Explore topic-wise InterviewSolutions in .

In four schools $B_1,B_2,B_3,B_4$ the percentage of girls students is 12, 20, 13, 17 respectively. From a school selected at random, one student is picked up at random and it is found that the student is a girl. The probability that the school selected is $B_2$, is

For $r=0,1,...,10$, let $A_r,B_r,$ and $C_r$ denote, respctively, the coefficient of $x^r$ in the expansions of $(1+x{)}^{10},(1+x{)}^{20}$ and $(1+x{)}^{30}$. Then ${\sum }_{r=1}^{10}{A}_r(B_{10}{B}_r-C_{10}{A}_r)$is equal to

Sketch the graph of [y] = sin x

The points $(\frac{a}{\sqrt{3}},a),(\frac{2a}{\sqrt{3}},2a),(\frac{a}{\sqrt{3}},3a)$ are the vertices of

If f(x)=$$\{\begin{array}{cc}x,& \text{when 0≤ x ≥ 1}\\ 2-x,& \text{2-x when 1 ≤ x ≥ 2}\end{array}$$
then $li{m}_{x\to 1}$ f(x) =

If the value of sinx + secx + tanx is a, find 156a.

If $a>b,$ where $a,b<0,$ then $a^r<b^r$ when

The standard deviation of a variate x is $\sigma$. Then the standard deviation of the variate $\frac{ax+b}{c}$ where a, b, c are constants, is

Prove $x=(2n\pi \pm \frac{2\pi }{3})orx=m\pi +(-1{)}^m.\frac{7\pi }{6}$, where m, $n\in I$

Evaluate the following limit:
$\underset{x\to -2}{\text{lim}}\frac{\frac{1}{x}+\frac{1}{2}}{x+2}$

There are two die $A$ and $B$ both having six faces. Die $A$ has three faces marked with $1$, two faces marked with $2$, and one face marked with $3$. Die $B$ has one face marked with $1$, two faces marked with $2$, and three faces marked with $3$. Both dices are thrown randomly once. If $E$ be the event of getting sum of the numbers appearing on top faces equal to $x$, let $P\left(E\right)$ be the probability of event $E$, then
$P\left(E\right)$ is minimum when $x$ equals to

$Therangeofthefunctionf\left(x\right)=co{s}^2\frac{x}{4}+sin\frac{x}{4},xϵRis$

A box contains two white balls, three black balls and four red balls. In how many ways can three balls be drawn from the box if at least one black ball is to be included in the draw

The origin of the coordinate axes is shifted to (3,4) and the axes are rotated through an angle of ${30}^{\circ }$ in the clockwise direction. Find the new coordinates of (7,-2)

$\underset{x\to 0}{lim}\frac{\sqrt{1-cos2x}}{\sqrt{2}x}$ is

(JEE 2002)

The value of ${\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)$

Let $y=e^{\left\{\right({\sin }^{2}x+{\sin }^{4}x+{\sin }^{6}x+\dots \left){\log }_{e}2\right\}}$ satisfy the equation $x^2-17x+16=0,$ where $0<x<\frac{\pi }{2}.$ Then match the correct value of $\text{List I}$ from $\text{List II}.$

$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ \text{(a)}& \frac{2\sin 2x}{1+{\cos }^{2}x}& \left(p\right)& 1\\ \text{(b)}& \frac{2\sin x}{\sin x+\cos x}& \left(q\right)& \frac{4}{9}\\ \text{(c)}& \sum _{n=1}^{\infty }(\cot x{)}^n& \left(r\right)& \frac{2}{3}\\ \text{(d)}& \sum _{n=1}^{\infty }n(\cot x{)}^{2n}& \left(s\right)& \frac{4}{3}\end{array}$

Solve the equation $cosx+cos3x-2cos2x=0$

The last three digits of the number $(81{)}^{25}$ are x, y and z. Find x+y+z

$co{s}^2{48}^{\circ }-si{n}^2{12}^{\circ }=$

[MNR 1977]

For the three events A, B and C, P (exactly one of the events A or B occurs) = P(exactly one of the events B or C occurs) = P(exactly one of the events C or A occurs)=p and P(all the three events occur simultaneously)=$p^2$, where 0<p<1/2. Then the probability of at least one of the three events A, B and C occuring is

polygon has 35 diagonals, and then the number of its side's is__.

