Explore topic-wise InterviewSolutions in Current Affairs.

If $f\left(x\right)=\frac{1+cos2x+8si{n}^{2}x}{sin2x}$. Then the minimum value of f(x) is

Let $R$ be a reflexive relation on a set $A$ and $I$ be the identity relation on $A.$ Then

If $f:R\to R$ satisfies f(x+y) = f(x) + f(y), for all x, y $\in R$ and f(1) = 7, then ${\sum }_{r=1}^{n}f\left(r\right)$ is equal to

Let $x=my+c$ is normal to $x^2=4y$. If $k^2+mk+m=0$ is satisfies by only one real value of $k$, then value(s) of $c$ is/are

If the equation ${\sin }^{-1}(x-4)+{\cos }^{-1}(x-6)+{\tan }^{-1}(\frac{40}{15+x^2})=m$ holds, then value of ${}^{\prime }{m}^{\prime }$ is

The points of the ellipse $16x^2+9y^2=400$ at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

Sum up to $16$ terms of the series $\frac{1^3}{1}+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\dots \dots$ is

The coefficient of $t^8$ in ${(1+t)}^2{(1+t+t^2+....+t^9)}^3$ is

A rectangle with sides 2m -1 and 2n -1 is divided into squares of unit length by drawing parallel lines as shows in the diagram, then the number of rectangles possible with odd side lengths is

The value of $(\cos {75}^{\circ }-\cos {15}^{\circ }{)}^2+(\sin {75}^{\circ }-\sin {15}^{\circ }{)}^2$ is

If $P_1$ and $P_2$ are the perpendiculars from any point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ on its asymptotes, then :

If $\frac{\cos \alpha }{\cos \beta }+\frac{\sin \alpha }{\sin \beta }=-1$, then the value of $\frac{{\cos }^3\beta }{\cos \alpha }+\frac{{\sin }^3\beta }{\sin \alpha }$ is

For the differential equation in given question find a particular solution satisfying the given condition.​​

$\frac{dy}{dx}=ytanx,y=1whenx=0$

${\int }_0^{\pi }xlogsinxdx$

Prove that :

tanA/1-cotA + cotA/1-tanA = secAcosecA+1

For any two complex number $z_1,z_2$ and any two real numbers $a$ and $b$,
$|a{z}_1-b{z}_2{|}^2+|b{z}_1+a{z}_2{|}^2=$

If $P={\sec }^{6}A-{\tan }^{6}A$ and $Q=3{\sec }^{2}A{\tan }^{2}A,$ then $P-Q$ is equal to

Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of onto functions from A into B is

All the rearrangements for the letters of the word ${}^{\prime }DEMAN{D}^{\prime }$ are written without including any word that has two $D^{\prime }$s appearing together. If all these are arranged in dictionary order, then the rank of the word $"DEMAND"$ will be

If A = {x: x is a natural number}

B = {x: x is even natural number}

C = {x: x is prime number}

Then (A ∪ B)∩ C =

$\sqrt{3}cosec{20}^{\circ }-sec{20}^{\circ }$=

Which of the following equation has imaginary roots?

2ZS : EG£ : : $ 9 $\xi$ : ?

Given $f\left(x\right)=\frac{1}{\sqrt{|x|-x}}$ and $g\left(x\right)=\frac{1}{\sqrt{x-|x|}}$. Then

If the product of three positive real numbers is 1 and their sum is greater than sum of their reciprocals, then

The angle of intersection of the curves :

xy = 6 and x²y = 12 is ... .

Which of the following is an orthogonal matrix

Given that $g\left(x\right)=\left[f\right(x)-1{]}^2$. Find the domain of f(x) = 1 - 2x, given that $0\le g\left(x\right)<4$.

$se{c}^2\left[co{t}^{-1}\left(\frac{1}{2}\right)\right]+cose{c}^2\left[ta{n}^{-1}\left(\frac{1}{3}\right)\right]=$

The seolution set of $x^2-5x+6\ge 2$ is

The length and foot of the perpendicular from the point (7, 14, 5) to the plane 2x + 4y - z = 2, are

If $A={280}^{\circ }$ then $\sqrt{(1+sinA)}$ + $\sqrt{(1-sinA)}$ =

${lim}_{x\to 2}(\frac{1}{x-2}-\frac{4}{x^3-2x^2})$

$4(bcco{s}^2\frac{A}{2}+caco{s}^2\frac{B}{2}+abco{s}^2\frac{C}{2})={(a+b+c)}^2$

Which of the following equations is a linear equation of order 3?

The domain of the function $f\left(x\right)=\sqrt{10-\sqrt{x^4-21x^2}}$ is

If n is any integer, then ${\int }_0^{\pi }{e}^{co{s}^{2}x}co{s}^3(2n+1)xdx=$ [IIT 1985; RPET 1995; UPSEAT 2001]

If $\overrightarrow{a},\overrightarrow{b},\overrightarrow{c}$ are non coplanar vectors, then
$[\overrightarrow{a}\times \overrightarrow{b},\overrightarrow{b}\times \overrightarrow{c},\overrightarrow{c}\times \overrightarrow{a}]$is equal to

Give an example of a statement P(n) which is true for all $n\ge 4$ but P(1), P(2), P(3) are not true. Justigy your answer.

In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find :

(i) how manycan speak both Hindi and English

(ii) how many can speak Hindi only

(iii) how many can speak English only.