The energy of a hydrogen atom in its ground state is $-13.6 \,eV$. The energy of the level corresponding to $n=5$ is ........ $eV$.

The centre of mass of three particles of masses $1 ~kg, 2 ~kg$ and $3 ~kg$ is at $(2,2,2)$. The position of the fourth mass of $4 ~kg$ to be placed in the system so that the new centre of mass is at $(0,0,0)$ is:

$\cos ^{-1}\left(\frac{-1}{2}\right)-2 \sin ^{-1}\left(\frac{1}{2}\right)+3 \cos ^{-1}\left(\frac{-1}{\sqrt{2}}\right)-4 \tan ^{-1}(-1)$ equals:

The time period of a particle in simple harmonic motion is $8 \ s$. At $t=0$,it is at the mean position. The ratio of the distances travelled by it in the first and second seconds is

In a $\triangle ABC$,the expression $\frac{(a+b+c)(b+c-a)(c+a-b)(a+b-c)}{4b^2c^2}$ is equal to:

On what basis are the three types of lichens classified?