Explore topic-wise InterviewSolutions in Current Affairs.

The value of $\int \frac{\sin \theta d\theta }{(4+{\cos }^2\theta )(2-{\sin }^2\theta )}$ is equal to (where $C$ is integration constant)

The price of certain comic books is listed





The sales tax for each book is 2 dollars. Which of the following gives the mean and median of the given data with and without tax?

The number of ordered pair(s) of $(x,y)$satisfying $3y=[\sin x+[\sin x+\left[\sin x\right]\left]\right]$ and $[y+[y\left]\right]=2\cos x$ is

​​​​​​​(correct answer + 1, wrong answer - 0.25)

The area enclosed by the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is equal to

The area of the region bounded by the curve $y=\tan x$, the tangent to the curve at $x=\frac{\pi }{4}$ and the $x$-axis is

If x + y = 1, then ${\sum }_{r=0}^{n}r{}^n{C}_r{x}^r{y}^{n-r}$ equals:

Solve the equation 21x² – 28x + 10 = 0

The circle $C$ passing through the origin, has the line $3x+4y=0$ as its tangent at the origin. If the image of the centre of $C$ w.r.t the line $\frac{x}{\frac{25}{3}}+\frac{y}{\frac{25}{4}}=1$ lies on the line $3x+4y=0,$ then the equation of $C$ is

If $\underset{0}{\overset{x}{\int }}tf\left(t\right)dt=\sin x-x\cos x-\frac{x^2}{2}$ for all $x\in R-\left\{0\right\},$ then the value of $f\left(\frac{\pi }{6}\right)$ is

The number of solution(s) for ${\tan }^{-1}\frac{x+1}{x-1}+{\tan }^{-1}\frac{x-1}{x}={\tan }^{-1}(-7)$ is

Solve the given inequality graphically in two-dimensional plane: 3y – 5x < 30

Let $f:(0,\infty )\to (0,\infty )$ be a differentiable function satisfying, $x\underset{0}{\overset{x}{\int }}(1-t)f\left(t\right)dt=\underset{0}{\overset{x}{\int }}tf\left(t\right)dt\forall x\in R^{+}$ and $f\left(1\right)=1.$ Then $f\left(x\right)$ can be

Equation of the common tangent to the parabola $y^2=4ax$ and $x^2=4by$ is

If the difference between two prime numbers is $59,$ then sum of their squares is

Question 77.Consider the following matrix-

Select a suitable figure from the four alternatives that would complete the figure matrix-

Let $\left[y\right]$ and $\left\{y\right\}$ denote the greatest integer less than or equal to $y$ and fractional part of $y$ respectively. Then the number of points of discontinuity of the function $f\left(x\right)=\left[5x\right]+\left\{3x\right\}$ in $[0,5]$ is

$IfA=\left[\begin{array}{ccc}cosx& sinx& 0\\ -sinx& cosx& 0\\ 0& 0& 1\end{array}\right]=f\left(x\right),then{A}^{-1}$ is equal to

$IfA=si{n}^8\theta +co{s}^{14}\theta$, then for all values of $\theta$

A sample space consists of 9 elementary events

$E_1,E_2{E}_3,....,E_8,E_9$

whose probabilities are

$P\left(E_1\right)=P\left(E_2\right)=0.08,$

$P\left(E_3\right)=P\left(E_4\right)=0.1,$

$P\left(E_6\right)=P\left(E_7\right)=0.2$

$P\left(E_8\right)=P\left(E_9\right)=0.07$

Suppose $A=\{E_1,E_5,E_8\}$,

B =$\{E_2,E_5,E_8,E_9\}$

(i) Compute $P\left(A\right),P\left(B\right)$, $P(A\cap B)$

(ii) Using the addition law of probability, find $P(A\cup B)$

(iii) List the composition of the even $A\cup B$, and calculate

$P(A\cup B)$ by adding the probabilities of the elementary events.

(iv) Calculate $P\left(\overline{B}\right)$ from $P\left(B\right)$, also calculate

$P\left(\overline{B}\right)$ directly from the elementary events of $\overline{B}$

In Fig., if AB = AC, prove that BE = EC [2 MARKS]

21 m of cloth was used to make 2 cushion covers. Length of cloth required per cushion is .

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

In $R^3$, consider the planes $P_1:y=0$ and $P_2:x+z=1.$ Let $P_3$ be a plane, different from $P_1$ and $P_2$, which passes through the intersection of $P_1$ and $P_2.$ If the distance of the point $(0,1,0)$ from $P_3$ is $1$ and the distance of a point $(\alpha ,\beta ,\gamma )$ from $P_3$ is $2$, then which of the following relations is/are true?

The equation of the plane passing through the point $(1,2,–3)$ and perpendicular to the planes $3x+y-2z=5$ and $2x-5y-z=7$ is:

Let $a,b,x$ and $y$ be real numbers such that $a-b=1$ and $y\ne 0$. If the complex number $z=x+iy$ satisfies $Im\left(\frac{az+b}{z+1}\right)=y$, then which of the following is(are) possible value(s) of $x$?

The locus of the point which moves so that the square of its distance from the point $(3,-2)$ is numerically equal to its distance from the line $5x-12y=13$ can be

1. -64

Suppose
that for a particular economy, investment is equal to 200, government
purchases are 150, net taxes (that is lump-sum taxes minus transfers)
is 100 and consumption is given by C = 100 + 0.75Y (a)
What is the level of equilibrium income? (b) Calculate the value of
the government expenditure multiplier and the tax multiplier. (c) If
government expenditure increases by 200, find the change in
equilibrium income.

Number of solutions of the equation
$2^x+x=2^{\sin x}+\sin x$ in $[0,10\pi ]$ is

The number of ways in which we can get a sum of $11$ by throwing three dice is :