Explore topic-wise InterviewSolutions in Current Affairs.

The area (in sq. units) of the region $\{x\in R:x\ge 0,y\ge 0,y\ge x-2\text{and}y\le \sqrt{x}\},$ is :

The solution set of the in equation$\frac{x^2+6x–7}{|x+4|}<0$ is

Three concentric circles of which biggest is $x^2+y^2=1$, have their radii in A.P. If the line $y=x+1$ cuts all the three circles in real and distinct points, then the interval in which the common difference of $AP$ will lie, is

If $y={\cot }^{-1}\left[\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right](0<x<\pi /2)$ then $\frac{dy}{dx}=$

The approximate value of $\sin {31}^{\circ }$ is

If $f\left(x\right)=(x-1{)}^2(x+1{)}^2$, then the function $f$ has

A set contains $(2n+1)$ elements. Then the number of subsets of the set which contains at most $n$ elements.

For the straight lines 4x + 3y – 6 = 0 and 5x + 12y + 9 = 0, the equation of the bisector of the obtuse angle between them is

There are three addressed envelopes and three letters. Find the probability that the typist inserts exactly one letter in the envelope incorrectly.

If $ax+by+c=0$ is the polar of $(1,1)$ for the circle $x^2+y^2-2x+2y+1=0$ and $H.C.F.$ of $b,c$ is equal to $1$, then the value of $a^2+b^2+c^2$ is

If 3sin $\theta$ + 5 cos $\theta$ = 5, then 5 sin $\theta$ - 3 cos $\theta$ is equal to

$\underset{x\to 0}{lim}\left(\frac{a^x-b^x}{x}\right)=$

The mean deviation from mean of the data 25,20,16,22,24,17,23 is

Let $f(x,y)$ be a function satisfying the relation $f(x,0)=x$ and $f(x,y+1)=f\left(f\right(x,y),y)$ for all non-negative integers. Then which of the following is the largest?

General solution of the equation $2{\sin }^{2}x+3{\cot }^{2}x-4\sin x-6\cot x+5=0$ is

Let L = 0 be a common normal to the circle $x^2+y^2-2ax-36=0$ and the curve $S:(1+x{)}^y+e^{xy}=y$ drawn at a point x = 0 on S, then the radius of the circle is

If a, b, c are in G.P. and $a^{\frac{1}{x}=b^{\frac{1}{y}}=c^{\frac{1}{z}}}$

Evaluate the definite integrals.
${\int }_0^1\frac{1}{1+x^2}dx.$

Prove that:

$si{n}^2(\frac{\pi }{8}+\frac{A}{2})-si{n}^2(\frac{\pi }{8}-\frac{A}{2})=\frac{1}{\sqrt{2}}sinA$

The value of ${lim}_{n\to \infty }[\frac{n}{1+n^2}+\frac{n}{4+n^2}+\frac{n}{9+n^2}+\cdots +\frac{1}{2n}]$ is equal to [Bihar CEE 1994]

The sum of the first n terms of the series 6 + 66 + 666 + ….. is

A box contains 10 white, 6 red and 10 black balls. A ball is drawn at

random from the box. What is the probability that the ball drawn is either

white or red?

If $A+B+C=\pi$ and $\cot 2\theta =\cot 2A+\cot 2B+\cot 2C$, then $\frac{\sin 2(A-\theta )}{{\sin }^{2}2A}+\frac{\sin 2(B-\theta )}{{\sin }^{2}2B}+\frac{\sin 2(C-\theta )}{{\sin }^{2}2C}$ is equal to

The constraints of the problems are x ≥ 0, y ≥ 0, 3x+5y ≤ 15, 5x+2y ≤ 10. The optimal solution for the constraints above is equal to .

If $a\to (b\wedge c)$ is false, then the truth values of $a,b$ and $c$ are

Let r and n be positive integers such that $1\le r\le n.$ Then prove the following :

(i) $\frac{{}^n{C}_r}{{}^n{C}_{r-1}}=\frac{n-r+1}{r}$
(ii) $n{}^{n-1}{C}_{r-1}=(n-r+1{)}^n{C}_{r-1}$
(iii) $\frac{{}^n{C}_r}{{}^{n-1}{C}_{r-1}}=\frac{n}{r}$
(iv) ${}^n{C}_r+2^n{C}_{r-1}{+}^n{C}_{r-2}{=}^{n+2}{C}_r$

An insurance company insured 2000 scooter drivers, 4000 car drivers and 6000 truck drivers. The probability of accidents are 0.01, 0.03 and 0.15, respectively, One of the insured persons meets with an accident. What is the probability that he is a scooter driver?

If parabola y=(x−2)2 is shifted by 3 units toward right, then will be the equation of new parabola obtained.

Determine $P\left(\frac{E}{F}\right)$
Mother, father and son line up at random for a family picture

$Ifx=a(cost+tsint)andy=a(sint-tcost),find\frac{d^{2}y}{d{x}^2}.$ Mention the domain in which it is valid.

If $A^{\prime }=\left[\begin{array}{cc}3& 4\\ -1& 2\\ 0& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-1& 2& 1\\ 1& 2& 3\end{array}\right]$, then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'

If $x\in R$ and $x+\frac{x}{2}+\frac{x}{4}<7$, then $x$ lies in

If $A=\left[\begin{array}{ccc}-1& 2& 3\\ 5& 7& 9\\ -2& 1& 1\end{array}\right]$ and $B=\left[\begin{array}{ccc}-4& 1& -5\\ 1& 2& 0\\ 1& 3& 1\end{array}\right]$, then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'

Question 160(ii)

For each hook-up, determine whether there is a single repeater machine that will do the same work. If so, describe or draw it.

Range of the function ${\log }_{0.5}(x^4-2x^2+3)$ is

The area enclosed between the lines x = 2 and x = 7 is

The range of $f\left(x\right)=\frac{1}{2x^2-6x+7}$ is

sin p = sin q .So, p=?

If in a certain language 'SOLDIER' is written as 'JFSCRNK', then how will `GENIOUS' be written in that language?