Explore topic-wise InterviewSolutions in .

If $A=\{1,2,3,4\}$ and $B=\{5,7,9\}$, then the number of onto function from $A$ to $B$ is

If $P(x_1,y_1),Q(x_2,y_2),R(x_3,y_3)$ and $S(x_4,y_4)$ are four concyclic points on the rectangular hyperbola $xy=c^2$, then coordinates of the orthocenter of the $△PQR$ is

If $a,b,c$ are non zero real numbers, then minimum value of the expression$\left(\frac{(a^4+a^2+1)(b^4+7b^2+1)(c^4+11c^2+1)}{\left(a^2{b}^2{c}^2\right)}\right)$ is

If $\alpha$ is one real root of quadratic equation $x^2-4x+1=0$ then $2^{nd}$ root $\beta$ is $(\alpha <\beta )$

Find the local maxima and local minima, if any of the following functions. Also, find the local maximum and the local minimum values, as the case may be as follows.
$f\left(x\right)=x^2$

$g\left(x\right)=x^3-3x$

$h\left(x\right)=sinx+cosx,0<x<\frac{\pi }{2}$

$f\left(x\right)=sinx-cosx,0<x<2\pi$

$f\left(x\right)=x^3-6x^2+9x+15$

$g\left(x\right)=\frac{x}{2}+\frac{2}{x},x>0$

$g\left(x\right)=\frac{1}{x^2+2}$

$f\left(x\right)=x\sqrt{1-x},x>0$

If p is the probability that a man aged x years will die in a year, find the probability that out of n men $A_1,A_2,...A_n$ each aged x years, $A_1$ will die in a year and will be the first to die.

An open cylindrical can has to be made with $100$ square units of tin. If its volume is maximum, then the ratio of its base radius and the height is

The angle between the planes $r.(2\hat{i}-\hat{j}+2\hat{k})=3$ and $r.(3\hat{i}-6\hat{j}+2\hat{k})=4$

An aeroplane flying horizontally $1\text{km}$ above the ground is observed at an elevation of ${60}^{\circ }$ and after $10$ seconds the elevation is observed to be ${30}^{\circ }.$ The uniform speed of the aeroplane in $\text{km/h}$ is

In quadrilateral $ABCD,\overrightarrow{AB}=\overrightarrow{a},\overrightarrow{BC}=\overrightarrow{b},\overrightarrow{AD}=\overrightarrow{b}-\overrightarrow{a}.$ If $M$ is the mid point of $\overrightarrow{BC}$ and $N$ is a point on $\overrightarrow{DM}$ such that $\overrightarrow{DN}=\frac{4}{5}\overrightarrow{DM,}$ then $\overrightarrow{AN}=$

Number of real normals to the parabola $y^2=16x,$ passing through $(4,0)$ is

Evaluate $\underset{0}{\overset{2}{\int }}|(x-1){|}^{3}dx$

An integrating factor of the differential equation $(1+y+x^{2}y)dx+(x+x^3)dy=0$ is

Let $E_1=\{x\in R:x\ne 1\text{and}\frac{x}{x-1}>0\}$

and $E_2=\{x\in E_1:{\sin }^{-1}\left({\log }_e\left(\frac{x}{x-1}\right)\right)\text{is a real number}\}.$

$($Here, the inverse trigonometric function ${\sin }^{-1}x$ assumes values in$[-\frac{\pi }{2},\frac{\pi }{2}]$.$)$

​Let $f:E_1\to R$ be the function defined by $f\left(x\right)={\log }_e\left(\frac{x}{x-1}\right)$

and $g:E_2\to R$ be the function defined by$g\left(x\right)={\sin }^{-1}\left({\log }_e\left(\frac{x}{x-1}\right)\right).$



$\begin{array}{cccc}& \text{List I}& & \text{List II}\\ P.& \text{The range of}f\text{is}& 1.& (-\infty ,\frac{1}{1-e}]\cup [\frac{e}{e-1},\infty )\\ Q.& \text{The range of}g\text{contains}& 2.& (0,1)\\ R.& \text{The domain of}f\text{contains}& 3.& [-\frac{1}{2},\frac{1}{2}]\\ S.& \text{The domain of}g\text{is}& 4.& (-\infty ,0)\cup (0,\infty )\\ & & 5.& (-\infty ,\frac{e}{e-1}]\\ & & 6.& (-\infty ,0)\cup (\frac{1}{2},\frac{e}{e-1}]\end{array}$

The correct option is:

The eigen values of the following matrix are

$\left[\begin{array}{ccc}-1& 3& 5\\ -3& -1& 6\\ 0& 0& 3\end{array}\right]$

1. 0.3

The general solution of $\frac{\tan 2x-\tan x}{1+\tan x\tan 2x}=1$ is

The value of integral $\underset{0}{\overset{\pi /2}{\int }}\frac{{\sin }^{5/2}x}{{\sin }^{5/2}x+{\cos }^{5/2}x}dx$ is

The distance (in units) of the point on the line $\frac{x-2}{-1}=\frac{y+1}{-1}=\frac{z-1}{1},$ which is nearest to origin is equal to

Every set is a collection of object but every collection of object is not a set examples

The greatest value of $c\in R$ for which the system of linear equations

$x-cy-cz=0cx-y+cz=0cx+cy-z=0$

has a non-trivial solution, is :

The number of solutions of the equation $\frac{x}{7}=\left\{x\right\}$ is

(where {.} is the fractional part function)

Find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum.
$x^2=-9y$