The total work done on a particle is equal to the change in its kinetic energy. This is applicable:

$A$ mixture of $2$ moles of helium gas (atomic mass = $4 \ amu$) and $1$ mole of argon gas (atomic mass = $40 \ amu$) is kept at $300 \ K$ in a container. The ratio of the rms speeds $\left( \frac{V_{rms}(\text{helium})}{V_{rms}(\text{argon})} \right)$ is

The sum of two numbers is $20$. If the product of the square of one number and the cube of the other is maximum,then the numbers are:

An inductive circuit contains a resistance of $10 \, \Omega$ and an inductance of $2.0 \, H$. If an $AC$ voltage of $120 \, V$ and frequency of $60 \, Hz$ is applied to this circuit,the current in the circuit would be nearly......$A$.

An object with a mass $10 \ kg$ moves at a constant velocity of $10 \ m/s$. $A$ constant force then acts for $4 \ s$ on the object and gives it a speed of $2 \ m/s$ in the opposite direction. The impulse acting on the object is (in $N \cdot s$):

If the angle between the pair of lines $x^2+2 \sqrt{2} x y+k y^2=0, k>0$ is $45^{\circ}$,then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line $x+2 y+1=0$ is