$A$ parallel plate capacitor with oil (dielectric constant $K = 2$) between the plates has capacitance $C$. If the oil is removed,the capacitance of the capacitor becomes:

The volume of the tetrahedron formed by the coterminous edges $\vec{a}, \vec{b}, \vec{c}$ is $3$. Then the volume of the parallelepiped formed by the coterminous edges $\vec{a} + \vec{b}, \vec{b} + \vec{c}, \vec{c} + \vec{a}$ is

$A$ driver applies the brakes on seeing the red traffic signal $400 ~m$ ahead. At the time of applying the brakes,the vehicle was moving with $15 ~m/s$ and retarding at $0.3 ~m/s^2$. The distance covered by the vehicle from the traffic light $1$ minute after the application of brakes is (in $~m$)

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

The refractive index of a glass convex lens is $1.5$. The radius of curvature of each of the two surfaces of the lens is $20 ~cm$. The ratio of the power of the lens when immersed in a liquid of refractive index $1.25$ to that when placed in air is:

Which of the following halogens is most easily reduced?