If a force $\overrightarrow{\mathrm{F}}=\left(3\hat{\mathrm{i}}+4\hat{\mathrm{j}}-5\hat{\mathrm{k}}\right)$ unit acts on a box and the displacement of the box is$\overrightarrow{\mathrm{d}}=\left(5\hat{\mathrm{i}}+4\hat{\mathrm{j}}+3\hat{\mathrm{k}}\right)$ unit, the angle between force and displacement is:

1.   ${\cos }^{-1}\left(0.32\right)$

2.  $\frac{\mathrm{\pi }}{2}$

3.  0

4.  ${\cos }^{-1}\left(0.2\right)$

It is well known that a raindrop falls under the influence of the downward gravitational force and the opposing resistive force. The latter is known to be proportional to the speed of the drop but is otherwise undetermined. Consider a drop of mass \(1.00\) g falling from a height of \(1.00\) km. It hits the ground with a speed of \(50.0\) m/s. Work done by the gravitational force and work done by the unknown resistive force respectively are:

A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 200 N and is directly opposed to the motion. Work done by the road on the cycle and work done by the cycle on the road respectively are:

1.   - 2000 J and 2000 J

2.   2000 J and - 2000 J

3.   0 J and 2000 J

4.   - 2000 J and 0 J

The values of energy required to break one bond in DNA \((10^{-20}~\mathrm{J})\) and the kinetic energy of an air molecule \((10^{-21}~\mathrm{J})\) in eV respectively are:

The value of the daily intake of a human adult $\left({10}^7 \mathrm{J}\right)$ in kilocalories is:

1.   24 k cal

2.   2.4 kcal

3.   2400 kcal

4.   240 kcal