$100 \ g$ of water is heated from $30^{\circ}C$ to $50^{\circ}C$. Neglecting the slight expansion of water,the change in its internal energy is ....... $kJ$? (Specific heat of water = $4184 \ J/kg\cdot K$)

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by:

If the tangents at the extremities of a chord $PQ$ of a parabola intersect at $T$,then the distances of the focus of the parabola from the points $P, T, Q$ are in-

There are two holes,one each along the opposite sides of a wide rectangular tank. The cross-section of each hole is $0.01 ~m^2$ and the vertical distance between the holes is $1 ~m$. The tank is filled with water. The net force on the tank in newtons when the water flows out of the holes is (Density of water $= 1000 ~kg/m^3$,$g = 10 ~m/s^2$):

$A$ wire has a resistance of $12 \, \Omega$. It is bent in the form of an equilateral triangle. The effective resistance between any two corners of the triangle is:

Heavy water $(D_2O)$ is primarily prepared by which of the following methods?