Explore topic-wise InterviewSolutions in .

The area of the region bounded by the curve $y=e^x,y=e^{-x}$ and the straight line $x=1$ is

The equation of the plane bisecting the angle between the planes 3x+4y=4 and 6x−2y+3z+5=0 that contains the origin, is

Let $b$ be a non-zero real number. Suppose the quadratic equation $2x^2+bx+\frac{1}{b}=0$ has two distinct real roots. Then

Find X+1/X if X raised to power 2+1/X raised to power 2=62

The equation of the line(s) passing through the intersection of the lines $4x-3y-1=0$ and $2x-5y+3=0$ and equally inclined to the axis is/are

Given slope m, find the equation of normal having slope m to the parabola $y^2=4ax$

Locus of mid points of normal chords of the parabola $y^2=4ax$ is :

For $0<x_1<x_2<\frac{\pi }{2}$,

which inequality holds ?

A variable circle whose centre lies on $y^2-36=0$ cuts rectangular hyperbola $xy=16$ at $(4t_i,\frac{4}{t_i}),i=1,2,3,4$ then $\sum _{i=1}^4\frac{1}{t_i}$ can be

The sum of $n$ terms of the series $2\cdot 5+5\cdot 8+8\cdot 11+\dots$ is

Let $f\left(x\right)=\frac{x}{1+x^2}$. Then range of $f$ is

In a triangle the sum of two sides is $x$ and the product of the same two sides is $y$. If $x^2-c^2=y$, where $c$ is the third side of the triangle, then the ratio of the in-radius to the circum-radius of the triangle is

If the sum of terms of an A.P is given by $S_n=3n+2n^2$,then the c.d of the A.P is

The value of $\frac{C_1}{2}+\frac{C_3}{4}+\frac{C_5}{6}+\cdots$ equals to

${\int }_0^{1}x{e}^{x^2}dx=\lambda {\int }_0^1{e}^{x^2}dx,$ then

If $△\left(x\right)=\left|\begin{array}{ccc}{x}^2+4x-3& 2x+4& 13\\ 2x^2+5x-9& 4x+5& 26\\ 8x^2-6x+1& 16x-6& 104\end{array}\right|=a{x}^3+b{x}^2+cx+d,$ then

The image of the point $(1,6,3)$ in the line $\frac{x}{1}=\frac{y-1}{2}=\frac{z-2}{3}$

If $a_1,a_2$ and $a_3$ are the three value of $‘a^{\prime }$ which satisfy the equation $\underset{0}{\overset{\pi /2}{\int }}(\sin x+a\cos x{)}^{3}dx-\frac{4a}{\pi -2}\underset{0}{\overset{\pi /2}{\int }}x\cos xdx=2$, then the value of $a_1^2+a_2^2+a_3^2$ is

If $\alpha =ta{n}^{-1}\left(\frac{4x-4x^3}{1-6x^2+x^4}\right),\beta =2si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ and $tan\frac{\pi }{8}=k$, then

Football teams $T_1$ and $T_2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T_1$ winning, drawing and losing a game against $T_2$ are $\frac{1}{2},\frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets 3 points for a win, 1 point for a draw and 0 points for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T_1$ and $T_2$, respectively, after two games.



$P(X>Y)$ is

Two persons $A,B$ speaks truth with probabilities $0.6$ and $0.7$ respectively. The probability that they will say the same thing while describing a single event is:

Let p, q and r denote the lengths of the sides QR, PR and PQ of a triangle PQR respectively. Then p cos²(R/2)+r cos²(P/2)

If $f\left(x\right)=\underset{0}{\overset{x}{\int }}\left[\cos \right(\sin t)+\cos (\cos t\left)\right]dt,$ then $f(x+\pi )$ is equal to

If $\overrightarrow{a}=\hat{i}-\hat{j}+\hat{k}and\overrightarrow{b}=\hat{j}-\hat{k},$ then find a vector $\overrightarrow{c}$ such that $\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{b}and\overrightarrow{a}.\overrightarrow{c}=\mathrm{3.....}$

A metal wire of length ‘l’ is held between two rigid supports and cooled through a fall of temperature T. For the wire metal, Y = Young's modulus, $\rho$ = density and $\alpha$ = coefficient of linear expansion. Then the frequency of oscillation of the wire is proportional to

If f(x+y)= f(x) f(y) for all x,y belonging to R and f(1)=2 then, area enclosed by 3|x| + 2|y| <= 8

is :-

a) f(4) sq unit

b) (1/2) f(6) sq unit

c) 1/3 f(6) sq unit

d) 1/3 f(5) sq unit

Let $f\left(x\right)=\underset{0}{\overset{x}{\int }}\left\{\right(a-1\left)\right(t^2+t+1{)}^2-(a+1)(t^4+t^2+1)\}dt.$ Then the set of values of ${}^{\prime }{a}^{\prime }$ for which $f^{\prime }\left(x\right)=0$ has two distinct real roots is:

The number of diagonals in a octagon will be

Match the following. Equation of the parabola is $y^2=4ax$

$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{P) Focal distance}& \text{T) Focal chord perpendicular to axis}\\ \text{Q) Double ordinate}& \text{U) A chord perpendicular to axis}\\ \text{R) Latus rectum}& \text{V) Distance of a point on parabola from directrix}\\ \text{S) Vertex}& \text{W) Meeting point of axis and parabola}\end{array}$

Let P, Q, R and S be the points on the plane with position vectors

$-2\hat{i}-\hat{j},4\hat{i},3\hat{i}+3\hat{j}and-3\hat{i}+2\hat{j}$, respectively. The quadrilateral PQRS must be a

If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then

If possible, using elementary row transformations, find the inverse of the following matrices.
$\left[\begin{array}{ccc}2& 3& -3\\ -1& -2& 2\\ 1& 1& -1\end{array}\right]$

A live load 20 kN/m, 6 m long, moves on simply supported girder AB 12 m long. For maximum bending moment to occur at 4 m from left end A. Where will the head of load be, as measured from A?

Find the direction cosines of the vector $\hat{i}+2\hat{j}+3\hat{k}$