Find the binomial probability distribution whose mean is $3$ and variance is $2$.

The internal and external diameters of a hollow cylinder measured with vernier calipers are $(5.73 \pm 0.01) \text{ cm}$ and $(6.01 \pm 0.01) \text{ cm}$ respectively. Then the thickness of the cylinder wall is

$5.6 \, \text{liter}$ of helium gas at $STP$ is adiabatically compressed to $0.7 \, \text{liter}$. Taking the initial temperature to be $T_1$,the work done in the process is

The ratio of the magnetic field at the centre of a current-carrying circular coil to its magnetic moment is $x$. If the current and the radius are both doubled,the new ratio will become:

If $m_1$ and $m_2$ $(m_1 > m_2)$ are the slopes of the lines represented by $5x^2 - 8xy + 3y^2 = 0$,then $m_1 : m_2$ equals

The path of a projectile is given by the equation $y = ax - bx^2$,where $a$ and $b$ are constants and $x$ and $y$ are respectively horizontal and vertical distances of the projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively: