One litre of oxygen at a pressure of $1\, atm$ and two litres of nitrogen at a pressure of $0.5\, atm$ are introduced into a vessel of volume $1\, L$. If there is no change in temperature,the final pressure of the mixture of gas (in $atm$) is

The length of the perpendicular from the point $P(2, -1, 4)$ to the straight line $\frac{x+3}{10} = \frac{y-2}{-7} = \frac{z}{1}$ is:

$A$ whistle of frequency $540 \ Hz$ rotates in a horizontal circle of radius $2 \ m$ at an angular speed of $15 \ rad/s$. What is the highest frequency heard by a listener at rest with respect to the centre of the circle (in $Hz$)? (Velocity of sound in air $= 330 \ m/s$)

The wavelengths of two sound notes in air are $\frac{40}{195} ~m$ and $\frac{40}{193} ~m$. Each note produces $9$ beats per second separately with a third note of fixed frequency. The velocity of sound in air in $m/s$ is

The displacements of two particles of same mass executing $SHM$ are represented by the equations $x_1 = 4 \sin \left(10 t + \frac{\pi}{6}\right)$ and $x_2 = 5 \cos (\omega t)$. The value of $\omega$ for which the energies of both the particles remain same is (in $text{ unit}$)

Which phase of the cell cycle is characterized by the replication of $DNA$ and the synthesis of histone proteins?