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Evaluate : $tan\{2ta{n}^{-1}\left(\frac{1}{5}\right)+\frac{\pi }{4}\}.$

Vector A has magnitude of 5 units and makes an angle of ${30}^{\circ }$ with the x-axis. Vector B has magnitude 10 units & make an angle of ${60}^{\circ }$ with the x-axis. Find $\overrightarrow{A}+\overrightarrow{B}$

Using vectors, find the value of k, such that the points (k, -10, 3), (1, -1, 3) and (3, 5, 3) are collinear.

If $\sin (\theta +\alpha )=\cos (\theta +\alpha )$, then which of the following is/are correct?
where $\theta ,\alpha \in (0,\frac{\pi }{2})-\left\{\frac{\pi }{4}\right\}$

A box contains $10$ green, $20$ red, $30$ black and $40$ orange marble. One marble is drawn from the box at random. The probability that marble is neither green nor orange is:

If $(a,b,c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1},$ then $a+b+c$ is

Show that the following statement is true by the method of contrapositive p : If x is an integer and $x^2$ is odd, then x is also odd".

Differentiate $x^{2}tanx.$

What is the angle between the two vectors shown in the figure?

For
the matrices A
and B,
verify that (AB)′
=

where

(i)

(ii)

The general solution of the differential equation y $(x^{2}y+e^x)dx-e^{x}dy=0$ is ___ {c is arbitrary constant}

The range of the function $f\left(x\right)=\frac{x+3}{|x+3|},x\ne -3$ is

A plane makes intercept $3$ and $4$ respectively on $z-$axis and $x-$axis. If the plane is parallel to y-axis, then its equation is

Discuss
the continuity of the function f,
where f is
defined by

Write the coordinates of the incentre of the triangle having its vertices at(0,0),(5,0) and (0,12).

If $(4co{s}^2{40}^{\circ }-3)(3-4si{n}^2{40}^{\circ })=a+bcos{20}^{\circ }$ then |a|+|b|= ___

If $\omega$ and ${\omega }^2$ are non-real cube roots of unity, and $\sqrt{-1}=i$, then
$\left|\begin{array}{ccc}1& 1+i+{\omega }^2& {\omega }^2\\ 1-i& -1& {\omega }^2-1\\ -i& -i+\omega -1& -1\end{array}\right|=$

Value of the determinant $\left|\begin{array}{ccc}secx& sinx& tanx\\ 0& 1& 0\\ tanx& cotx& secx\end{array}\right|$ is given by………………………

Also try to think on the lines that expanding along which row or column will make the calculation easier.

If $\int \frac{x^{2018}}{1+x+\frac{x^2}{2!}+\cdots +\frac{x^{2018}}{2018!}}dx=m!x-m!\ln |P\left(x\right)|+C$ for arbitrary constant of integration $C,$ then

The solution set for the inequality $\sin \alpha {\cos }^3\alpha >{\sin }^3\alpha \cos \alpha$ where $\alpha \in (0,\pi )$ is

Find the function corresponding to the graph given below, $1\le x\le 3$ ( The function which closely describes the graph )

Let $f\left(x\right)=\{\begin{array}{cc}{x}^3-x^2+10x-5,& x\le 1\\ -2x+{\log }_2(b^2-2),& x>1\end{array}.$

If $f\left(x\right)$ has the greatest value at $x=1,$ then the set of values of $b$ is

A bag contains tickets numbered from I to 20. Two tickets are drawn. Find the probability that

(i) both the tickets have prime numbers on them

(ii) on one there is a prime number and on the other there is a multiple of 4.

Let P(6, 3) be a point on hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1.$ If the normal at the point P intersect the x - axis at (9, 0), then the eccentricity of the hyperbola is

(IIT JEE 2011)

Let $f\left(x\right)=\{\begin{array}{cc}2+\sqrt{1-x^2},& \left|x\right|\le 1\\ 2e^{{(1-x)}^2},& \left|x\right|>1\end{array}$

The points where $f\left(x\right)$ is not differentiable is/are :

Find the
angle between two vectorsandwith
magnitudesand
2, respectively having.

If $f:R\to R$ and $g:R\to$ are defined by $f\left(x\right)=2x+3$ and $g\left(x\right)=x^2+7$, then the values of x such that $g\left(f\right(x\left)\right)=8$ are

If $\alpha ,\beta$ are the solutions of $\sin x=-\frac{1}{2}$ in $[0,2\pi ]$ and $\alpha ,\gamma$ are the solutions of $\cos x=-\frac{\sqrt{3}}{2}$ in $[0,2\pi ],$ then

If $ax+by+c=0$ is the polar of $(1,1)$ for the circle $x^2+y^2-2x+2y+1=0$ and $H.C.F.$ of $b,c$ is equal to $1$, then the value of $a^2+b^2+c^2$ is