Consider a modified Bernoulli equation.
$$\left( P + \frac{A}{B t^2} \right) + \rho g (h + B t) + \frac{1}{2}\,\rho V^2 = \text{constant}$$
If t has tile dimension of time then the dimensions of A and B are ___.___ respectively.

Bernoulli equation: $$(P + \frac{A}{Bt^2}) + \rho g(h + Bt) + \frac{1}{2}\rho V^2 = \text{const}$$

$$Bt$$ must have dimensions of length (added to h): $$[B] = [L/T] = M^0LT^{-1}$$.

$$A/(Bt^2)$$ must have dimensions of pressure $$[ML^{-1}T^{-2}]$$:

$$[A] = [P] \times [B] \times [T^2] = ML^{-1}T^{-2} \times LT^{-1} \times T^2 = ML^0T^{-1}$$.

The answer is Option 4: $$[ML^0T^{-1}]$$ and $$[M^0LT^{-1}]$$.