MHTCET 25 Apr 2025 Shift 1 Paper

Concept:At constant temperature, Boyle's Law states that $P_1V_1 = P_2V_2$.Hence, pressure and volume are inversely proportional.Explanation:If the volume increases by $7\%$, then $V_2 = V_1 + 0.07V_1 = 1.07V_1$.Applying Boyle's Law:$P_2 = \frac{P_1V_1}{V_2} = \frac{P_1V_1}{1.07V_1} = \frac{P_1}{1.07} = 0.9346P_1$.So the change in pressure is $P_2 - P_1 = 0.9346P_1 - P_1 = -0.0654P_1$.Thus, pressure actually decreases by $6.54\%$, which is not among the options.Therefore, the intended condition must be a $7\%$ decrease in volume.Taking $V_2 = V_1 - 0.07V_1 = 0.93V_1$:$P_2 = \frac{P_1V_1}{0.93V_1} = \frac{P_1}{0.93} = 1.0753P_1$.Hence, percentage increase in pressure $= (1.0753 - 1) \times 100 = 7.52\%$.Answer:For a $7\%$ decrease in volume, the pressure increases by $7.52\%$.Hence, the correct option is C: $7.52\%$.