Explore topic-wise InterviewSolutions in Current Affairs.

Let $f:Z\to Z$ be defined by $f\left(n\right)=\{\begin{array}{ccc}2,& \text{if}n=3k,& k\in Z\\ 10-n,& \text{if}n=3k+1,& k\in Z\\ 0,& \text{if}n=3k+2,& k\in Z\end{array}$

If $S=\{n\in Z:f(n)>2\},$ then the sum of the positive elements in $S$ is

The angle between the lines joining the origin to the points of intersection of the line y = 3x + 2 with the curve $x^2$ + 2xy + ${3y}^2$ + 4x + 8y = 11, is

The rank of the word $SUCCESS$, if all possible permutations of the word $SUCCESS$ are arranged in dictionary order is

For the following question verify that the given function (explicit or implicit) is a solution of the corresponding differential equation.

y=xsinx and $x{y}^{\prime }=y+x\sqrt{x^2-y^2}(x\ne 0andx>yorx<-y).$

If for non-zero x, $af\left(x\right)+bf\left(\frac{1}{x}\right)=\frac{1}{x},-5$, where $a\ne b$, then find $f\left(x\right)$.

A committee of five is to be chosen from a group of 9 people. The probability

that a certain married couple will either serve together or not at all, is

[CEE 1993]

The minimum value of $f\left(x\right)=81{\tan }^{2}x-16{\sin }^{2}x,$ is

Find the following integrals.
$\int$ sec x (sec x +tan x)dx.

The vector $\hat{i}+x\hat{j}+3\hat{k}$ is rotated through an angle $\theta$ and is doubled in magnitude. It now becomes $4\hat{i}+(4x-2)\hat{j}+2\hat{k}$. The possible value(s) of $x$ is(are)

The area of the region

$A=\left\{(x,y):0\le y\le x|x|+1\text{and}-1\le x\le 1\right\}$ in sq. units, is :

In $\Delta$ABC Orthocentre is (2, 3) Circum centre is (6, 10) and equation of side $\overline{BC}$ is 2x + y = 17. Then the radius of the Circum circle of $\Delta$ABC is ___

If a, b, c are in H.P, value of b in terms of a & c is

Find the equation of the sphere having extremities of one of its diameters as the
points (2,3, 5) and (-4, 7,11).

If the function $f\left(x\right)=2x^3-9a{x}^2+12a^{2}x+1,$ where a > 0, attains its maximum and minimum at p and q respectively such that $p^2=q$, then a equals

For $2$ sets $A$ and $B$, which of the following is/are true always?

Let $R$ be the region of the disc $x^2+y^2\le 1$ in the first quadrant. Then the area of the largest possible circle contained in $R$ is

If 4a+5b+6c=0 then the set of lines ax+by+c=0 are concurrent at the point

From the sum of $5p^2+6pq-7q^2$, $4pq+5q^2$ and $2p^2-3pq$ subtract the sum of $p^2+3pq$ and $4pq+5q^2$.

A straight line L through the poit $(3,-2)$ is inclined at an angle ${60}^0$ to the line $\sqrt{3}x+y=1$. If L also intersects the x-axis, then the equation of L is

The roots of the equation $\sqrt{3x+1}+1$ = $\sqrt{x}$ are

A line passes through the point $(2,2)$ and is perpendicular to the line $3x+y=3.$ Its y-intercept is

If $I={\int }_0^{1}cos\left(2Co{t}^{-1}\sqrt{\frac{1-x}{1+x}}\right)dxthen$

The integral value of $x$, that satisfies $1<{\log }_2(x-2)\le 2$, is