The molar heat capacity of water at constant pressure is $75 \ J \ K^{-1} \ mol^{-1}$. When $1.0 \ kJ$ of heat is supplied to $100 \ g$ of water which is free to expand,the increase in temperature of water is ............. $K$.

There are two identical small holes of cross-sectional area $a$ on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. The tank is resting on a smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it in equilibrium is

If $A(1,2,3), B(3,7,-2), C(6,7,7)$ and $D(-1,0,-1)$ are points in a plane, then the vector equation of the line passing through the centroids of $\triangle ABD$ and $\triangle ACD$ is

$A$ thin metallic spherical shell contains a charge $Q$ on it. $A$ point charge $+q$ is placed at the centre of the shell and another charge $q'$ is placed outside it as shown in the figure. All the three charges are positive. The force on the charge at the centre is:

If $f(x)=(x-1)(x-2)(x-3)$ for $x \in[0,4]$,then the value of $c \in(0,4)$ satisfying Lagrange's mean value theorem is:

In which of the following is the $P - O - P$ bond present?