$A$ metal $M$ which is not affected by strong acids like conc. $HNO_3$,conc. $H_2SO_4$ and conc. solutions of alkalies like $NaOH$,$KOH$ forms $MCl_3$ which finds use for toning in photography. The metal $M$ is

$A$ pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve $x^2+y^2=4$ with $x+y=a$. The set containing the value of $a$ is

$A$ clock pendulum made of invar has a period of $0.5 \, s$ at $20^{\circ} C$. If the clock is used in a climate where the temperature averages to $30^{\circ} C$, how much time does the clock lose in each oscillation? (For invar, $\alpha = 9 \times 10^{-7} /{ }^{\circ} C$, $g = \text{constant}$)

The radius of the first orbit of hydrogen is $r_{H}$,and the energy in the ground state is $-13.6 \text{ eV}$. Considering a $\mu^{-}$-particle with a mass $207 m_e$ revolving around a proton as in a hydrogen atom,the energy and radius of the proton and $\mu^{-}$-combination respectively in the first orbit are (assume the nucleus to be stationary):

Five capacitors,each of capacitance $C$,are connected as shown in the figure. The ratio of the equivalent capacitance between $P$ and $R$ to the equivalent capacitance between $P$ and $Q$ is:

The angle of elevation of the top of a $T.V.$ tower from three points $A, B, C$ in a straight line through the foot of the tower are $\alpha, 2\alpha, 3\alpha$ respectively. If $AB = a$,the height of the tower is