If the energy of an electron in the first Bohr orbit of the $H$-atom is $-2.18 \times 10^{-18} \text{ J}$, then the energy of the electron in the second orbit will be:

Read each statement below carefully and state with reasons,if it is true or false:
$(a)$ The magnitude of a vector is always a scalar.
$(b)$ Each component of a vector is always a scalar.
$(c)$ The total path length is always equal to the magnitude of the displacement vector of a particle.
$(d)$ The average speed of a particle (defined as total path length divided by the time taken to cover the path) is either greater or equal to the magnitude of average velocity of the particle over the same interval of time.
$(e)$ Three vectors not lying in a plane can never add up to give a null vector.

A body cools according to Newton's law of cooling from $100^\circ C$ to $60^\circ C$ in $20$ minutes. The temperature of the surroundings being $20^\circ C$, then the total time required for the body to cool down to $30^\circ C$ is

Find the energy of the third stationary orbit of Bohr's model of the hydrogen atom if the energy of the ground state is $-E \text{ J}$.

If $0.5 \hat{i} + 0.8 \hat{j} + c \hat{k}$ is a unit vector, then $c$ is

The resultant of two vectors $A$ and $B$ makes an angle $\alpha$ with $A$ and $\beta$ with $B$. Which of the following is correct?