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:

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is $$0.5 \mathrm{~mm}$$, the Vernier constant of traveling microscope is

If mass is written as $$m=k \mathrm{c}^{\mathrm{P}} G^{-1 / 2} h^{1 / 2}$$ then the value of $$P$$ will be : (Constants have their usual meaning with $k a$ dimensionless constant)

Match List I with List II.

Choose the correct answer from the options given below :