For the block diagrm shown in the figure, the transfer function

Solution of  Gate EE 2023 Question paper \\\;\\Step 1 \\\;\\Draw single Flow graph \\\;\\\\\;\\Step 2 \\\;\\Transfer functions of Forward paths\\\;\\P_{1}=3\;\;\Delta_{1}\\\;\\P_{2}=\frac{2}{s}\;\;\Delta_{2}\\\;\\\textrm{Loop}, L_{1}=\frac{1}{s}\\\;\\ Using Masson’s gain formula \\\;\\\frac{Y(s)}{R(s)}=\frac{P_{1}\Delta_{1}+P_2\Delta_2}{1-L_1} = \frac{3S+2}{S - 1}