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

$A$ fully charged capacitor has a capacitance $C$. It is discharged through a small coil of resistance wire,embedded in a block of specific heat $s$ and mass $m$ under thermally isolated conditions. If the temperature of the block is raised by $\Delta T$,the potential difference $V$ across the capacitor initially is

The standard reduction potentials of $Zn^{2+}|Zn$,$Cu^{2+}|Cu$ and $Ag^{+}|Ag$ are respectively $-0.76 \ V$,$0.34 \ V$ and $0.8 \ V$. The following cells were constructed:
$(1)$ $Zn|Zn^{2+}||Cu^{2+}|Cu$
$(2)$ $Zn|Zn^{2+}||Ag^{+}|Ag$
$(3)$ $Cu|Cu^{2+}||Ag^{+}|Ag$
What is the correct order of $E_{cell}^{\circ}$ of these cells?

Let $\overline{a}, \overline{b}$ and $\overline{c}$ be three non-zero vectors such that no two of them are collinear and $(\overline{a} \times \overline{b}) \times \overline{c}=\frac{1}{3}|\overline{b}||\overline{c}| \overline{a}$. If $\theta$ is the angle between the vectors $\overline{b}$ and $\overline{c}$,then the value of $\sin \theta$ is

The temperature of the system decreases in the process of

If $A$ and $B$ are events of a random experiment such that $P(A \cup B) = \frac{4}{5}$,$P(\bar{A} \cup \bar{B}) = \frac{7}{10}$ and $P(B) = \frac{2}{5}$,then $P(A)$ equals