Mathematics Tes...

Every integer \(n \geq 1\). \(\frac{d^{n}}{d^{n} x}\left(x e^{2 x}\right)\) is equal to:

Evaluate: \(\int \frac{\sin x}{(\cos x)^3} d x\)

The set of all real \(x\) satisfying the inequality \(\frac{3-|x|}{4-|x|} \geq 0\):

If a curve passes through the origin and the slope of the tangent to it at any point \((x, y)\) is \(\frac{x^2-4 x+y+8}{x-2}\), then this curve also passes through the point:

The value of \(\left|\begin{array}{ccc}\sin ^2 x & \cos ^2 x & 1 \\ \cos ^2 x & \sin ^2 x & 1 \\ -10 & 12 & 2\end{array}\right|\) is:

An iso-profit line represents ______________.

\(\sin \theta+\sin 3 \theta+\sin 5 \theta+\operatorname{sin} 7 \theta\) is equal to:

A man speaks the truth 2 out of 3 times. He picks one of the natural numbers in the set \(S=\{1,2,3,4,5,6,7\}\) and reports that it is even. The probability that it is actually even is:

If \(\tan \left(\frac{\pi}{9}\right), x, \tan \left(\frac{7 \pi}{18}\right)\) are in arithmetic progression and \(\tan \left(\frac{\pi}{9}\right), \mathrm{y}, \tan \left(\frac{5 \pi}{18}\right)\) are also in arithmetic progression, then \(|\mathrm{x}-2 \mathrm{y}|\) is equal to:

\(\lim _{x \rightarrow \frac{\pi}{2}} \frac{\left[1-\tan \left(\frac{x}{2}\right)\right][1-\sin x]}{\left[1+\tan \left(\frac{x}{2}\right)\right][\pi-2 x]^3}\) is: