The amplitude of a damped oscillator decreases to $0.9$ times its original magnitude in $5 \ s$. In another $10 \ s$,it will decrease to $\alpha$ times its original magnitude,where $\alpha$ equals:

Steam at $100^{\circ} C$ is passed into $1 \ kg$ of water contained in a calorimeter of water equivalent $0.2 \ kg$ at $9^{\circ} C$ until the temperature of the calorimeter and water in it increases to $90^{\circ} C$. The mass of steam condensed in $kg$ is nearly (specific heat of water $= 1 \ cal/g^{\circ} C$,latent heat of vaporisation $= 540 \ cal/g$)

Which of the following cylindrical rods will conduct the most heat when their ends are maintained at the same steady temperatures?

The diagram shows a venturimeter through which water is flowing. The speed of water at $X$ is $2\,cm/s$. The speed of water at $Y$ (taking $g = 1000\,cm/s^2$) is ........ $cm/s$.

The temperature-entropy $(T-S)$ diagram of a reversible engine cycle is given in the figure. Its efficiency is

What does a mature sperm contain?