Explore topic-wise InterviewSolutions in Current Affairs.

Find the integrals of the functions.
$\int si{n}^{-1}\left(cosx\right)dx.$

The probability that an event $A$ occurs in a single trial of an experiment is $0.6$. In the first three independent trials of the experiment, the probability that $A$ occurs at least once is

The general solution of $\sin 4x\cos 2x=\cos 5x\sin x$ is

For what value of k does the equation $12x^2-10xy+2y^2+11x-5y+k=0$ represents a pair of straight lines?

If $0<x,y<\pi$ and $\cos x+\cos y-\cos (x+y)=\frac{3}{2},$ then $\sin x+\cos y$ is equal to :

For all the values of x, the minimum value of $\frac{1-x+x^2}{1+x+x^2}$ is

Which of the following vector identities is /are false?

If $\pi <\theta <\frac{3\pi }{2}$and z = cos $\theta +i\sin \theta$. Then arg $(z^2-z)$ is

Decreasing (-I) power of given groups:-
(A) -CN
(B) $-N{O}_2$
(C) $-NH{­}_2$
(D) -F

A solution of differential equation is a relation between the variables (independent and dependent), which is free of derivatives of any order and satisfies the differential equation identically.
$$\begin{array}{cc}\text{Differential equation}& \text{General solution}\\ \text{(A)}2x{y}^{2}dx=e^x(dy-ydx)& \text{(P)}4x^{3}y+6e^x-3y^3=cy\\ \text{(B)}y(2x^{2}y+e^x)dx=(e^x+y^3)dy& \text{(Q)}x+{\log }_e(x^2+y^2)=c\\ \text{(C)}(x^2+y^2+2x)dx+2ydy=0& \text{(R)}{x}^2{\log }_e\left(x^2{y}^2\right)+y^3=c{x}^2\\ \text{(D)}(2x^{2}y-2y^4)dx+(2x^3+3x{y}^3)dy=0& \text{(S)}{x}^{2}y+e^x=cy\end{array}$$
Here, $c$ is an integration constant.

Which of the following is the CORRECT combination?

If $A\equiv (9,-1)$ and $B\equiv (-9,5)$, then the locus of moving point $P$ such that $|\overline{AP}|:|\overline{BP}|=1:2$, where $|\overline{AP}|$ denotes the length of $AP$, is

The value of k for which f (x) = kx³ - 9 kx² + 9x + 3 is increasing on R.is...

$cos\left[ta{n}^{-1}\left\{sin\left(co{t}^{-1}x\right)\right\}\right]$ is equal to

Value of sin35⁰cos45⁰

If $f\left(x\right)=sin\left\{co{t}^{-1}\right(x+1\left)\right\}-cos\left(ta{n}^{-1}x\right)andv=cos\left(ta{n}^{-1}\right(sin\left(co{t}^{-1}x\right)\left)\right)$ then the value of $v^2$ for f(x) = 0 is equal to

Let $U=\{x\in N\mid x<20\}$ be the universal set. Let $A=\{x\in N\mid x\text{is prime less than}20\}$,
$B=\{x\in N\mid x\text{is}3n,n\in N,n\le 6\}$,
$C=\{x\in N\mid x=2n–1,n\in N,n\le 10\}$. Then $n\left[\right(A\cup B{)}^{\prime }\cup (A\cap C)]=$

${lim}_{x\to 0}\frac{1-cosmx}{x^2}$

If $f:R\to R$ is defined by $f\left(x\right)=x^2-3x+2$, find f(f(x)).

The feasible solution of a L.P.P. belongs to

Equation $12x^2-10xy+2y^2+11x-5y+2=0$ represent a pair of straight lines. Find the pair of angle bisector.

The tangent to the curve $y=x^3+1$ at (1, 2) makes an angle $\theta$ with y axis, then the value of tan $\theta$ is

Which one of the following Boolean expressions is a tautology ?

The number of $6$ digit numbers that can be formed using the digits $0,1,2,5,7$ and $9$ which are divisible by $11$ and no digit is repeated, is :

The angle of elevation of the top of a vertical tower standing on a horizontal plane is observed to be ${45}^{\circ }$ from a point $A$ on the plane. Let $B$ be the point $30$ m vertically above the point $A$. If the angle of elevation of the top of the tower from $B$ be ${30}^{\circ }$, then the distance (in m) of the foot of the tower from the point $A$ is :

If $z+z^3=0$ then which of the following must be true on the complex plane?

The reflection of the point 3i + 5j + 7k with respect to the plane $\overline{r}.$ (2i + j + k) = 6 is

The shortest distance between the line through the points (2, 3, 1), (4, 5, 2) and parallel to the vectors (3, 4, 2), (4, 5, 3) respectively is

Find the derivative of f(x) = cos x at x = 0

Suppose $A_1,A_2,.....A_{30}$ are thirty sets each having 5 elements and $B_1,B_2,.....B_n$ are n sets each with 3 elements , let ${\bigcup }_{r=1}^{30}$ = ${\bigcup }_{f=1}^n{B}_j=S$ and each of S belongs to exactly 10 of the $A_i^{{}^{\prime }s}$ and exactly 9 of the $B_i^{{}^{\prime }s}$, then n is equal to

Let $A$ and $B$ be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that $A$ or $B$ occurs is $\frac{1}{2}$, then the probability of both of them occur together is :

The length of the latus-rectum of the parabola $y^2+8x-2y+17=0$ is

Put the equation $\frac{x}{a}+\frac{y}{b}=1$ to the slope intercept form and find its slope and y-intercept.

Let A = {1,2,4,5}, B = {2,3,5,6} C = {4,5,6,7}. Verify the following identities :

$\left(i\right)A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$

(ii) $A\cap (B\cup C)=(A\cap B)\cup (A\cap C)$

(iii) $A\cap (B-C)=(A\cap B)-(A\cap C)$

(iv) $A-(B\cup C)=(A-B)\cap (A-C)$

(v) $A-(B\cap C)=(A-B)\cup (A-C)$

(vi) $A\cap \left(B\Delta C\right)=(A\cap B)\Delta (A\cap C)$

$\frac{2x+3}{5}-2<\frac{3(x-2)}{5}$

There are 10 professors and 20 students out of whom a committee of 2 professors and 3 students is be formed. Find the number of ways in which this can be done. Further find in how many of these committees :

(i) A particular professor is included.

(ii) A particular student is included.

(iii) A particular student is excluded

In set -builde method the null set is represented by

$\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+....+\frac{1}{(4n-1)(4n+3)}=\frac{n}{3(4n+3)}$

A fair dice is thrown eight times, then the probability that on the eighth throw, a third 6 is obtained, is

In a single day Raju, the barber, collects Rs. 500 from haircuts; over this day, his equipment depreciates in value by Rs. 50. Of the remaining Rs. 450, Raju pays sales tax worth Rs. 30, takes home Rs. 200 and retains Rs. 220 for improvement and buying of new equipment. He further pays Rs. 20 as income tax from his income. Based on this information, complete Raju's contribution to the following measures of income:

(a) Gross Domestic Product

(b) NNP at Market Price

(c) NNP at Factor Cost

(d) Personal Income

(e) Personal Disposable Income.

A circle with centre $(a,b)$ passes through the origin. The equation of the tangent to the circle at the origin is