Explore topic-wise InterviewSolutions in Current Affairs.

The principal value of tan^-1 1 is given by

Let the straight line 5x + 12y = k touches the hyperbola $x^2-9y^2=9$ at the point P. Then

Term independent of $x$ in the expansion of ${(x-\frac{1}{x^2})}^{3n}$ (where $n$ is even natural number)

If $z$ is a complex number satisfying $|z^3+z^{-3}|\le 2,$ then the maximum possible value of $|z+z^{-1}|$ is

If $\sum _{k=1}^{n}f\left(k\right)=\frac{n}{2(n+2)}$, then the value of $\sum _{k=1}^{10}\frac{1}{f\left(k\right)}$ is equal to

If in $△ABC\frac{2cosA}{a}+\frac{cosB}{b}+\frac{2cosC}{c}=\frac{a}{bc}+\frac{b}{ca}=then\angle A$ is equal to

The last two digits of the number $3^{400}$ is

$\begin{array}{c}IfA=\left[\begin{array}{cc}i& 0\\ 0& \frac{i}{2}\end{array}\right](i=\sqrt{-1}),then{A}^{-1}=\end{array}$ [MP PET 1992]

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral is

Three six faced fair dice are thrown together. The probability that the sum of the numbers appearing on the dice is 8, is:

Find the value of ${}^{15}{C}_2$+ 2 ${}^{15}{C}_3$ + 3 ${}^{15}{C}_4$ . . . . . 14 ${}^{15}{C}_{15}$

If OA and OB be the tangents to the circle $x^2+y^2-6x-8y+21=0$ drawn from the origin O, then AB =

Two cards are drawn one by one at random from a pack of 52 cards. The probability that both of them are king, is

[MP PET 1994]

The value of the definite integral ${\int }_{-1}^1\frac{dx}{(1+e^x)(1+x^2)}$ is

The solution of $\frac{dv}{dt}+\frac{k}{m}v=-g$ is

Find the equation of the straight line perpendicular to $5x-2y=8$ and which passes through the mid-point of the line segement joining $(2,3)$ and $(4,5)$.

The value of $ta{n}^{-1}\frac{1}{2}+ta{n}^{-1}\frac{1}{3}+ta{n}^{-1}\frac{7}{8}$ is

If $msin\theta =nsin(\theta +2\alpha ),provethattan(\theta +\alpha )cot\alpha =\frac{m+n}{m-n}$

$f(A-A^{\theta })=$

Out of 18 points in a plane, no three are in the same straight line except five points which are collinear. How many (i) straight lines (ii) triangles can be formed by joining them ?

In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 reas newspaper I, 9 read both H and I, 11 read both H and T, 8 read both T and I, 3 read all three newspaper,

Find :

(i) the numbers of people who read at least one of the newspapers.

(ii) the numbers of people who read exactly one newspaper.

Two sides of a parallelogram are along the lines, $x+y=3$ and $x-y+3=0$. If its diagonals intersect at $(2,4)$ then one of its vertex is :

Let R be a relation from a set A to a set B. then

For which of the following ordered pairs $(\mu ,\delta )$, the system of linear equations
$x+2y+3z=1$
$3x+4y+5z=\mu$
$4x+4y+4z=\delta$
is inconsistent?

The side length of the square whose area is equal to the $7^{th}$ term of the sequence $2,\sqrt{8},4,\dots ,$ is

Prove that

(i) $\frac{\text{sin}2x}{1-\text{cos}2x}=\text{cot}x$

(ii) $\frac{1-\text{cos2x}}{1+\text{cos}2x}={\text{tan}}^{2}x$

Solve the following equation for x:

$si{n}^{-1}(1-x)-2si{n}^{-1}x=\frac{\pi }{2}$, then x is equal to
a) $0,\frac{1}{2}$
b) $1,\frac{1}{2}$
c) zero
d) $\frac{1}{2}$

For the given differential equation find the general solution.

$\frac{dy}{dx}+\frac{y}{x}=x^2$

Passing through $(2,2\sqrt{3})$ and inclined with the x-axis at an angle of ${75}^{\circ }$

Let $P\left(x\right)$ be a polynomial, which when divided by $x-3$ and $x-5$ leaves remainders $10$ and $6$ respectively. If the polynomial is divided by $(x-3)(x-5)$ then the remainder is

Find the tangent of the angle between the lines which have intercepts 3, 4 and 1, 8 on the axes respectively.

If the line $y=mx+7\sqrt{3}$ is normal to the hyperbola $\frac{x^2}{24}-\frac{y^2}{18}=1$, then a value of $m$ is

Consider the region formed by the lines x = 0, y = 0, x = 2, y = 2. Area enclosed by the curves $y=e^x$ and $y=\text{ln}x$, within this region is removed, then the area of the remaining region is

The number of solution(s) of $e^x=|x|$ is

If $a^x$ = b which of the following is/are true?

Let $f:R\to R$ be a differentiable function satisfying $f\left(y\right)f(x-y)=f\left(x\right)\forall x,yϵR$ and $f^1\left(0\right)=p,f^1\left(5\right)=qthenf\left(5\right)$ is