Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\int \frac{e^x(x^2{\tan }^{-1}x+{\tan }^{-1}x+1)dx}{x^2+1}$ is equal to

The quadratic expression $(2x+1{)}^2-px+q\ne 0$ for any real $x$ if

The Sum of the coefficients in $(x+2y+z{)}^{10}$ is:

Find the value of ${}^n{C}_r{+}^n{C}_{r-1}$.

The distance of the plane 6x - 2y + 3z = 12 from the origin is:

If second, third and sixth terms of an A.P. are consecutive terms of a G.P., write the common ratio of the G.P.

If Relation R is set A = {1, 2, 3 . . . . . . 13, 14} defined as R = {(x, y):3x - y = 0}. Find range

The coordinates of end point of latus rectum of the parabola (y-1)²=4(x+1) is

Let $\hat{a},\hat{b}and\hat{c}$ be three unit vectors such that
$\hat{a}\times (\hat{b}\times \hat{c})=\frac{\sqrt{3}}{2}(\hat{b}+\hat{c}).$ If
$\hat{b}$ is not parallel to $\hat{c}$, then the angle between $\hat{a}$ and $\hat{b}$ is

If $f(x+y)=f\left(x\right)+f\left(y\right)-xy-3$ and $f\left(1\right)=3$, then the number of solutions for $f\left(n\right)=3n$, where $n\in N$ is

Find the sum of the infinite G.P. 2, $\frac{2}{3}$, $\frac{2}{9}$, $\frac{2}{27}$ . . . . .

Five horses are in a race. Mr. A selects two of the horses at random and belts on them. The probability that Mr. A selected the winning horse is

If $|z-\frac{4}{z}|=2$, then the greatest value of $|z|$ is

sinA + cosA =

If $\alpha =3{\sin }^{-1}(\frac{6}{11})$ and $\beta =3{\cos }^{-1}(\frac{4}{9}),$ where the inverse trignometric functions takes only the principal values, then the correct option(s) is(are)

If $P(0,0),Q(1,0)$ and $R(\frac{1}{2},\frac{\sqrt{3}}{2})$ are three given points, then the centre of the circle for which the lines $PQ,QR$ and $RP$ are the tangents is

If $S$ and $S^{\prime }$ are the foci of the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1,$ and $P$ is any point on it then range of values of $SP\cdot S^{\prime }P$ is

The number of terms in the expansion of $(x^3+9x^2+27x+27{)}^{25}$ is

The parametric coordinates of the circle whose center coordinates are $(-4,3)$ and touches the $y$-axis, is

Probability of solving a particular question by person $A$ is $\frac{1}{3}$ and probability of solving that question by person $B$ is $\frac{2}{5}.$ What is the probability of solving that question by at least one of them ?

If a spherical balloon has a variable diameter $3x+\frac{9}{2}$, then the rate of change of its volume with respect to x is

Prove that the curves xy = 4 and $x^2+y^2=8$ touch each other.

If $\alpha ,\beta$ are non real numbers satisfying $x^3-1=0$ then the value of $\left|\begin{array}{ccc}\lambda +1& \alpha & \beta \\ \alpha & \lambda +\beta & 1\\ \beta & 1& \lambda +\alpha \end{array}\right|$ is equal to

The locus of the centre of a circle which touches the circles$|z-z_1|=aand|z-z_2|=b$ externally is

If $\Delta$ denotes the area of any triangle and s its semi - perimeter, then

Question 6
Explain why $7\times 11\times 13+13$ and $7\times 6\times 5\times 4\times 3\times 2\times 1+5$ are composite numbers.

Find the principal argument of $(1+i\sqrt{3})$.

If $a_1,a_2,.......,a_n$are positive real numbers whose product is a fixed number c, then the minimum value of $a_1+a_2+.......+a_{n-1}+2a_n$ is

Find the values of a and b such that the function defined by f(x)=$\{\begin{array}{c}5,ifx\le 2\\ ax+b,if2<x<10\\ 21,ifx\ge 10\end{array}$ is a continuous function.

$If\alpha ,\beta aretherootsof{x}^2-ax+b=0andif{\alpha }^n+{\beta }^n=V_n,then$

The given circle $x^2+y^2+2px=0$, $pϵR$ touches the parabola $y^2=4x$ externally, then

The fraction exceeding its pth power by the greatest number possible, where p $\ge$ 2, is

${lim}_{x\to 0}\frac{e^{x+2}-e^2}{x}$