Explore topic-wise InterviewSolutions in .

If $y=2^{\frac{1}{{\log }_{x}4}}$. Then

The solution set of the inequality $(0.5{)}^{{\log }_3{\log }_{0.2}(x^2-\frac{4}{5})}<1$ is

If the co-ordinates of two points A and B are (3,4) and (5,-2) respectively, find the co-ordinates of any point P if PA=PB and Area of triangle PAB =10

For any two complex number $z_1,z_2$ and any two real numbers $a$ and $b$,

$|a{z}_1-b{z}_2{|}^2+|b{z}_1+a{z}_2{|}^2=$

The standard deviation and mean of a data are $6.5$ and $12.5$ respectively. Then the coefficient of variation is

Let $C_1$ and $C_2$ be the centres of the circles $x^2+y^2-2x-2y-2=0$ and $x^2+y^2-6x-6y+14=0$ respectively. If $P$ and $Q$ are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral $P{C}_{1}Q{C}_2$ is :

The integral $\int (1+x-\frac{1}{x})e^{x+\frac{1}{x}}dx$ is equal to:

If the arithmetic mean and harmonic mean between two numbers are $27$ and $12$ respectively, then the geometric mean of those two numbers is

Find the mean deviation about median for the following data :

$\begin{array}{ccccccc}\text{Marks}& 0-10& 10-20& 20-30& 30-40& 40-50& 50-60\\ \text{Number of Girls}& 6& 8& 14& 16& 4& 2\end{array}$

The sum of $(11{)}^2+(12{)}^2+(13{)}^2+\dots +(20{)}^2$ is

What the equation of the auxiliary circle of a hyperbola $\frac{x^2}{16}-\frac{y^2}{9}=1$

If $\frac{cosx}{a}=\frac{sinx}{b}$ then $|acos2x+bsin2x|=$

sin ${75}^0$ =

The series ${\sum }_{m=0}^{\infty }\frac{1}{4^m}(x-1{)}^{2m}$converges for

The area of an equilateral triangle with the equation of base as x+y-2=0 and the opposite vertex with the coordinates (2, -1) is sq. units.

Using mathematical Induction, the numbers $a_n{}^{\prime }s$ are defined by $a_0=1,a_{n+1}=3n^2+n+a_n(n\ge 0)$ Then $a_n=$

For two positive real number's $a$ and $b$, If the A.M. exceeds their G.M. by $2$ and the G.M. exceeds their H.M. by $\frac{8}{5}$, then the value of $a+b$ is

$li{m}_{x\to 1}$ $\frac{1}{|1-x|}$ =

The real order pair $(x,y)$ which satisfies $(x^4+2xi)-(3x^2+yi)=(3-5i)+(1+2yi)$ is

If the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ is inscribed in a rectangle whose length to breadth ratio is $2:1$ in such a manner that it touches the sides of rectangle, then the area of the rectangle is

Which of the following function is identity function?

The number of real roots of the equation $e^{6x}-e^{4x}-2e^{3x}-12e^{2x}+e^x+1=0$ is

$\underset{x\to 1}{lim}f\left(x\right)=5$, $\underset{x\to 2}{lim}g\left(x\right)=6$ and $\underset{x\to 1}{lim}g\left(x\right)=2$ find the value of $\underset{x\to 1}{lim}$ $\left(\right[g\left(x\right){]}^{f\left(x\right)})$

A box contains 2 fifty paise coins, 5 twenty five paise coins and a certain fixed number $n(\ge 2)$ of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these 5 coins is less than one rupee and fifty paise.

If $\alpha ,\beta$ are two non zero complex numbers and $\beta$ is uni modular then the value of $\left|\frac{\alpha -\beta }{1-\overline{\alpha }\beta }\right|$ is

If area of the triangle formed by the lines $y^2-9xy+18x^2=0$ and y=9 is A sq. unit find the value of 4A.

The solution set of the inequality $(0.5{)}^{{\log }_3{\log }_{0.2}(x^2-\frac{4}{5})}<1$ is

$C_0-C_1+C_2-C_3+........+(-1{)}^n{C}_n$ is equal to

If i$z^3$ + $z^2$ - z + i = 0, where i = $\sqrt{-1}$ then |z| is equal to :

The smallest natural number $n,$ such that the cofficient of $x$ in the expansion of ${(x^2+\frac{1}{x^3})}^n$is ${}^n{C}_{23}$, is :

If some three consecutive coefficients in the binomial expansion of $(x+1{)}^n$ in powers of $x$ are in the ratio $2:15:70$, then the average of these three coefficients is :

Let $a,b\in R,a\ne 0,$ such that the equation, $a{x}^2-2bx+5=0$ has a repeated root $\alpha ,$ which is also a root of the equation $x^2-2bx-10=0.$ If $\beta$ is the other root of this equation, then ${\alpha }^2+{\beta }^2$ is equal to:

If $\omega$ is a complex number stisfying $|\omega +\frac{1}{\omega }|$=2,

then maximum distance of $\omega$ from origin is

If A and B are 2 sets such that A U B has 40 elements, A has 18 elements and B has 29 elements, how many elements does A ∩ B have? __

The maximum value of f(x) = -3 $x^2$ + 5x + 2 ∀ x $ϵ$ [0, 2] is

The number of distinct solutions of sin5$\theta$.cos3$\theta$ = sin9$\theta$.cos7$\theta$ in [0, $\frac{\pi }{2}$] is

If the third term in the binomial expansion of $(1+x{)}^m$ is $-\frac{1}{8}{x}^2$, then the rational value of m is

If $x\ge 1,then2Ta{n}^{-1}x+Si{n}^{-1}\left(\frac{2x}{1+x^2}\right)$ =___

Find the asymptotes of the hyperbola xy - 3y - 2x = 0

A relation R defined on the set A = {1,2,3,5} as

{(x, y): x+y >10: x,y ∈ A }is

Let $\overrightarrow{a},\overrightarrow{b}$ and $\overrightarrow{c}$ be three non -zero vectors such that they are mutually non collinear. If the vector $\overrightarrow{a}+2\overrightarrow{b}$ is collinear with $\overrightarrow{c}$ and $\overrightarrow{b}+3\overrightarrow{c}$ is collinear with $\overrightarrow{a}$ then $\overrightarrow{a}+2\overrightarrow{b}+6\overrightarrow{c}$ equals

Which of the following is not a tautology ?

A G. P consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.