Which of the following is the most stable?

$\int e^x \left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx$ is equal to

Suppose a pure $Si$ crystal has $5 \times 10^{28} \text{ atoms } m^{-3}$. It is doped by $1 \text{ ppm}$ concentration of pentavalent $As$. Calculate the number of electrons and holes. Given that $n_{i} = 1.5 \times 10^{16} \text{ m}^{-3}$.

In which of the following processes does entropy decrease?

The displacement equations of two waves are given as $y_1 = 10 \sin(3\pi t + \pi/3)$ and $y_2 = 5(\sin 3\pi t + \sqrt{3} \cos 3\pi t)$. What is the ratio of their amplitudes?

The work functions for metals $A, B$ and $C$ are respectively $1.92\, eV$,$2.0\, eV$ and $5\, eV$. According to Einstein's photoelectric equation,the metals which will emit photoelectrons for a radiation of wavelength $4100\, \mathring{A}$ is/are: