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Let $z_1$ and $z_2$ be two complex numbers such that $|z_1|=12$ and $|z_2-3-4i|=5.$ Then the minimum value of $|z_1-z_2|$ is

sin105° + cos105° is equal to:

If $xϵR$, the solution set of the equation
$4^{-x+0.5}-{7.2}^{-x}-4<0$ is equal to

Let $x_1{x}_2{x}_3{x}_4{x}_5{x}_6$ be a six digit number. The numbers of such numbers if
$x_1<x_2<x_3\le x_4<x_5<x_6$ is

The exhaustive domain of $f\left(x\right)={\cot }^{-1}\left(\frac{x}{\sqrt{x^2-\left[x^2\right]}}\right)$ is

(where [.] denotes the greatest integer function)

The root of the equation $ta{n}^{-1}\left(\frac{x-1}{x+1}\right)+ta{n}^{-1}\left(\frac{2x-1}{2x+1}\right)=ta{n}^{-1}\left(\frac{23}{36}\right)$ is

Analyze the given table:





The correct equation for the given table is .

In a $△ABC,a=5,c=2\sqrt{6},\angle C={60}^0.$ If $b_1,b_2$ are two possible values of third side, then the value of $\frac{b_1+b_2}{b_1{b}_2}=$

(In $△ABC,$ usual notations are given.)

A hyperbola, having the transverse axis of length $2sin\theta$, is confocal with the ellipse $3x^2+4y^2=12$. Then, its equation is

A box contains $N$ coins, $m$ of which are fair and the rest are biased. The probability of getting a head when a fair coin is tossed is $\frac{1}{2}$, while it is $\frac{2}{3}$ when a biased coin is tossed. A coin is drawn from the box at random and is tossed twice. Then the probability that the coin drawn is fair, when first toss head, second toss tail is:

If both mean and the standard deviation of $50$ observation $x_1,x_2,...,x_{50}$ are equal to $16$, then the mean of $(x_1-4{)}^2,(x_2-4{)}^2,...,(x_{50}-4{)}^2$ is :

Let R be the set of all real numbers and let f be a function R to R such that that $f\left(x\right)+(x+\frac{1}{2})f(1-x)=1$ for all x $ϵ$ R.Then 2f(0)+3f(1)is equal to

A fair die is tossed until six is obtained on it. Let $X$ be the number of required tosses, then the conditional probability $P(X\ge 5|X>2)$ is:

Let $A\subset Z$ and a function $f:A\to B$ be defined as $f\left(x\right)=\sqrt{\frac{|x|-1}{|x|+1}}-\sqrt{\frac{2+|x|}{2-|x|}}.$ Then

Find Minimize Z=3x+9y subject to

x+3y≤60 , x≤y and x,y≥0

The sides of a square are x= 6, x =9, y = 3 and y = 6.
Find the equation of a circle drawn on di diagonal of the square as its diameter.

The tangent at any point on the curve $x=a{\cos }^3\theta ,y=a{\sin }^3\theta$ meets the coordinate axes at $P$ and $Q$.

The locus of the mid point of $PQ$ is

Equation of the straight line passing through the point of intersection of the lines $3x+4y=7,x-y+2=0$ and having slope $3$ is

$In\Delta ABC\text{prove that,if}\theta \text{be any angle, then b cos}\theta =ccos(A-\theta )+acos(C+\theta ).$

The distance between a point P and the centre of a circle is 'd'. The given circles radius is r. Then what is the minimum distance between the circle and the point.

The vector(s) which is/are coplanar with vectors $\hat{i}+\hat{j}+2\hat{k}\text{and}\hat{i}+2\hat{j}+\hat{k}$ and perpendicular to the vector $\hat{i}+\hat{j}+\hat{k}$ is/are

If for a unit vector $\overrightarrow{a},(\overrightarrow{x}-\overrightarrow{a})\cdot (\overrightarrow{x}+\overrightarrow{a})=12,$ then the value of $|\overrightarrow{x}|$ is

The measure of the angle between the line $\overrightarrow{r}=(2,-3,1)+k(2,2,1);k\in R$ and the plane $2x-2y+z+7=0$ is

If $\left(\cot {\alpha }_1\right)\left(\cot {\alpha }_2\right)...\left(\cot {\alpha }_n\right)=1$ and $0<{\alpha }_1,{\alpha }_2,...,{\alpha }_n<\frac{\pi }{2}$, then the maximum value of $\left(\cos {\alpha }_1\right)\left(\cos {\alpha }_2\right)...\left(\cos {\alpha }_n\right),$ is

For the series $S=1+\frac{1}{(1+3)}(1+2{)}^2+\frac{1}{(1+3+5)}(1+2+3{)}^2+\frac{1}{(1+3+5+7)}(1+2+3+4{)}^2+.....$

Let $f_1\left(x\right)=e^x,f_2\left(x\right)=e^{f_1\left(x\right)},...,f_{n+1}\left(x\right)=e^{f_n\left(x\right)}\forall n\ge 1.$ The for any fixed $n,\frac{d}{dx}{f}_n\left(x\right)$ is

What will be the pass code for the batch at 3.00 p.m. if input is `four of the following five form a group'?

If $x^y=e^{x-y}$, then $\frac{dy}{dx}$ = is equal to