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If a=$\sqrt[2]{22i}$ then which of the following is correct?

If $x\in [-4,-1]$,

then $\frac{1}{x^2}$ belongs to

The sum of the finite series of natural numbers upto the nth term, that is
$1+2+3+...+n$ is equal to

The value of $\cot 10°(\cot 40°-\cot 50°)$ is equal to

The value of ‘a’ for which $a{x}^2+si{n}^{-1}(x^2-2x+2)+co{s}^{-1}(x^2-2x+2)=0$ has a real solution is

If $\text{adj}B=A,|P|=|Q|=1,$ then $\text{adj}\left(Q^{-1}B{P}^{-1}\right)$ is

tan 75˚ is equal to.

$f\left(x\right)=-3x^2+2x+5$ is concave at

In how many ways 3 friends Ram, Rajat and Rupesh having 6 one rupee coins, 7 one rupee coins, 8 one rupee coins respectively donate 10 rupee coin collectively?

Integration of $f\left(x\right)$ with respect to $x$ where $f\left(x\right)=\frac{1}{(x-1/2{)}^2+3/4}$ will be-

Find the equations of the lines which cut off intercepts on the axes whose sum and product are 1 and -6 respectively.

How many of the following functions are even [sin x is odd and cosx is even]

(a) f(x) = $x^2|x|$ (b) f(x) = $e^x+e^{-x}$

(c) f(x) = log[$\frac{1-x}{1+x}$] (d) log($\sqrt{x^2+1}$- x)

(e) f(x) = log(x + $\sqrt{x^2+1}$ (f) $a^x-a^{-x}$

(g) f(x) = $\sin x+\cos x$ (h) $\sin x\times (e^x-e^{-x})$

Check the validity of the statements given below by the method given against it

(i) p : The sum of an irrational number and a rational number is irrational (by contradiction method)

(ii) q : If n is a real number with n > 3, then $n^2>9$ (by contradiction method)

Let f(x) be a function defined on [0, 1] such that $f\left(x\right)=\{\begin{array}{ccc}x,& ifxϵQ& \\ 1-x,& ifx\text{/}ϵQ& \end{array}$

Then, for all $xϵ[0,1],f\left(f\right(x\left)\right)=$

The number of ways of selectig $5$ letters from the letter of word $TRIGONOMETRY$ is

In how many ways can $17$ persons depart from railway station in $2$ cars and $3$ autos, given that $2$ particular persons depart by same car ($4$ persons can sit in a car and $3$ persons can sit in an auto)?

If the line $ky-2x-k^2+2h=0\&$ parabola $x^2=4y$ touches each other, then

If the range of n observations $x_1,x_n$ is zero , then the mean of these observations is

If a $5$ digit number is made using all the digits from $1,3,4,6,8$, such that all the digits of number from $1$st position to $5$th should not be in increasing order, then the position of number ${}^{\prime \prime }{63184}^{\prime \prime }$ after listing all the numbers formed in ascending order is

Find the real numbers x and y such that : (x + iy)(3 + 2i) = 1 + i

The coefficient of $x^3{y}^4{z}^5$ in the expansion $(xy+yz+xz{)}^6$ is

If $z^2-z+1=0,$ then possible value(s) of $z^n-z^{-n},$ where $n$ is even number

Find the value of ${\sum }_{r=0}^{n-1}\frac{{}^n{C}_r}{{}^n{C}_r+{}^n{C}_{r+1}}$ when n=100

If the $2^{nd}$ and $5^{th}$ terms of a G.P. are 24 and 3 respectively, then the sum of first six terms is _______​.

if $z_1,z_{2}and{z}_3$ are complex numbers such that

|$z_1$|=|$z_2$|=|$z_3$|=$|\frac{1}{z_1}+\frac{1}{z_2}+\frac{1}{z_3}|=1$,

then |$z_1$+$z_2$+$z_3$|

Evaluate $\int {\sec }^2(-3x+4)dx$

'Failure had a tempo faster than success.'

Match the following graphs with respective trigonometric ratio:

If a complex number $z=\frac{\sqrt{3}}{2}+i\frac{i}{2}$ then $z^4$ is

Which of the following statements are correct?

1. For triangle orthocenter,circumcenter and

centroid are collinear.

2. Centroid divides the line joining the circumcenter $\&$ orthocenter

in the ratio of $2:1$ i.e.,$\frac{CS}{OC}=\frac{2}{1}$

Where C-Coordinate of centroid

O-Coordinate of orthocenter

S--Coordinate of circumcenter

If a tan $\theta$ = b, then a cos 2$\theta$ + b sin 2$\theta$ =

[EAMCET 1981, 82; MP PET 1996; J & K 2005]

Which of the following best describes the terms of the series? $\frac{1}{2}$${}^n{C}_1$ - $\frac{2}{3}$${}^n{C}_2$ + $\frac{3}{4}$${}^n{C}_3$...................$(-1{)}^{n+1}$ $\frac{1}{n+1}$${}^n{C}_n$

$f\left(x\right)=\{\begin{array}{cc}3x-8& \text{if}x\le 5\\ 2k& \text{if}x>5\end{array}$ is continuous, find k

Find $(5\sqrt{5}+11{)}^{2n+1}$ - $(5\sqrt{5}-11{)}^{2n+1}$

The y - intercept of tangent drawn to the curve $x=t^2+3t-8$ and $y=2t^2-2t-5$ at the point $(2,-1)$ is

A five digit number is chosen at random.The probability that all the digits are distinct and digits at odd place are odd and digits at even places are even is

There are 16 points in a plane out of which 6 are collinear, then how many lines can be drawn by joining these points

Suppose $z_1,z_2,z_3$ are the vertices of an equilateral triangle inscribed in the circle $|z|=2$. If $z_1=1+i\sqrt{3}$, then the other two vertices are

Two masses - $\sqrt{3}$ m and - $\sqrt{2}$m toed by a light string are placed on a wedge of mass 4 m. The wedge is placed on a smooth horizontal surface. Find out the value of $\theta$ so that the wedge does not move after the system is set free from the state of rest.

Using DeMorgan's law, which of the following is equivalent to the statement $C\cap (B\cup A\text{'}){}^{\prime }$ ?

$\underset{x\to \infty }{lim}(\sqrt{x^2+x}-x)$ equals

If the 8th term of an H.P. is 1/2 and the 14th term is 1/3, then the 20th term is

The identity function is mathematically represented by the formula

If the roots of the equation $x^2-2ax+a^2+a-3=0$ are real and less than 3, then

If $a,b,c$ are the sides of the $\Delta ABC$ and $a^2,b^2,c^2$ are the roots of $x^3-p{x}^2+qx-k=0,$ then

The coordinates of a point at unit distance from the lines 3x - 4y + 1 = 0 and 3x + 6y + 1 = 0 are

The general solution(s) of $4\sin \theta \sin 2\theta \sin 4\theta =\sin 3\theta$ can be