Explore topic-wise InterviewSolutions in Current Affairs.

In a $△ABC,$ if 2s = a + b + c and (s-b)(s-c)=x $si{n}^2\frac{A}{2},$ then x = [MP PET 1992]

${lim}_{x\to 0}\frac{sin(a+x)+sin(a-x)-2sina}{xsinx}$

Why is the tax multiplier smaller than the government spending multiplier?

$si{n}^{-1}x+si{n}^{-1}y+si{n}^{-1}z=\frac{3\pi }{2},$ then the value of $x^{100}+y^{100}+z^{100}-\frac{9}{x^{101}+y^{101}+z^{101}}=$

If A and B are independent events such that
$P\left(A\right)=p,P\left(B\right)=2p$ and
$P\left(\text{Exactly one of A and B}\right)=\frac{5}{9}$
then $p=$

$\frac{d^{2}x}{d{y}^2}$ equals:

A variable circle passes through the fixed point (2, 0) and touches the y-axis then the locus of its centre is

The line $\frac{x-2}{3}=\frac{y-3}{4}=\frac{z-4}{5}$ is parallel to the plane
[BIT Ranchi 1991; Pb. CET 1991]

If z is a complex number, then z.$\overline{z}$ = 0 if and only if

In an A.P of which 1 is the first term if the sum of the first p terms is zero, then the sum of the (p+q) terms is

Distinguish between objectives and policies on the basis of
(i) Meaning (ii) Aim /Purpose
(iii) Scope / Focus

Let W denote the words in the English dictionary. Define the relation R by $R=\left\{\right(x,y)ϵW\times W|$ the words x and y have at least one letter in common.} Then R is

A bag contains 9 balls marked with the digits 1,2,3.....9. If two balls are drawn from the bag then find the number of ways of getting the sum of digits on the balls as odd?

Find the orthogonal trajectory of $x^2+y^2=c$

A nunclear missile is fired from the ship.The probability of it being detected by radar is $\frac{1}{3}$.The probability that the missile hits the target given that it went unnoticed is $\frac{3}{4}$.If 4 missiles are targeted from the ship then the probability that all 4 hit the target is.

Locus of centroid of the triangle whose vertices are (a cos t, a sin t), (b sin t, -b cos t) and (1,0), where t is a parameter is

If A = $\left[\begin{array}{cc}x& 1\\ 1& 0\end{array}\right]$ and $A^2$ = I , then x =

If $x^2-11x+a$ and $x^2-14x+2a$ have common factor, then value(s) of $a$ is/are

The value of $co{s}^{-1}x+co{s}^{-1}(\frac{x}{2}+\frac{1}{2}\sqrt{3-3x^2})$ where $(\frac{1}{2}\le x\le 1)$ is equal to

The equation ${\sin }^{-1}x=|x-a|$ will have atleast one solution if

'The number of squares of side at least 6 with vertices in S = {(x, y)1 ≤ x, y ≤ 8} is

Find ${lim}_{x\to 3^{+}}\frac{x}{\left[x\right]}$. Is it equal to ${lim}_{x\to 3^{-}}\frac{x}{\left[x\right]}$.

How many different committees of 5 can be formed from 6 men and 4 women on which exact 3 men and 2 women serve ?

Evaluate ${}^{20}{C}_5+{\sum }_{r=2}^5{}^{25-r}{C}_4.$

Find the equation of the circle which passes through the origin and cuts off chords of lengths 4 and 6 on the positive side of the x-axis and y-axis respectively.

If ${}^{15}{C}_{3r}{=}^{15}{C}_{r+3},$ find r.

$\text{The value of}\frac{(i^5+i^6+i^7+i^8+i^9)}{(1+i)}$

If $a{x}^2+bx+c=0$ has no real roots and $a+b+c<0$ then

If the lines x+y=|a| and ax-y=1 intersect in the first quadrant then

$1\times 2+2\times 3+3\times 4+4\times 5+...$

If |x-1|>5,then

${lim}_{x\to \sqrt{3}}\frac{x^2-3}{x^2+3\sqrt{3}x-12}$

Find the equation of the ellipse in the following cases:
(i) focus is (0,1), directrix is x+y=0 and $e=\frac{1}{2}$.
(ii) focus is (-1,1), directrix is x-y+3=0 and $e=\frac{1}{2}$.
(iii) focus is (-2,3), directrix is 2x+3y+4=0 and $e=\frac{4}{5}$.
(iv) focus is (1,2), directrix is 3x+4y-5=0 and $e=\frac{1}{2}$.

If P(n,5) : P(n,3) = 2:1, find n.

In how many ways can 6 boys and 5 girls be arranged for a group photograph if the girls are to sit on chairs in a row and the boys are to stand in a row behind them?

If the tangent to the parabola $y^2=x$ at a point $(\alpha ,\beta ),(\beta >0)$ is also a tangent to the ellipse, $x^2+2y^2=1$, then $\alpha$ is equal to :

Answer each of the following questions in one word or one sentence or as per exact requirement of for question:

$\text{In any triangle ABC, find the value of a}sin(B-C)+bsin(C-A)+csin(A-B.)$

If $f:R\to R$ is a differentiable function and $f\left(2\right)=6$, then $\underset{x\to 2}{lim}\underset{6}{\overset{f\left(x\right)}{\int }}\frac{2tdt}{(x-2)}$ is :

If $C$ be the centroid of the triangle having vertices $(3,-1),(1,3)$ and $(2,4)$. Let $P$ be the point of intersection of the lines $x+3y-1=0$ and $3x-y+1=0$, then the line passing through the points $C$ and $P$ also passes through the point :

Let $f\left(x\right)=\{\begin{array}{cc}{x}^3-x^2+10x-7,& x\le 1\\ -2x+{\log }_2(k^2-4),& x>1\end{array}$
The set of values of $k$ for which $f\left(x\right)$ has greatest value at $x=1$, is

Area bounded by $y=x^3,y=8$ and $x=0$ is ……..

A particle of mass m is allowed to oscillate on a smooth parabola $x^2=4ay,a>0$, about the origin O (see fig). For small oscillations, find the angular frequency $\left(\omega \right)$
.

From the point $P(1,5)$ tangents $PQ$ and $PR$ are drawn to the ellipse $\frac{x^2}{4}+\frac{y^2}{25}=1$, then the acute angle $QOR,$ where $O$ is the origin, is

Equation of a line which is parallel to the line common to the pair of lines given by $6x^2-xy-12y^2=0$ and $15x^2+14xy-8y^2=0$ and at a distance of $7$ units from it, is

The point of concurrence of the lines $17x+2y-28=0,x+5y+13=0$ and $7x+2y-8=0$ is

The probability that an event $A$ occurs in a single trial of an experiment is $\mathrm{0.3.}$ Six independent trials of the experiment are performed. What is the variance of probability distribution of occurrence of event $A$?