Explore topic-wise InterviewSolutions in Current Affairs.

Given that tan A, tan B are the roots of the equation $x^2$ - px + q = 0, then the value of $si{n}^2$(A + B) is

${lim}_{x\to 0}\frac{ta{n}^{3}x-si{n}^{3}x}{x^5}=$

The solution of the differential equation $2x^{2}y\frac{dy}{dx}=\tan \left(x^2{y}^2\right)-2x{y}^2,$ given $y\left(1\right)=\sqrt{\frac{\pi }{2}},$ is

Let A = {1, 2, 3, 4} and R = {(a, b) : $aϵA,bϵA,$ a divides b} Write R explicity.

${lim}_{x\to 0}\frac{log(2+x)+log0.5}{x}$

If $y=x\tan \frac{x}{2},$ then $(1+\cos x)\frac{dy}{dx}-\sin x=$

The value of the definite integral $\underset{0}{\overset{\pi }{\int }}\frac{\pi \tan x}{\sec x+\tan x}dx$ is equal to

The following integral

$\underset{\pi /4}{\overset{\pi /2}{\int }}(2\text{cosec}x{)}^{17}dx$

is equal to

If the number of elements in each of universal set, set A and set B are represented as $n\left(U\right)$, $n\left(A\right)$, $n\left(B\right)$ respectively, then the number of elements that are not in set A and not in set B is given by ___.

If $a{x}^2+(1-\lambda )x+(a-1-\lambda )=0$ where $a\ne 0,$ has real roots for all $\lambda \in R,$ then

A box open from top is made from a rectangular sheet of dimension $a\times b$ by cutting squares each of side $x$ from each of the four corners and folding up the flaps. If the volume of the box is maximum, then $x$ is equal to

The value of ${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)$ is

If $e^{\sin x}-e^{-\sin x}-4=0$, then the number of real values of $x$ is

Suppose f(x) = and iff(x) = f(1) what are possible values of a and b?

The value of ${}^{404}{C}_4$ - ${}^4{C}_1$${}^{303}{C}_4$ + ${}^{202}{C}_4$ - ${}^4{C}_3$${}^{101}{C}_4$ =

Mr. $A$ is known to speak truth $3$ out of $4$ times and Mr. $B$ speaks truth $4$ out of $5$ times. A pair of dice is thrown. Both reported that the result (sum of the numbers) is $9$. Then the probability that the result is actually $9$ is:

A straight line through A(6, 8) meets the curve $2x^2+y^2=2$ at B and C. P is a point on BC such that AB, AP, AC are in H.P, then the minimum distance of the origin from the locus of ‘P’ is

The equation of plane parallel to the plane $2x-y+2z=5$ and is at unit distance from origin, is(are)

If the sum of the roots of the equation $a{x}^2+bx+c=0$ is equal to the sum of the squares of their reciprocals, then $\frac{b^2}{ac}+\frac{bc}{a^2}=$

The general value of the real angle $\theta ,$ which satisfies the equation, $(\cos \theta +i\sin \theta )(\cos 2\theta +i\sin 2\theta )...(\cos n\theta +i\sin n\theta )=1$ is given by, (assuming $k$ is an integer)

The transformed equation of $3x^2+3y^2+2xy=2$ when the coordinate axes are rotated through an angle ${45}^{\circ }$ is

If x = asecθ + btanθ and y = atanθ + bsecθ, then, x² – y² = a² – b²

The root(s) of the equation $x^4=16$ is/are :

If a,b,c,d are positive real numbers such that a+b+c+d = 2, then M = (a+b)(c+d) satisfies the relation

Examine the following functions for continuity :

(d) $f\left(x\right)=|\times -5|$.

Find the vector equation of the line that passes through the origin and (-6, 2, 1).

If ${\int }_0^{\frac{\pi }{2}}cos\left(x\right)dx=athen{\int }_0^{\pi }cos\left(x\right)dx$ is equal to -

Let $A$ is a non-singular matrix such that $A^2=I.$ Then the inverse of $\frac{A}{2}$ will be (where $I=$ identity matrix)

1. 1.81

If both the roots of $a{x}^2+bx+c=0$ are negative and $b<0$, then which of the following statements is always true?

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