Explore topic-wise InterviewSolutions in Current Affairs.

If $g$ is the inverse of a function $f$ and $f\text{'}\left(x\right)=\frac{1}{1+x^5}$, then $g\text{'}\left(x\right)$ is equal to:

Let $E_1$ and $E_2$ be two independent events such that $P\left(E_1\right)=P_1$ and $P\left(E_2\right)=P_2$. Describe in words of the events whose probabilities are

$(1-P_1)P_2$

Find the equation of the line joining the point (3, 5) to the point of intersection of the lines $4x+y-1=0and7x-3y-35=0.$

In the binomial expansion of $(a–b{)}^n,n\ge 5$, sum of $5^{th}and{6}^{th}$ terms is zero, then $\frac{a}{b}$ equals

A coin is tossed. Find the total number of elementary events and also the total number events associated with the random experiment.

The equation of a line passing through the point (-3, 2, - 4) and equally inclined to the axes, are

A father has 3 children with atleast one boy. The probability that he has 2 boys and one girl is:

What is the length of latusrectum of the ellipse $16x^2+y^2=16?$

Three of the six vertices of a regular hexagon are chosen at random. What is the probability that the triangle with these vertices is equilateral.

If 2 more than m is a negative integer and if 5 more than m is a positive integer, which of the following could be the value of m ?

If ${1690}^{2608}+{2608}^{1690}$ is divided by $7$, then the remainder is

The solution of differential equation $\frac{dy}{dx}+\frac{2xy}{1+x^2}=\frac{1}{(1+x^2{)}^2}$ is
(a) $y(1+x^2)=C+ta{n}^{-1}x$
(b) $\frac{y}{1+x^2}=C+ta{n}^{-1}x$
(c) $ylog(1+x^2)=C+ta{n}^{-1}x$
(d) $y(1+x^2)=C+si{n}^{-1}x$

Write the value of $\frac{sinA+sin3A}{cosA+cos3A}$

A divisor of 1200 is selected at random . Find the probability that it is even

If tan $tan22{\frac{1}{2}}^{\circ }=x$ what is the value of tan${135}^{\circ }$?

If the ${10}^{th}$ term of an $A.P.$ is $35$ and the $5^{th}$ term is $20$, then

Let $(1+x^2{)}^2(1+x{)}^n=\sum _{k=0}^{n+4}{a}_k{x}^k.$
The $a_1,a_2\text{and}{a}_3$ are in A.P, then the possible values of $n$ is/are

$\int \frac{x^2-1dx}{x\sqrt{x^4+4x^3-6x^2+4x+1}}$ equals

If $a{l}^2-b{m}^2+2dl+1=0$, where a, b, d are fixed real numbers such that a + b = $d^2$. Then, the line lx + my + 1 = 0 touches a fixed circle

${lim}_{x\to 0}\frac{x}{\sqrt{1+x}-\sqrt{1-x}}$

Find the point(s) where the function f(x) = $x^3$ - 3x + 2 is increasing

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16}+\frac{y^2}{9}=1$, and having centre at $(0,3)$ is

The value of 'a' for which the function f(x) = a sin x + $\frac{1}{3}$ sin 3x has an extremum at x = $\frac{\pi }{3}$ is

The equation of the incircle fonned by the coordinate axes and the line $4x+3y=6$ is

The value of$\frac{sin5\alpha -sin3\alpha }{cos5\alpha +2cos4\alpha +cos3\alpha }$ is

Which of the following is correct for any two complex number $z_1$ and $z_2$ ?

Let the straight line x=b divide the area enclosed by y= (1-x)², y=0 and x=0 into two parts R₁(0≤x≤b) and R₂ (0≤x≤1) such that R₁-R₂ = 1/4 then b equals

If $cos\theta =\frac{3}{5}$,and $\pi <\theta <\frac{3\pi }{2}$, find the values of other five trigonometric functions and hence evaluate $\frac{cosec\theta +cot\theta }{sec\theta -tan\theta }$.

Find the 12th term from the end of the following arithmetic progressions:

(i) 3, 5, 7, 9, ...... 201

(ii) 3, 8, 13, ....... 253

(iii) 1, 4, 7, 10, ....... 88

The number of terms which are identical in the sequence $2,5,8,11,\dots \text{upto}60\text{terms}$ and $3,5,7,9,\dots \text{upto}50\text{terms}$, is

A house is constructed using $112$ bricks . If there are $8$ bricks for each wall, then the number of walls in the house is .

If the diagonals of the quadrilateral formed by the lines $l-1x+m_{1}y+n_1=0,l_{2}x+m_{2}y+n_2=0,l_{1}x+m_{1}y+n_1^{\prime }=0$ and $(l_{2}x+m_{2}y+n_2^{\prime }=0$are perpendicular,then write the value of $l_1^2-l_2^2+m_2-m_2^2$

A delivery man drives his bike from the point $A(5,-2)$ and collects the order from the store $C$, which lies on $y$ - axis. He then delivers the order to $B(3,2).$
If the distance covered by the delivery man is minimum, then the co-ordinates of $C$ is

If $\alpha ={}^m{C}_2,$ then find the value of ${}^{\alpha }{C}_2$.

If $S=\sum _{n=1}^{10}{I}_n,$ where $I_n=\underset{0}{\overset{\frac{\pi }{2}}{\int }}\frac{\sin (2n+1)x}{\sin x}dx$ then the value of $S$ is

If $p,q,r$ are in A.P., then the value of determinant $\left|\begin{array}{ccc}{a}^2+2^{n+1}+2p& b^2+2^{n+2}+3q& c^2+p\\ 2^n+p& 2^{n+1}+q& 2q\\ a^2+2^n+p& b^2+2^{n+1}+2q& c^2-r\end{array}\right|$ is

In a triangle ABC, if angle C is obtuse and angles A and B are given by roots of the equation $ta{n}^{2}x+ptanx+q=0$, then the value of q is

If a vector $\overrightarrow{r}$ has magnitude 14 and direction ratios 2, 3 and -6. Then, find the direction cosines and components of $\overrightarrow{r}$, given that $\overrightarrow{r}$ makes an acute angle with X- axis.

Integrate the rational functions.
$\int \frac{cosx}{(1-sinx)(2-sinx)}dx.$

Consider a binary operation $\ast$ on set{1,2,3,4,5} given by the following multiplication table:
(i)Compute $(2\ast 3)\ast 4$ and $2\ast (3\ast 4)$

$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

(ii) Is $\ast$ commutative?

$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

(iii)Compute $(2\ast 3)\times \left(4ast5\right)$
$\begin{array}{cccccc}\ast & 1& 2& 3& 4& 5\\ 1& 1& 1& 1& 1& 1\\ 2& 1& 2& 1& 2& 1\\ 3& 1& 1& 3& 1& 1\\ 4& 1& 2& 1& 4& 1\\ 5& 1& 1& 1& 1& 5\end{array}$

Find the coordinates of the foci, the vertices, the eccentricity and the length of the latus rectum of the hyperbola,

$5y^2-9x^2=36$