The value of the series $\cos 12^{\circ} + \cos 84^{\circ} + \cos 132^{\circ} + \cos 156^{\circ}$ is

In which plants does pollination occur exclusively by wind?

An ideal gas is subjected to a cyclic process involving four thermodynamic states. The amounts of heat $(Q)$ and work $(W)$ involved in each of these states are:
$\begin{aligned} & Q_1=6000 \text{ J}, \quad Q_2=-5500 \text{ J}, \quad Q_3=-3000 \text{ J}, \quad Q_4=3500 \text{ J} \\ & W_1=2500 \text{ J}, \quad W_2=-1000 \text{ J}, \quad W_3=-1200 \text{ J}, \quad W_4=x \text{ J} \end{aligned}$
The ratio of the net work done by the gas to the total heat absorbed by the gas is $\eta$. The values of $x$ and $\eta$ respectively are:

In $\triangle ABC$,with usual notation,observe the two statements given below:
$(I)$ $r r_1 r_2 r_3 = \Delta^2$
$(II)$ $r_1 r_2 + r_2 r_3 + r_3 r_1 = s^2$
Which of the following is correct?

In a compound,$C$,$H$,and $N$ atoms are present in the ratio $9 : 1 : 3.5$ by weight. The molecular weight of the compound is $108$. Its molecular formula is:

Let $a, b, c$ be positive integers such that $\frac{a \sqrt{2}+b}{b \sqrt{2}+c}$ is a rational number,then which of the following is always an integer?