$\begin{array}{1 1} 12.5\;R \\ 25\;R \\ 50 R \\ 100 R \end{array}$

For an ideal gas, $PV = nRT$

Here, its given that $TP^{\large\frac{3}{5}} = $ constant $\rightarrow P^{\large\frac{8}{5}}$$V = k = $ constant.

$\Rightarrow P = KV^{\large\frac{-5}{8}}$

Differentiating the equation: $V (KV^{\large\frac{-5}{8}})$$ = nRT$, we get:

$\large\frac{3K}{8}$$V^{\large\frac{-5}{8}}$$dV = nRDT$

$\Rightarrow PdV = \large\frac{8}{3}$$nrDT = \Delta w$

Now, $\Delta Q = \Delta u + \Delta w \rightarrow \Delta Q = n \large\frac{3R}{2}$$\Delta T + \large\frac{8nR}{3}$$\Delta T$

$\Rightarrow \Delta Q = nR\Delta T \large \frac{25}{6}$$ = 25 R$

(b) option is correct.

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