2+10x+22$ and $y=e^x$ is

Show that the points (a, b, c), (b, c, a) and (c, a, b) are the vertices of an equilateral triangle.

The value of $\text{cosec}\theta +\sec (270°-\theta )-\text{cosec}(270°+\theta )+\sec (180°-\theta )$ is

Let $A=[a_{ij}{]}_{3\times 3},B=[b_{ij}{]}_{3\times 3},$ where $b_{ij}=3^{i-j}{a}_{ij}$ and $C=[c_{ij}{]}_{3\times 3},$ where $c_{ij}=4^{i-j}{b}_{ij}$ be any three matrices. If det.A = 2 then ‘det.B + det.C’ is equal to

1. The probablity of getting exactly 2 tails in 6 tosses of a fair coin?

2. 3 dice are rolled simultaneously the probablity that the sum of the numbers on them is 16 ?

A box contains 6 red marbles numbers from 1 through 6 and 4 white marbles 12 through 15. Find the probability that a marble drawn at random is white and odd numbered.

Find the sine of the angle between the vectors $\overrightarrow{a}=3\hat{i}+\hat{j}+2\hat{k}and\overrightarrow{b}=2\hat{i}-2\hat{j}+4\hat{k}$.

If x = -9 is a root of $\left|\begin{array}{ccc}x& 3& 7\\ 2& x& 2\\ 7& 6& x\end{array}\right|=0$, then other two roots are ___

If $A$ is a square matrix of order $3$ and $||adj\left(A\right)|\cdot |A|\cdot A|=|A{|}^{\lambda },$ then the value of $\lambda$ is

$\begin{array}{ccc}\text{Column I}& \text{Column II}& \text{Column III}\\ \text{P)}\overline{\text{v}}={\text{v}}_0\hat{\text{i}}& 1)\overline{\text{E}}={\text{E}}_0\hat{\text{k}}& \text{i)}\overline{\text{B}}={\text{B}}_0(\hat{\text{i}}+\hat{\text{j}})\\ \text{Q)}\overline{\text{v}}={\text{v}}_0(\hat{\text{i}}+\hat{\text{j}})& 2)\overline{\text{E}}={\text{E}}_0\hat{\text{i}}& \text{ii)}\overline{\text{B}}={\text{B}}_0\hat{\text{k}}\\ \text{R)}\overline{\text{v}}={\text{v}}_0\hat{\text{j}}& 3)\overline{\text{E}}=\text{0}& \text{iii)}\overline{\text{B}}=0\\ \text{S)}\overline{\text{v}}=0& 4)\overline{\text{E}}={\text{E}}_0(\hat{\text{i}}+\hat{\text{j}})& \text{iv)}\overline{\text{B}}={\text{B}}_0\hat{\text{j}}\end{array}$

Which of the following combinations should be true for the particle to travel along a straight line?

If for three non-zero and unequal real numbers $a,b$ and $c$; $\frac{1}{a+\omega }+\frac{1}{b+\omega }+\frac{1}{c+\omega }=2{\omega }^2$ and $\frac{1}{a+{\omega }^2}+\frac{1}{b+{\omega }^2}+\frac{1}{c+{\omega }^2}=2\omega$, where ${\omega }^2$ and $\omega$ are the complex cube roots of unity, then $\frac{1}{a+1}+\frac{1}{b+1}+\frac{1}{c+1}=$

Let $f$ be a differentiable function with $\underset{x\to \infty }{lim}f\left(x\right)=0.$ If $y^{\prime }+y{f}^{\prime }\left(x\right)-f\left(x\right)f^{\prime }\left(x\right)=0,$ $\underset{x\to \infty }{lim}y\left(x\right)=0,$ then
$($where $y^{\prime }\equiv \frac{dy}{dx})$

If the total number of $m$-element subsets of the set $A=\{a_1,a_2,...,a_n\}$ is $k$ times the number of $m$ element subsets containing $a_4$ then $n$ is

How many number of four digits can be formed with the digits 1,2,3,4,5 if the digit can be repeated in any number of times?

The remainder when $3^{100}$ is divided by $100$ is

If $C_r$ represents ${}^{100}{C}_r,$ then $5C_0-8C_1+11C_2-\dots$ upto $101$ terms equal to

Integrate the function.
$\int \sqrt{1-4x-x^2}dx.$

The common ratio of a G.P. is 3 and the last term is 486. If the sum of these terms be 728, find the first term.

Let $A$ and $B$ be two sets containing $4$ and $7$ elements respectively. If the minimum and maximum number of elements in $A\cup B$ are $m$ and $n$ respectively, then $m+n$ is