Explore topic-wise InterviewSolutions in Current Affairs.

Let total revenue received from the sale of $x$ units of a product is given by $R\left(x\right)=12x+2x^2+6.$

Then the average revenue is



[2 marks]

If $I_1=\underset{0}{\overset{2\pi }{\int }}\ln (1-{\tan }^2\frac{x}{8})dx,I_2=\underset{0}{\overset{2\pi }{\int }}\ln (1+{\tan }^2\frac{x}{8})dx$, then the value of $(I_1-I_2)$ is

Find the equation of the circle with centre (1, 1) and radius

How many different words, each containing $2$ vowels and $3$ consonants can be formed with $5$ vowels and $17$ consonants ?

The area bounded by y = cos x, y = x + 1, y = 0 is

Describe the following sets in set-builder form :

(i) A = {1,2,3,4,5,6}

(ii) B = {1, $\frac{1}{2},\frac{1}{3},\frac{1}{4},\frac{1}{4},......$}

Column Matching:



$$\begin{array}{cc}\text{Column (I)}& \text{Column (II)}\\ \begin{array}{cc}\text{(A)}& \text{In}{R}^2,\text{if the magnitude of the projection}\\ & \text{vector of the vector}\alpha \hat{i}+\beta \hat{j}\text{on}\sqrt{3}\hat{i}+\hat{j}\\ & \text{is}\sqrt{3}\text{and if}\alpha =2+\sqrt{3}\beta ,\text{then possible}\\ & \text{value(s) of}|\alpha |\text{is (are)}\end{array}& \text{(P) 1}\\ & \\ \begin{array}{cc}\text{(B)}& \text{Let}a\text{and}b\text{be real numbers such that}\\ & \text{the function}\\ & f\left(x\right)=\{\begin{array}{c}-3a{x}^2-2,x<1\\ bx+a^2,x\ge 1\end{array}\\ & \text{is differentiable for all}x\in R.\text{Then}\\ & \text{possible value(s) of}a\text{is (are)}\end{array}& \text{(Q) 2}\\ & \\ \begin{array}{cc}\text{(C)}& \text{Let}\omega \ne 1\text{be a complex cube root of}\\ & \text{unity. If}(3-3\omega +2{\omega }^2{)}^{4n+3}+\\ & (2+3\omega -3{\omega }^2{)}^{4n+3}+(-3+2\omega +3{\omega }^2{)}^{4n+3}=0,\\ & \text{then possible value(s) of}n\text{is (are)}\end{array}& \text{(R) 3}\\ & \\ \begin{array}{cc}\text{(D)}& \text{Let the harmonic mean of two positive real}\\ & \text{numbers}a\text{and}b\text{be}4.\text{If}q\text{is a positive real}\\ & \text{number such that}a,5,q,b\text{is an arithmetic}\\ & \text{progression, then the value(s) of}|q-a|\text{is (are)}\end{array}& \text{(S) 4}\\ & \\ & \text{(T) 5}\\ & \end{array}$$

Option $\text{(D)}$ matches with which of the elements of right hand column?

$\int \frac{x^{1/2}}{1+x^{3/4}}dx$

The coefficient of $x^3$ in the expansion of $(x+1{)}^5$ is

Differentiate the
function with respect to x.

The value of $\frac{2\log 2+\log 3}{\log 48-\log 4}$ is

If $A=\left[\begin{array}{cc}5a& -b\\ 3& 2\end{array}\right]$ and A adj A = A $A^T$ , then 5a + b is equal to:

Which of the following is a property of mutual information $I(X:Y)$ where $X$ and $Y$ are two random variables.

Find $\frac{dy}{dx}$, if x and y are connected parametrically by the equations given in questions without eliminating the parameter.

$x=cos\theta -cos2\theta ,y=sin\theta -sin2\theta .$

If ${\overrightarrow{a}}_1$ and ${\overrightarrow{a}}_2$ are two non collinear unit vectors inclided at ${60}^{\circ }$ to each other then the value of (${\overrightarrow{a}}_1$ - ${\overrightarrow{a}}_2$) .($\overrightarrow{2}{a}_1$ + ${\overrightarrow{a}}_2$ ) is

If function $f\left(x\right)=\lambda \cos 2x+2\sin x$ has only one extremum point in $[0,\pi ],$ then the value of $\lambda$ can not be

If $ta{n}^{-1}\frac{1-x}{1+x}=\frac{1}{2}ta{n}^{-1}x$, then the value of x is

The vertex of the parabola $x^2+8x+12y+4=0$ is

If $x^2+2ax+10-3a>0$ for all x ∈ R, then

Sketch the graph of the following functions:
$y=si{n}^2(x-\frac{\pi }{4})$

The harmonic conjugate of the point $C(-6,-2)$ with respect to the points $A(-10,0)$ and $B(0,-5)$ is

What is the negation of the statement 3 + 7 = 10

If cos x = cosy

So, x =

The orthocentre of the triangle PAB is

If $\left|\begin{array}{ccc}{a}^2& bc& c^2+ac\\ a^2+ab& b^2& ca\\ ab& b^2+bc& c^2\end{array}\right|=k{a}^2{b}^2{c}^2$, then $k=$

Solve the equation

Find the sum to n
terms in the geometric progression

The radius of a sphere is changing at the rate of 0.1 cm/sec. The rate of change of its surface area when the radius is 200 cm, is

Given the sequence $\left\{a_n\right\}$ is a $G.P.$ such that $\frac{a_4}{a_6}=\frac{1}{4}$ and $a_2+a_5=216$, then the first term is (common ratio is positive)

The approximate value of $(1.0002{)}^{3000}$ is

In Question 2 what the indexof the matrix A is__

The value of integral $\underset{-1}{\overset{2}{\int }}\left[\frac{\left[x\right]}{1+x^2}\right]dx,$ where $[\cdot ]$denotes the greatest integer function, is equal to

The sum of the series $\frac{1}{2\times 3}\times 2+\frac{2}{3\times 4}\times 2^2+\frac{3}{4\times 5}\times 2^3+\cdots \cdots \cdots$ to n terms is