In a switching circuit, if the combination $(S_1 \land S_2)$ is connected in parallel to the combination $(S_1' \land S_2')$, then the room is lit only when

Find $|\Delta \overrightarrow{a}|$ and $\Delta a$ when a vector $\overrightarrow{a}$ is rotated by an angle $d\theta$.

Two vectors of same magnitude act at a point. Twice the product of the magnitudes of two vectors is equal to the square of the magnitude of their resultant. The angle between the two vectors is (in $^{\circ}$)

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

Which of the following statement$(s)$ is/are correct?

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.