Explore topic-wise InterviewSolutions in Current Affairs.

If A and B are two sets such that $n(A\cup B)$ = 50, n(A) = 28 and n(B) = 32, find $n(A\cap B)$.

The value of ${}^{19}{C}_2$ is

1. 0

If p(11,r)= P (12, r-1) find r.

Number of terms in the expansion of general determinant of order n is

If range of the function $f\left(x\right)={\sin }^{-1}x+2{\tan }^{-1}x+x^2+4x+1$ is $[p,q]$, then the value of $p+q$ is

Let $f\left(x\right)=|x^2-4x+3|$ be a function defined on $x\in [0,4]$ and $\alpha ,\beta ,\gamma$ be the abscissas of the critical points of $f\left(x\right).$ If $m$ and $M$ are the local and absolute maxima values of $f\left(x\right)$ respectively, then the value of ${\alpha }^2+{\beta }^2+{\gamma }^2+m^2+M^2$ is

Let $a$ and $b$ be five-digit palindromes (without leading zeroes) such that $a<b$ and there are no other five-digit palindromes strictly between $a$ and $b.$ Then sum of all possible values of $b-a$ is

The coefficient of $x^{10}$ in the expansion of $[1+x^2(1-x){]}^8$ is

Prove that
cos² 2x – cos² 6x = sin 4x
sin 8x

The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0, 3) is :

For a function f(x), a table is given below

The value of $\underset{0}{\overset{5}{\int }}f\left(x\right)dx$ by Trapezoidal’s rule is _____.

1. 2.75

If A = {0,1,2,3,4,5,6,7,8,9,10}, then insert the appropriate symbol $ϵor\text{/}ϵ$ in each of the following blank spaces :

(i) 4 ..... A

(ii) -4 ..... A

(iii) 12 ....... A

(iv) 9 ....... A

The equation of the hyperbola whose asymptotes are $2x-y=3$ and $3x+y=7$ and passing though the point $(1,1)$ is

Correct graph of the equation $y=\sin \left(|x+\frac{\pi }{4}|\right)-3$

A line with positive direction cosines passes through the point P (2 , -1 , 2 ) and makes equal angles with the coordinate axes. The line meets the plane 2x+6y +z = 9 at point Q. The length of the line segment PQ equals

The value of $I={\int }_0^3\left(\right[x]+[x+\frac{1}{3}]+[x+\frac{2}{3}])dx$, where $[\cdot ]$ denotes the greatest integer function, is equal to

A value of b for which the equations

$x^2+bx-1=0x^2+x+b=0$

have one root in common is -

Prove that:
(i) $i^n+i^{n+1}+i^{n+2}+i^{n+3}=0$
(ii) $i^{107}+i^{112}+i^{117}+i^{122}=0$
(iii) $(1+i{)}^4\times {(1+\frac{1}{i})}^4=16$

Let $\frac{dy}{dx}+y=f\left(x\right),$ where $y$ is a continuous function of $x$ with $y\left(0\right)=1$ and $f\left(x\right)=\{\begin{array}{cc}{e}^{-x},& 0\le x\le 2\\ e^{-2},& x>2\end{array}.$

Which of the following hold(s) good?

Fifteen identical balls have to be put in five different boxes. Each box can contain any number of balls. The total number of ways of putting the balls into the boxes so that each box contains at least two balls is equal to $k$. Then which of the following is/are divisor of $k$?