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If tan $\alpha =2$,then the values of x which satisfy the relation

$tanx=\frac{1}{2}are$ $0<x<$$2\pi and$$0<\alpha <$$\frac{\pi }{2}$

For any matrix A prove that A( adj A) = |A| × I_n

Which of the following is represented by $\frac{co{s}^2\theta -2co{s}^3\theta sin\theta }{si{n}^4\theta +si{n}^2\theta co{s}^2\theta -2si{n}^3\theta cos\theta }$ ?

$\frac{2(x-1)}{5}\le \frac{3(2+x)}{7}$

Let f(x) be a function defined on [0,2] by:

where a, b and c are constants such that f(x) has second derivative at x = 1. Then a equals

Express ${\tan }^{-1}\frac{\cos x}{1-\sin x},-\frac{3\pi }{2}<x<\frac{\pi }{2}$ in the simplest form.

If the equations $x^2+2x+3\lambda =0and2x^2+3x+5\lambda =0$have a non-zero common roots, then $\lambda =$

Match the following vectors with their correct Notation

$\begin{array}{cc}\begin{array}{cc}\left(i\right)& \text{Vector A}\\ \left(ii\right)& \text{Vector F}\\ \left(iii\right)& \text{Vector D}\\ \left(iv\right)& \text{Vector B}\\ \left(v\right)& \text{Vector E}\end{array}& \begin{array}{cc}\left(A\right)& 3\hat{i}\\ \left(B\right)& -2\hat{j}\\ \left(C\right)& -2\hat{i}\\ \left(D\right)& 2\hat{i}\\ \left(E\right)& 2\hat{i}+2\hat{j}\end{array}\end{array}$

If f(x)=$\frac{x^1}{2}$, g(x)=$\frac{x^1}{3}$ and h(x)=$\frac{x^2}{3}$. Find $\frac{(f+g)\left(x\right)}{(f+h)\left(x\right)}$

If $A^{\prime }=\left[\begin{array}{cc}-2& 3\\ 1& 2\end{array}\right]$ and $B=\left[\begin{array}{cc}-1& 0\\ 1& 2\end{array}\right]$, then find (A+2B)'.

If the points of intersection of the circle $x^2+y^2=16$ with $x-\text{axis}$ are foci of an ellipse and points of intersection of circle $x^2+y^2=16$ with $y-\text{axis}$ are end points of minor axis of the same ellipse, then eccentricity of the ellipse is

If $a_n$ is the $n^{th}$ term of an A.P. and $a_1+a_5+a_{10}+a_{15}+a_{20}+a_{24}=225,$ then the sum of first $24$ terms is

If $y=f\left(x\right),then\frac{d^{2}y}{d{x}^2}=$

Expand
the expression

The value of $f\left(0\right)$, so that the function $f\left(x\right)=\frac{\sqrt{1+x}-\sqrt[3]{31+x}}{x}$ is continuous at $x=0$ is

How to find decimal values of trigonometric ratio? Like cos or tan ?

The area enclosed by the curves $y=\sin x+\cos x$ and $y=|\cos x-\sin x|$ over the interval $[0,\frac{\pi }{2}]$ is

$\text{If}|z|=2\text{and}arg\left(z\right)=\frac{\pi }{4},\text{find z}.$

”Each of Rajat's students either scored distinction in chemistry or physics” is represented by which of the following expressions

X : set of Rajat's students

P : x scored distinction in chemistry

Q : x scored distinction in physics

Solve the equation 2x² + x + 1 = 0

1. 420

The number of subsets of a set containing n element is

Let $\ast$ be a binary operation on the set Q of rational number as follows:
$\left(i\right)a\ast b=a{b}^2$
Find which of the binary operation are commutative and which are associative?

Question 81

Solve the following:

The volume of water in a tank is twice of that in the other. If we draw out 25 litres from the first and add it to the other, the volumes of the water in each tank will be the same. Find the volumes of water in each tank.

If a regular pentagon and regular decagon have the same perimeter and $A_1,A_2$ are areas of regular pentagon and regular decagon respectively then $\frac{A_1}{A_2}$ is

Three numbers are chosen at random without replacement from {1, 2, ......, 15}. Let $E_1$ be the event that minimum of the chosen numbers is 5 and $E_2$ be that their maximum is 10 then: