Explore topic-wise InterviewSolutions in Current Affairs.

Find the slope of a line passing through the following points:

$\left(i\right)(-3,2)and(1,4)\left(ii\right)(a{t}_1^2,2a{t}_1)and(a{t}_2^2,2a{t}_2)\left(iii\right)(3,-5),and(1,2)$

Evaluate $\int e^x({\tan }^{-1}x+\frac{1}{1+x^2})dx$

(where $C$ is constant of integration)

In $\Delta ABC,$ if $b+c=3a$ then $\cot \frac{B}{2}\cot \frac{C}{2}=$

If A and B
be the points (3, 4, 5) and (–1, 3, –7), respectively,
find the equation of the set of points P such that PA² +
PB² = k², where k is a constant.

Let $f:(-1,1)\to R$ be such that $f\left(\cos 4\theta \right)=\frac{2}{2-se{c}^2\theta }$ for $\theta \in (0,\frac{\pi }{4})\cup \left(\frac{\pi }{4}\frac{\pi }{2}\right)$.Then the value (s) of $f\left(\frac{1}{3}\right)$ is (are)

Using the fact that sin(A+B)=sin A cos B + cos A sin B and differentiation,

obtain the sum formula for cosines.

The domain of the function $f\left(x\right)={\sin }^{-1}\left(\frac{3x^2+x-1}{(x-1{)}^2}\right)+{\cos }^{-1}\left(\frac{x-1}{x+1}\right)$ is

For $x\in (0,\frac{3}{2}),$ let $f\left(x\right)=\sqrt{x},g\left(x\right)=\tan x$ and $h\left(x\right)=\frac{1-x^2}{1+x^2}.$ If $\varphi \left(x\right)=\left(\right(hof\left)og\right)\left(x\right),$ then $\varphi \left(\frac{\pi }{3}\right)$ is equal to

The function $f\left(x\right)=\tan x$ where $x\in (\frac{-\pi }{4},\frac{\pi }{4})$.

Prove ${41}^n-{14}^n\text{is a multiple of 27.}$

Let $y=y\left(x\right)$ be the solution of the differential equation, $(x^2+1{)}^2\frac{dy}{dx}+2x(x^2+1)y=1$ such that $y\left(0\right)=0$. If $\sqrt{a}y\left(1\right)=\frac{\pi }{32}$, then the value of $a$ is:

Let R be a relation on a finite set A having n elements. Then, the number of relations on A is

If $A=\left[a_{ij}\right]$ is a $2\times 2$ matrix, such that sum of co-factors of its elements is equal to the sum of elements of $A.$ Then which of the following can be matrix $A$ ?

If $A$ and $B$ are two events such that $A\subset B$ and $P\left(B\right)\ne 0$, then which of the following is correct?

The letters of the words 'ZENTH' are written in all possible orders. How many words are possible if all these words are written out as in a dictionary? What is the rank of the word 'ZENTH'?

The value of $\int \frac{x^2+3x+3}{x^2-4}dx$ is

(where $C$ is constant of integration)

The number of different signals which can be given from 6 flags of different colours taking one or more at a time, is

The domain of the function $f\left(x\right)=x^{1/\ln x}$ is

Find all points of discontinuity of f,
where f is
defined by

The number of proper divisors of $2160$ is

If $\frac{\left(1.2\right)(0.5x+0.4)}{2}=0.6$, then $x=$

The acute angle between the lines $\frac{x-1}{l}=\frac{y+1}{m}=\frac{z}{n}$ and $\frac{x+1}{m}=\frac{y-3}{n}=\frac{z-1}{l},$ where $l>m>n$ and $l,m,n$ are the roots of the cubic equation $x^3+x^2-4x-4=0,$ is

On a rectangular hyperbola $x^2–y^2=a^2,a>0$, three points $A,B,C$ are taken as follows: $A=(–a,0)$; $B$ and $C$ are placed symmetrically with respect to the x-axis on the branch of the hyperbola not containing $A$. Suppose that the triangle $ABC$ is equilateral. If the side-length of the triangle $ABC$ is $ka$, then $k$ lies in the interval

Let $a_1,a_2,\dots ,a_{10}$ be a G.P. If $\frac{a_3}{a_1}=25$, then $\frac{a_9}{a_5}$ equals:

Write the value of ${lim}_{x\to 0}\frac{sin{x}^{\circ }}{x}$