Explore topic-wise InterviewSolutions in Current Affairs.

Primitive of $f\left(x\right)=x{.2}^{In(x^2+1)}$ with respect to x is

The differential equation of the family of curves $y^2=4a(x+a)$, where a is an arbitrary constant, is

The number of common tangents to the circles $x^2+y^2+2x+8y-23=0and{x}^2+y^2-4x-10y+19=0$ is

Let A = { x : x ∈ R, |x| < 1}; B = {x : x ∈ R, |x-1| ≥ 1} and

A ∪ B = R - D, then the set D is

Which of the following function is strictly increasing on$(0,\frac{\pi }{2})$.

Which of the following gives the area of y = (/x^{2} /) between x = 0, x = b and x-axis?

If the angle θ between the vectors $a=2x^2\hat{i}+4x\hat{j}+\hat{k}$ and $b=7\hat{i}-2\hat{j}+x\hat{k}$ is such that ${90}^{\circ }$ < $\theta$ < ${180}^{\circ }$
then x lies in the interval:

If the equation $a{x}^2+2hxy+b{y}^2=0$ has the one line as the bisector of angle between the coordinate axes, then

If graph of $y=a{x}^2-bx+c$ is following, then sign of $a,b,c$ are

If f(x - y) ,f(x) f(y) and f(x + y) are in A.P for all x, y $\in$ R and f (0) $\ne$ 0 then-

Consider a point given by position vector $\overline{a}.$ Distance of this point from the plane given $\overline{r}.\overline{n}=d$ will be.

Write the common difference of an A.P. whose nth term is xn + y.

Solve the following system of equations in R.
$\frac{1}{|x|-3}<\frac{1}{2}$

Let $y=y\left(x\right)$ be a solution of the differential equation, $\sqrt{1-x^2}\frac{dy}{dx}+\sqrt{1-y^2}=0,|x|<1$.
If $y\left(\frac{1}{2}\right)=\frac{\sqrt{3}}{2}$, then $y\left(\frac{-1}{\sqrt{2}}\right)$ is equal to:

Mark the correct alternative in each of the following :

$Inany\Delta ABC,\sum a^2(sinB-sinC)=$

$\text{What does the equation}(x-a{)}^2+(y-b{)}^2=r^2\text{become when the axes are transferred to parallel axes through the point (a-c,b)}?$

Planes are drawn parallel to the coordinate planes through the points

(3, 0, -1) and (-2, 5, 4). Find the lengths of the edges of the parallelopiped so formed.

The area of the region described by $A=\left\{\right(x,y):x^2+y^2\le 1\text{and}{y}^2\le 1-x\}$ is :

If $\frac{si{n}^{4}A}{a}+\frac{co{s}^{4}A}{b}=\frac{1}{a+b},then\frac{si{n}^{8}A}{a^3}+\frac{co{s}^{8}A}{b^3}=$

Let a, b, c be non-zero real numbers such that
${\int }_0^1(1+co{s}^{8}x)(a{x}^2+bx+c)dx={\int }_0^2(1+co{s}^{8}x)(a{x}^2+bx+c)dx$
Then the quadratic equation $a{x}^2+bx+c=0$ has [IIT 1981; CEE 1993]

The length of a tangent extended from a point P situated outside a circle is $\sqrt{5}$ units. Another line from P intersects the circle at 2 points R and S such that PR: RS = 1: 2. What is the length of PS?

Function $f\left(x\right)=\{\begin{array}{cc}({\log }_{2}2x{)}^{{\log }_{x}8};& x\ne 1\\ (k-1{)}^3;& x=1\end{array}$

is continuous at $x=1$, then $k=$____

Let $\overrightarrow{a}=2\hat{i}+\hat{j}-2\hat{k},\overrightarrow{b}=\hat{i}+\hat{j}$. If $\overrightarrow{c}$ is a vector such that $\overrightarrow{a}\cdot \overrightarrow{c}=|\overrightarrow{c}|,|\overrightarrow{a}-\overrightarrow{c}|=2\sqrt{2}$ and the angle between $\overrightarrow{a}\times \overrightarrow{b}$ and $\overrightarrow{c}$ is $\frac{\pi }{6}$, then

${lim}_{x\to 0}\frac{sin{x}^0}{x}$

The value of $\sum _{n=1}^{100}(2n-1)$ is

The range of the function $f\left(x\right)=\frac{8x^2+40x+28}{4x^2+20x+13},$ where $x\in R$ is

Find the equation of the right bisector of the line segment joining the points A (1, 0) and B (2, 3).

Sum of the series $567,189,63,...$ upto $5$ terms is

A coin is tossed repeatedly until a tail comes tip for the first time. Write the sample space for this experiment.

Let chords of the circle $x^2+y^2=a^2$ touch the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ Then their middle points lie on the curve

If $2+5+8+11+\cdots \text{upto}n\text{terms}=610$, then the value of $n$ is

The point on the parabola $y=x^2+7x+2$ which is closest to the line $y=3x-3$ is

For what value of k, the roots of the quadratic equation kx (x - 2 root5 )+ 10 = 0 are equal?

In each of the following cases, state whether the functions is one-one, onto or bijective. Justify answer.
$\left(i\right)f:R\to R$ defined by f(x) =3 - 4x.

$f:R\to R$ defined by $f\left(x\right)=1+x^2$.

Given that the $4^{th}$ term in the expansion of $(2+\frac{3}{8}a{)}^{10}$ has the maximum numerical value, then

If $8\sin \theta \cos \theta \cos 2\theta \cos 4\theta =\sin x$, then $x=$

How many three digit odd numbers can be formed by using the digits 1,2,3,4,5,6 if the repetition of digit is not allowed:

If $y=(1+x)(1+x^2)(1+x^4).........(1+x^{2n})$ then the value of $\left(\frac{dy}{dx}\right)$ at $x=0$ is