Mathematics Tes...

If \(2 y=\left(\cot ^{-1}\left(\frac{\sqrt{3} \cos x+\sin x}{\cos x-\sqrt{3} \sin x}\right)\right)^2, x \in\left(0, \frac{\pi}{2}\right)\) then \(\frac{d y}{d x}\) is equal to

If \(3 \sin \alpha=5 \sin \beta\) then \(\frac{\tan \frac{\alpha+\beta}{2}}{\tan \frac{\alpha-\beta}{2}}\) equals to:

\(ABCD\) is a quadrilateral, \(E\) is the point of intersection of the line joining the midpoints of the opposite sides. If \(O\) is any point and \(\overrightarrow{ OA }+\overrightarrow{ OB }+\overrightarrow{ OC }+\) \(\overrightarrow{ OD }=x \overrightarrow{O E}\), then \(x\) is equal to:

If \(p(x)=(4 e)^{2 x}\), then what is \(\int p(x) d x\) equal to?

If \(e^y+x y=e\), the ordered pair \(\left(\frac{d y}{d x}, \frac{d^2 y}{d x^2}\right)\) at \(x=0\) isequal to:

Find the value of \(\cos ^{-1}\left(4 x^3-3 x\right), x \in[-1,1]\).

If (x) is an odd periodic function with period 2, then f(4) equal to:

What is the point of intersection of the line \(\frac{x-1}{3}=\frac{y+2}{4}=\frac{z-3}{-2}\) and the plane \(2 x-y+3 z-1=0 ?\)

The coefficient of the term independent of \(x\) in the expansion of \(\left(\sqrt{\frac{x}{3}}+\frac{3}{2 x^{2}}\right)^{10}\) is: