Explore topic-wise InterviewSolutions in Current Affairs.

Integral of $\frac{1}{1+(logx{)}^2}$ with respect to log x

${lim}_{n\to \infty }nsin\left(\frac{\pi }{4n}\right)cos\left(\frac{\pi }{4n}\right)$

If the equation $x^n-1=0,n>1,n\in N,$ has roots $1,a_1,a_2,\dots ,a_{n-1},$ then

Prove that the following sets of three lines are concurrent:

$\left(i\right)15x-18y+1=0,12x+10y-3=0$ and $6x+66y-11=0$

$\left(ii\right)3x-5y-11=0,5x+3y-7=0$ and $x+2y=0$

$\left(iii\right)\frac{x}{a}+\frac{y}{b}=1,\frac{x}{b}+\frac{y}{a}=1$ and $y=x.$

Let A = .

If u₁ and u₂ are column matrices such that Au₁= and Au₂= ,

then u₁+u₂ is equal to

A coin is tossed and then a die is rolled only in case a head is shown on the coin. Describe the sample space for this experiment.

If the points $2\hat{i}+4\hat{J},7\hat{i}+x\hat{j},-\hat{i}+\hat{J}$ are collinear, then the value of x is

If $x,y,z$ are in G.P. and $2^{2x}=3^{4z}.e^y,$ then the sum of all possible values of $\frac{x}{y}$ is

Find the equation of plane passing through the points P (1,1,1) , Q (3, -1, 2) and R (-3, 5 , -4).

If the bisector of the lines $x^2-2pxy-y^2=0$ be $x^2-2qxy-y^2=0$, then

Insert A.M.s between 7 and 71 in such a way that the 5^th A.M. is 27. Find the number of A.M.s

If A is a subset of B , then prove that A union B is B .

The locus of the point of intersection of the tangents at the extremities of the chord of the ellipse $x^2+2y^2=6$ which also touches the ellipse $x^2+4y^2=4,$ is

If ${}^{20}{C}_{r+1}={}^{20}{C}_{r-1},$ then r is equal to

If $z$ is a complex number satisfying $z+\overline{z}=0$, then

If foot of the perpendicular of P(2,-3,1) on the line $\frac{x+1}{2}=\frac{y-3}{3}=\frac{z+2}{-1}$ is Q(a,b,c) then find the value of -14(a+b+c)

${lim}_{x\to a}\frac{cosx-cosa}{\sqrt{x}-\sqrt{a}}$

If $f\left(0\right)=0,f^{\prime }\left(0\right)=2$, then the derivative of $y=f\left(f\right(f\left(f\right(x\left)\right))$ at $x=0$ is,

The smallest positive divisor greater than 1 of a composite number ‘a’ is

If the angle between the lines, $\frac{x}{2}=\frac{y}{2}=\frac{z}{1}$ and $\frac{5-x}{-2}=\frac{7y-14}{p}=\frac{z-4}{4}$ is ${\cos }^{-1}\left(\frac{2}{3}\right)$, then $p$ is equal to:

Two different families A and B are blessed with equal number of children. There are 3 tickests to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of the family B is $\frac{1}{12}$, then the number of children in each family is :

The circle $x^2+y^2-2x-2y+1=0$ is rolled along the positive direction of x-axis and makes one complete roll. Find its equation in es new-position.

Prove that : ${}^{4n}{C}_{2n}{:}^{2n}{C}_n=\left[\mathrm{1.3.5...}\right(4n-1\left)\right]:\left[\mathrm{1.3.5....}\right(2n-1){]}^2.$

If $\alpha and\beta$ are acute angles satisfying $cos2\alpha =\frac{3cos2\beta -1}{3-cos2\beta },$ then $tan\alpha$ =

If both roots of the equation $x^2-2ax+a^2$ - 1 = 0 lie in the interval (-3,4), then sum of the integral parts of a is :

Add 1.2*10^5 and 2.8*10^7

The image of the complex number $\frac{2-i}{3+i}$, in the straight line $z(1+i)=\overline{z}(i-1)$, where $z$ is a complex number, is/are

The derivative of $y=x^{\sin x}$ is

If $(1+x+x^2{)}^{20}=a_0+a_{1}x+a_2{x}^2+\cdots +a_{40}{x}^{40}$, then the value of $a_0+3a_1+5a_2+\cdots +81a_{40}$ is:

Simplify the following expression;
$x(2x+3y-z)+y^2(3x+z-2y)-z(2x+3z-y).$

The domain of the function $co{s}^{-1}(2x-1)$ is

(a) $[0,1]$ (b) $[-1,1]$ (c) $(-1,1)$ (d) $[0,\pi ]$

Differentiate the given functions w.r.t. x.

$x^{xcosx}+\frac{x^2+1}{x^2-1}.$

$y=sin\sqrt{x}+co{s}^2\sqrt{x}$

Find $\frac{dy}{dx}$

Using integration, find the area of the region bounded by the line $2y=5x+7$, X - axis and the lines x = 2 and x = 8.

Find $\frac{dy}{dx}$in the following questions:

$y=si{n}^{-1}\left(\frac{1-x^2}{1+x^2}\right),0<x<1.$

Prove that $x^2-y^2=C(x^2+y^2{)}^2$ is the general solution of differential equation $(x^3-3x{y}^2)dx=(y^3-3x^{2}y)dy,$ where C is a parameter.

If f(x) = $\{\begin{array}{cc}|x|+1,& x<0\\ 0,& x=0\\ |x|-1,& x>0\end{array}$
for what values of a does $\underset{x\to a}{\text{lim}}$ f(x) exist?

The value of $\alpha$ so that the geometric mean of $x$ and $y$, where $x\ne y$ is $\frac{x^{\alpha +2}+y^{\alpha +2}}{x^{\alpha +1}+y^{\alpha +1}}$, is

If the normals at $(x_i,y_i),\text{where,}i=1,2,3,4$ on the rectangular hyperbola $xy=c^2$ meet at $(\alpha ,\beta )$. and $x_1^2+x_2^2+x_3^2+x_4^2$ is $a$ and $y_1^2+y_2^2+y_3^2+y_4^2$ is $b$, then $a+b$ is

prove that 1 + sec 20 = cot 40 cot 30

The equation of an ellipse with focus at $(1,–1),$ directrix $x-y-3=0$ and eccentricity $\frac{1}{2}$ is