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If acos2$\theta$ + bsin2$\theta$ = C has $\alpha$ and $\beta$ as its solution, then values of tan $\alpha$+ tan$\beta$,tan $\alpha$.tan$\beta$ are respectivly equal to

$\text{If}A=x:x\text{is a prime number}B=x:x\text{is an odd natural number},\text{then}A\cap B\text{is}$

Find the sum of the series $9+3+1+\frac{1}{3}+\frac{1}{3^2}+.....$

The value of

$x=1+\frac{1}{3+\frac{1}{2+\frac{1}{3+\frac{1}{2+.....\infty }}}}$ is

Find the set of real values of x for which ${\log }_{0.5}{\log }_2\frac{2x+1}{x+1}>0$

The value of $\underset{x\to \infty }{\lim }{\left(\frac{x+5}{x-1}\right)}^x$ is

If $\arg \left(z\right)=\frac{\pi }{3}$ and $\arg (z-1)=\frac{2\pi }{3},$ then $z$ is

In a meeting $70$ of the members favour and $30$ oppose a certain member is selected at random and we take $X=0$ if he opposed, and $X=1$ if he is in favour. Then variance is:

Let P(n) denote the statement that $n^2$ + n is odd. Then,

Let $\overrightarrow{a}=3\hat{i}+2\hat{j}+2\hat{k}$ and $\overrightarrow{b}=\hat{i}+2\hat{j}-2\hat{k}$ be two vectors. If a vector perpendicular to both the vectors $\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{a}-\overrightarrow{b}$ has the magnitude $12$ then one such vector is :

If the co-ordinates of the points P and Q be (1, –2, 1) and (2, 3, 4) and O be the origin, then

The tangent and normal to the ellipse $3x^2+5y^2=32$ at the point $P(2,2)$ meet the $x-$axis at $Q$ and $R$, respectively. Then the area (in sq. units) of the triangle $PQR$ is :

Prove $x=n\pi +(-1{)}^n.\frac{\pi }{2}$ or $x=(n\pi +\frac{3\pi }{4})$, where m, $n\in I$

The mean and the variance of five observations are $4$ and $5.20$, respectively. If three of observations are $3,4$ and $4;$ then the absolute value of the difference of the other two observations, is

The total number of $6$ digit numbers that can be formed, having the property that every succeeding digit is greater than the preceding digit is equal to

Let $z$ be a complex number such that the minimum value of $|z|+|z-1|+|2z-7|$ is $\lambda .$ If $y=2\left[x\right]+3=3[x-\lambda ],$ where $[.]$ denotes the greatest integer function, then the value of $[x+y]$ is

$\underset{x\to 0}{lim}\frac{e^x-1}{x}=$

Statement (1): Maximum value of $si{n}^2$x + $co{s}^2$y is 2

Statement (2): Maximum value of 2 $se{c}^2$z is 2

If the cube roots of unity are 1 ,$\omega$ , ${\omega }^2$ then the roots of the equation ${(x-1)}^3$ + 8 = 0 are

Let $\alpha$ and $\beta$ be two numbers where $\alpha <\beta .$ The geometric mean of these numbers exceeds the smaller number $\alpha$ by $12$ and the arithmetic mean of the same numbers is smaller by $24$ than the larger number $\beta .$ Then the value of $|\beta -\alpha |$ is

If three positive real numbers $a,b,c$ are in A.P. such that $abc=4$, then the minimum value of $b$ is .

In a matrix A of order 3, find $\left(\begin{array}{c}3A\end{array}\right|$?

For the expression $\sqrt{x^2+x}+\frac{1}{\sqrt{x^2+x}}>0,x\in$

A parallelogram is cut by two sets of $m$ lines parallel to its sides. The number of parallelograms thus formed is

Select the solution set of $-1<2x+3\le 10$ from given options

Let $P=(-1,0),Q=(0,0),andR=(3,3\sqrt{3})$ be three points. Then the equation of the bisector of $\angle PQR$ is

If ${(\frac{3}{2}{x}^2-\frac{1}{3x})}^9$ is expanded in descending powers of x, then $7^{th}$ term is given by:

What’s the equation of the circle passing through the points (0, 0), (0, 1) (6, 0)

If m is a positive integer, then $\left[\right(\sqrt{3}+1{)}^{2m}]+1$, where [x] denotes greatest integer $\le x$, is divisible by

If the normal at P on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ cuts the major and minor axes in Q and R respectively the PQ:PR =

Let $x_1,x_2$ be the roots of $a{x}^2+bx+c=0$ and $x_1.x_2<0$, $x_1+x_2$ is non - zero. Roots of $x_1(x-x_2{)}^2+x_2(x-x_1{)}^2=0$ are

Find the integral of the given function w.r.t x

$y=\frac{1}{\sqrt[3]{3x^2}}$

Let $f\left(x\right)$ be a function defined on $[-1,1]$.If the distance between $(0,0)$ and $(x,f(x\left)\right)$ is 1 unit , then the function $f\left(x\right)$ may be.

Let N be the universal set.
(i) if A={$x:xϵN$ and x is odd} find A'

(ii) if B={$x:xϵN$, x is divisible by 3 and 5 } find B'

The acute angle between the lines joining the points $(0,0),(3,2)$ and $(2,2),(3,4)$ is

Let $P$ be the point of intersection of the common tangents to the parabola $y^2=12x$ and the hyperbola $8x^2-y^2=8.$ If $S$ and $S^{\prime }$ denote the foci of the hyperbola where $S$ lies on the positive $x-$axis then $P$ divides $S{S}^{\prime }$ in a ratio

8+88+888+........=

Given $B=\left[\begin{array}{ccc}1& 2& 5\\ 2& 1& 3\\ 4& 0& 1\end{array}\right]$ . Find the minor and cofactor of the element $b_{23}$

If $\frac{a}{|z_1-z_2|}=\frac{b}{|z_2-z_3|}=\frac{c}{|z_3-z_1|}$, where $a,b,c\in R,$ then value of $\frac{a^2}{z_1-z_2}+\frac{b^2}{z_2-z_3}+\frac{c^2}{z_3-z_1}$ is

In how many ways a team of 11 players can be selected from 15 players if-

When a fair die is thrown twice, let $(a,b)$ denote the outcome in which the first throw shows $a$ and the second throw shows $b.$ Consider the following events: $A=\left\{\right(a,b\left)|a\text{is odd}\right\},B=\left\{\right(a,b\left)|b\text{is odd}\right\}$ and $C=\left\{\right(a,b)|a+b\text{is odd}\},$ then which of the following(s) is(are) correct?

Convert the complex numbers in to the polar form:

-i +i