A force is represented by $$F=a x^2+b t^{\frac{1}{2}}$$

where $$x=$$ distance and $$t=$$ time. The dimensions of $$b^2 / a$$ are:

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $$5 \times 10^{10} \mathrm{~Hz}$$ and an amplitude of $$50 \mathrm{~Vm}^{-1}$$. The total average energy density of the electromagnetic field of the wave is : [Use $$\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2$$ ]

Identify the logic operation performed by the given circuit.

A solid circular disc of mass $$50 \mathrm{~kg}$$ rolls along a horizontal floor so that its center of mass has a speed of $$0.4 \mathrm{~m} / \mathrm{s}$$. The absolute value of work done on the disc to stop it is ________ J.