$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:

If the direction cosines of two lines are given by $l+m+n=0$ and $l^2-5m^2+n^2=0$,then the angle between them is

The potential difference $V$ and the current $i$ flowing through an instrument in an $ac$ circuit of frequency $f$ are given by $V = 5 \cos \omega t \text{ volts}$ and $i = 2 \sin \omega t \text{ amperes}$ (where $\omega = 2\pi f$). The power dissipated in the instrument is....$W$

$A$ Zener diode,having a breakdown voltage equal to $15\ V$,is used in a voltage regulator circuit as shown in the figure. The current through the Zener diode is $.....\ mA$.

In a mass spectrometer used for measuring the masses of ions,the ions are initially accelerated by an electric potential $V$ and then made to describe semicircular paths of radius $R$ using a magnetic field $B$. If $V$ and $B$ are kept constant,the ratio $\left( \frac{\text{charge on the ion}}{\text{mass of the ion}} \right)$ will be proportional to

In which of the following processes is $CO_2$ not produced?