Consider the system of equations ${\cos }^{-1}x+({\sin }^{-1}y{)}^2=\frac{p{\pi }^2}{4}$ and $\left({\cos }^{-1}x\right)({\sin }^{-1}y{)}^2=\frac{{\pi }^4}{16},p\in Z$
The value of $p$ for which system has a solution is

In each of the following, find the general value of x satisfying the equation:

$\left(i\right)sinx=\frac{1}{\sqrt{2}}$

$\left(ii\right)cosx=\frac{1}{2}$

$\left(iii\right)tanx=\frac{1}{\sqrt{3}}$

Solve the inequalities:

$7\le \frac{(3x+11)}{2}\le 11$

In how many of the distinct permutations of the letters in MISSISSIPPI do the four 'I's not come together?

Write converse of the following statement.
If two lines are parallel, then they do not intersect in the same plane'.

"$$\begin{array}{cc}TrigonometricEquations& GeneralSolutions\\ 1.si{n}^2\theta =si{n}^{2}x& A.2n\pi \pm \alpha \\ 2.co{s}^2\theta =co{s}^{2}x& B.n\pi +(-1{)}^n\alpha \\ 3.ta{n}^2\theta =ta{n}^{2}x& C.n\pi \pm \alpha \\ & \end{array}$$

Given HM of 2 numbers = 4 and 2A + $G^2$ = 27. Use the relation $G^2$ = AH with 2A + $G^2$ = 27, to find A & G.​

The least difference between the roots of the equation $4cosx(2-3si{n}^{2}x)+(cos2x+1)=0(0\le x\le \frac{\pi }{2})$ is

$\text{If}f\left(x\right)=\{\begin{array}{cc}xsin\frac{1}{x}& x\ne 0\\ 0& x=0\end{array},\text{then}\underset{x\to 0}{lim}f\left(x\right)=$

12.11.10.9.8.7 can be written in factorial notation as :

If $x^{\left(\frac{3}{4}\right({\log }_{3}x{)}^2+{\log }_{3}x-\frac{5}{4})}=\sqrt{3}$ then x has _____.

If A, B and C be the sets such that $A\cup B=A\cup C$ and $A\cap B=A\cap C$ then prove that B= C

If x=-5+2$\sqrt{-4}$, then the values of the expression

$x^4$+9$x^3$+35$x^2$-x+4 is

Let y = ${\log }_{a^k}x$, z = $lo{g}_a$x. Find the relation between y and z.

There are 10 points in a plane, out of these 6 are collinear, if n is the number of triangles formed by joining these points. then:

A series, whose $n^{th}$ term is $\left(\frac{n}{x}\right)+y$, then sum of $r$ terms will be :

Find the derivative of $y=\frac{(t^2-1)}{(t^2+1)}$.

Let S denote the set of real values of x for which
$|x^3-x|\le x\left(1\right)and\frac{2}{|x-2|}>\frac{3}{|1-2x|}\left(2\right)$
then S equals

$\text{If}y=si{n}^{-1}x,then(1-x^2)y_2-x{y}_1$

$\frac{|x+2|-x}{x}<2,xϵR$

Solve $\frac{5}{x-2}>3$ and represent the solution set on the number line.

Or

Solve $|x|<4$ and represent the solution set on the number line.

If a root of the equation $a{x}^2+bx+c=0$ be reciprocal of the equation then $a^{\prime }{x}^2+b^{\prime }x+c^{\prime }=0$, then

If $a_1,a_2,a_3$ .... a_{n} are in A. P., then the common difference is--

The orthocentre of the triangle formed by the lines xy = 0 and x + y = 1 is

$\forall nϵN,P\left(n\right):{2.7}^n+{3.5}^n-5$ is divisible by