In a transistor amplifier, AC current gain is 64 , the load resistance is $5400 \Omega$ and the input resistance of the transistor is $540 \Omega$. The voltage gain is

A monoatomic ideal gas is heated at constant pressure. The percentage of total heat used in increasing the internal energy and that used for doing external work is $A$ and $B$ respectively. Then the ratio, $\mathrm{A}: \mathrm{B}$ is

An a.c. source is applied to a series LR circuit with $\mathrm{X}_{\mathrm{L}}=3 \mathrm{R}$ and power factor is $\mathrm{X}_1$. Now a capacitor with $\mathrm{X}_{\mathrm{c}}=\mathrm{R}$ is added in series to LR circuit and the power factor is $\mathrm{X}_2$. The ratio $\mathrm{X}_1$ to $\mathrm{X}_2$ is

When two tuning forks are sounded together, 6 beats per second are heard. One of the fork is in unison with 0.70 m length of sonometer wire and another fork is in unison with 0.69 m length of the same sonometer wire. The frequencies of the two tuning forks are