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If $\pi <\theta <2\pi$, then $\sqrt{\frac{1+cos\theta }{1-cos\theta }}$, is equal to

If A = {-1, 1}, find $A\times A\times A$.

Find the distance of the point (2, 5) from the line 3x + y + 4 = 0 measured parallel to the line 3x - 4y + 8 = 0.

A hoop rolls on a horizontal ground without Slipping with linear speed $v$. Speed of a particle $P$ on the circumference of the hoop at angle $\theta$ is

Let the line $\frac{x}{a}+\frac{y}{b}=1$ where $ab>0,$ passes through $P(\alpha ,\beta ),$ where $\alpha \beta >0.$ If the area formed by the line and the coordinate axes is $S,$ then the least value of $S$ is

If $n^3-9n^2+26n-24=2b,$ then the value of $n$ is
(where $n\in N$ and $b$ is a prime number)

If $3\tan A\tan B=1$, then $2\cos (A+B)$ is equal to

${lim}_{x\to 0}\frac{sec5x-sec3x}{sec3x-secx}$

One diameter of the circle circumscribing the rectangle ABCD is 4y= x + 7.
If the coordinates of A and B are (-3, 4) and (5, 4) respectively, find the equation of the circle.

If f is a real function satisfying $f(x+\frac{1}{x})=x^2+\frac{1}{x^2}$ for all $xϵR-\left\{0\right\}$, then write the expression for f(x).

If $P=2^4\cdot 6^3\cdot 5^2\times {15}^2$, then the number of proper odd divisors of $P$ will be

The equation of line whose slope is $\frac{1}{3}$ and $x-$ intercept is $4$ will be

The angle bisectors BD and CE of a triangle ABC are divided by the incentre I in the ratio of 3 : 2 and 2 :1 respectively. Then the ratio in which I divide the angle bisector through A is.

If a couple dance competition happens between $7$ married couples, then the number of such possible pairs that can be made such that no couple dances in the same pair is

Let A = {a, b}. List all relations on A and find their number.

If $\theta$ denotes the angle between the curves $y=30-2x^2$ and $y=3+x^2$ at a point of their intersection, then $71|\tan \theta |$ is equal to

From a group of 15 cricket players, a team of 11 players is to be chosen. In how many ways can this be done ?

What is the smallest positive integer n for which $(1+i{)}^{2n}=(1-i{)}^{2n}?$

The sum $1+\frac{1^3+2^3}{1+2}+\frac{1^3+2^3+3^3}{1+2+3}+\cdot \cdot \cdot +\frac{1^3+2^3+3^3+\cdot \cdot \cdot +{15}^3}{1+2+3+\cdot \cdot \cdot +15}-\frac{1}{2}(1+2+3+\cdot \cdot \cdot +15)$ is equal to :

If $A=\left[\begin{array}{ccc}1& 4& 4\\ 4& 1& 4\\ 4& 4& 1\end{array}\right]$, then $A^2-6A=$

Let the curve $C$ be the mirror image of the parabola $y^2=4x$ with respect to the line $x+y+4=0$. If $A$ and $B$ are the points of intersection of $C$ with the line $y=-5$, then the distance between $A$ and $B$ is___

The range of $f\left(x\right)=cos\left[x\right]$, for $-\frac{\pi }{2}<x<\frac{\pi }{2}$ is

The equation of two sides of a square are $5x-12y-65=0$ and $5x-12y+26=0$. Find the area of the square.

How many terms of the series 2 + 6 + 18 + .... must be taken to make the sum equal to 728 ?

The system of linear equations $x+y=0,x–y=0,z=0$ will have

If $\sec x+\tan x=p$, then which of the following is/are correct?

Differentiate the following functions with respect to x :

2 sec x + 3 cot x - 4 tan x

$Ify=3^{lo{g}_9^{(1+ta{n}^{2}z)}}then\frac{dy}{dx}=$

If $(1+x)(1+x^2)(1+x^4)...(1+x^{128})=\sum _{r=0}^n{x}^r,$ then n is equal to

Find the area of the region included between $y^2=9xandy=x$.

Refer to question 14. How many sweaters of each type should the company make in a day to get a maximum profit ? What is the maximum profit?

The parametric eqauation of the circle $x^2+y^2-2x-4y-4=0$ is .

The area of the triangle ABC, in which a = 1, b = 2, $\angle$ $C={60}^0,$ is

If A+B +C =${180}^{\circ }$, then $\sum tan\frac{A}{2}tan\frac{B}{2}$ is equal

Construct $2\times 2$ matrix,$A=\left[a_{ij}\right]$ whose elements are given by
$\left(i\right)a_{ij}=\frac{(i+j{)}^2}{2}$

$\left(ii\right)a_{ij}=\frac{\left(i\right)}{j}$

$\left(iii\right)a_{ij}=\frac{(i+2j{)}^2}{2}$

A die is thrown 6 times. If getting an odd number is a success, What is the probability of

(i) sucessses?

(ii) atleast 5 sucesses?

(iii) atmost 5 sucesses?

$\frac{1}{\mathrm{1.2.3}}+\frac{1}{\mathrm{2.3.4}}+\frac{1}{\mathrm{3.4.5}}+\cdots +\frac{1}{n(n+1)(n+2)}=\frac{n(n+3)}{4(n+1)(n+2)}.$