If water at $100^\circ C$ cools in $10$ minutes to $80^\circ C$ and to $65^\circ C$ in the next $10$ minutes, then the room temperature will be ...

Can you associate vectors with $(a)$ the length of a wire bent into a loop,$(b)$ a plane area,$(c)$ a sphere? Explain.

What is the result of multiplying a vector $\overrightarrow{A}$ by a positive real number $\lambda$?

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^6 \text{ m s}^{-1}$, calculate the de Broglie wavelength associated with it. [$h = 6.626 \times 10^{-34} \text{ J s}$ and mass of electron = $9.10938 \times 10^{-31} \text{ kg}$] (in $\text{ pm}$)

Find the length of the component of $\vec{a}$ along $\vec{b}$,where $\vec{a} = 4 \hat{i} + 5 \hat{j}$ and $\vec{b} = -\hat{i} + \hat{j}$.

Which of the following is a unit vector?