Explore topic-wise InterviewSolutions in Current Affairs.

The number of $4$ letter words containing equal number of vowels and consonants, where repetition is allowed, is

If $\underset{0}{\overset{\pi /3}{\int }}\frac{\tan \theta }{\sqrt{2k\sec \theta }}d\theta =1-\frac{1}{\sqrt{2}},(k>0)$, then the value of $k$ is :

The circumradius of the triangle whose sides are 13, 12 and 5 is

In how many ways can the letters of the word 'ALGEBRA'be arranged without changing the relative order of the vowels and consonants ?

Evaluate the definite integrals.
${\int }_{\frac{\pi }{6}}^{\frac{\pi }{4}}cosecxdx.$

The value of $\underset{n\to \infty }{lim}\sum _{k=0}^n\frac{{}^n{C}_K}{n^K(K+3)}$ is equal to

The equation of a plane passing through the line of intersection of the planes $x+2y+3z=2$ and $x-y+z=3$ and at a distance$\frac{2}{\sqrt{3}}$from the point (3,1,-1) is

Differentiate the
following w.r.t. x:

If $x<2$, then $\frac{1}{x}$ lies in the interval

Which of the following is true about f(x), where$f\left(x\right)=\frac{x^7}{\sqrt[3]{3\left(1+x^8\right)}}$?

The set of values of $a$ for which the equation $\sqrt{a}\cos x-2\sin x=\sqrt{2}+\sqrt{2-a}$ possesses a solution, is

The equation of the plane passing through the point (1,1,1) and perpendicular to the planes 2x+y-2z=5 and 3x-6y-2z=7 is

Find the quotient when polynomial $2x^3+6x^2+7x+60$ is divide by $2x^2-2x+15$

The principal value of ${\sin }^{-1}(-1)$ is

Discuss
the continuity of the function f,
where f is
defined by

1. F

Find the probability distribution of

number of heads in four tosses of a coin.

A geometric progression with common ratio $r,$ consists of an even number of terms. If the sum of all terms is $5$ times the sum of the terms occupying the odd places, then $\sum _{i=1}^4(ir{)}^2$ is

Number of ways to divide $21$ different things into two groups of $10$ and $11$ things are?

If $(1+\tan 1^{\circ })(1+\tan 2^{\circ })........(1+\tan {45}^{\circ })=2^n,$ then $n$ is

If $[A{]}_{m\times n}$ and $[B{]}_{n\times p}$ are two matrices, then the order of $AB$ will be

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

The positive integer value of n>3 satisfying the equation

The area bounded by the curve $(y-{\text{sin}}^{-1}x{)}^2=x-x^2$ is

Determine the unit vector parallel to the cross product of the vectors $\overrightarrow{A}$ = $3\hat{i}-5\hat{j}+10\hat{k}$ and $\overrightarrow{B}$ = $6\hat{i}+5\hat{j}+2\hat{k}$

Let $A=\{x_1,x_2,x_3,\dots ,x_8\},B=\{y_1,y_2,y_3\}$ then the total number of functions from $A$ to $B$ such that all the elements of $B$ has atleast one pre image and there are exactly four elements in $A$ having image as $y_3,$ are

If $P$ be the point $(2,6,3),$ then the equation of the plane through $P$, at right angles to $OP$, where $O$ is the origin is:

$a>0,\underset{-\pi }{\overset{\pi }{\int }}\frac{si{n}^{2}x}{1+a^x}dx=$

The solution set of the equation $\left|\begin{array}{ccc}x& 2& -1\\ 2& 5& x\\ -1& 2& x\end{array}\right|=0$ is

If $\alpha ={30}^{\circ }$ and $\beta ={60}^{\circ }$, then the value of $\frac{\sin \alpha +\sec 2\alpha +\tan (\alpha +{15}^{\circ })}{\tan \beta +\cot (\frac{\beta }{2}+{15}^{\circ })+\tan \alpha }$ is

Show that the following statement is true

"The integer n is even if and only if $n^2$ is even"