Explore topic-wise InterviewSolutions in Current Affairs.

Show that the diagonals of the parallelogram whose sides are $lx+my+n=0$, $lx+my+n^{{}^{\prime }}=0$, $mx+ly+n=0$ and $mx+lu+n^{{}^{\prime }}=0$ include an angle $\frac{\pi }{2}$

If $(1+x+x^2{)}^{25}=a_0+a_{1}x+a_2{x}^2+...+a_{50}{x}^{50}$ then $a_0+a_2+a_4+....+a_{50}$ is

The coordinates of the foot of the perpendicular from a point P(6,7,8)

on x-axis are

Find the cartesian form of equation of the straight line $z(1-i)+\overline{z}(1+i)$ = 4

If $\left|\begin{array}{ccc}4-x& 4+x& 4+x\\ 4+x& 4-x& 4+x\\ 4+x& 4+x& 4-x\end{array}\right|=0$, then find the value of x.

All the points on the x- axis have
[MP PET 1988]

If $2si{n}^{-1}x+co{s}^{-1}x=\frac{2\pi }{3}$, then x =

If |$z_1|=|z_2|=|z_3|=|z_4|=1$ and $z_1+z_2+z_3+z_4=0$
then least value of the expression
$E=|z_1-z_2{|}^2+|z_2-z_3{|}^2+|z_3-z_4{|}^2+|z_4-z_1{|}^2$ is

Given that ${\log }_{10}2=0.3010$, the number of digits in the number ${2000}^{2000}$ is

A box contains $24$ identical balls of which $8$ are white and $16$ are black. The balls are drawn at random from the box one at a time with replacement. Then the probability that a white ball is drawn for the $4^{\text{th}}$ time on the $8^{\text{th}}$ draw is

Let a, b, c and d be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c=0$ and $5bx+2by+d=0$ lies in the fourth quadrant and is equdistant from the two axes, then

The value of the summation $\sum _{i=1}^{\infty }\frac{2i-1}{2^{i+1}}$ is

Let $z$ and $\omega$ be complex numbers such that $\overline{z}+i\overline{\omega }=0$ and $argz\omega =\pi$. Then $argz$ equals

Assuming vector X & Y to be of equal magnitude.

Which of the following approximately represent $\overrightarrow{X}+\overrightarrow{Y}$

If $y={\cos }^2\frac{3x}{2}-{\sin }^2\frac{3x}{2}$ , then $\frac{d^{2}y}{d{x}^2}$ is

Integral of sin 2x = ?

For the function, $f\left(x\right)=ta{n}^{-1}x+si{n}^{-1}x+co{s}^{-1}x$

Write down all possible proper subsets each of the following sets :

(i) {1, 2} (ii) {1, 2, 3}

(iii) {1}

From a class of 12 boys and 10 girls, 10 students are to be chosen for a competition; at least including 4 boys and 4 girls. The 2 girls who won the prizes last year should be included. In how many ways can the selection be made ?

Let $A$ and $B$ be two events such that $P\left(A\right)=\frac{3}{8},P\left(B\right)=\frac{1}{2}$ and $P(A\cup B)=\frac{5}{8}$. Then which of the following do/does hold good?

The integral $\int \cos \left({\log }_{e}x\right)dx$ is equal to: (where $C$ is a constant of integration)

The value of is equal to ${\int }_3^6(\sqrt{x+\sqrt{12x-36}}+\sqrt{x-\sqrt{12x-36}})dx$is equal to

The value of $e^{2+i}$ is

If the $n\text{th}$ term of a sequence is given by $t_n=8n+3$, then the sum of first $20$ terms is

What is the maximum and minimum value of cos(cosx)

The co-ordinates of the vertices of the triangle are A(-2, 3, 6), B(-4, 4, 9) and C(0, 5, 8). The direction cosines of the median BE are:

If $x$ is so small that $x^3$ and higher powers of $x$ may be neglected and $\frac{(1+x{)}^{3/2}-{(1+\frac{1}{2}x)}^3}{(1-x{)}^{1/2}}$ may be approximated as $a+bx+c{x}^2$, then

If cos a + cos b + cos c = 0 = sin a + sin b + sin c

cos²a + cos²b + cos²c = ?

$1+3+5+.....+(2n-1)=n^2$ i.e., the sum of first n odd natural numbers is $n^2$.

Let $f\left(x\right)=a{x}^2-2+\frac{1}{x}$ where $\alpha$ is a real constant. The smallest $\alpha$ for which $f\left(x\right)\ge 0$ for all x > 0 is

Find the value of $\underset{x\to 0}{lim}\frac{tanx}{x}$

If $A=\{1,2,2,1,3,4,3,4\}$, then $n\left(A\right)=$

The value of the expression $\cos \frac{\pi }{15}\cos \frac{2\pi }{15}\cos \frac{4\pi }{15}\sin \frac{\pi }{30}$ is

Statement 1: For every natural number $n\ge 2.$
$\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+...+\frac{1}{\sqrt{n}}>\sqrt{n}.$
Statement 2: For every natural number $n\ge 2,$
$\sqrt{n(n+1)}<n+1.$

Period of $f\left(x\right)=x-[x+\lambda ]-\mu$ where, $\lambda ,\mu \in R$ and [.] denotes the G.I.F is

If 8 is a root of the equation x² - 10x + k = 0, then the value of k is:

Using section formula, show that the points A(2, -3, 4), B(-1, 2, 1) and

C(0, $\frac{1}{3}$, 2\) are collinear.

The noise level in a classroom in absence of the teacher is 50 dB when 60 students are present. Assuming that on the average each student outputs same sound energy per second, what will be the noise level if the number of students is increased to 100 ?

If $\cos \frac{A}{2}=\sqrt{\frac{b+c}{2c}}$, then :

Let $f^{\prime }\left(x\right)=e^{x^2}$ and $f\left(0\right)=10.$ If $A<f\left(1\right)<B$ can be concluded from the mean value theorem, then the largest value of $(A-B)$ equals

Find the angle between the vectors $\hat{i}-\hat{j}and\hat{j}-\hat{k}.$

${lim}_{x\to 0}(\cos x{)}^{\frac{1}{\sin x}}$