MHTCET 19 Apr 2026 Shift 2 Paper

Concept:When a physical quantity is expressed as a power of a measured variable, the relative error in that quantity equals the exponent multiplied by the relative error in the measured variable.Explanation:The volume of the cuboid is:$$V = l \times l \times \sqrt{l} = l^{5/2}$$Using the rule of error propagation for a power law,$$\frac{\Delta V}{V} = \frac{5}{2} \cdot \frac{\Delta l}{l}$$The relative percentage error in volume is given as $6.25\%$, so:$$\frac{\Delta V}{V} \times 100 = 6.25\%$$Substituting this value,$$\frac{5}{2} \cdot \frac{\Delta l}{l} \times 100 = 6.25\%$$Hence, the relative percentage error in length is:$$\frac{\Delta l}{l} \times 100 = \frac{2}{5} \times 6.25\% = 2.5\%$$The least count of the meter scale is:$$\Delta l = 1 \text{ mm} = 0.1 \text{ cm}$$Now, using the percentage error definition,$$\frac{\Delta l}{l} \times 100 = 2.5$$Substituting $\Delta l = 0.1 \text{ cm}$,$$\frac{0.1}{l} \times 100 = 2.5$$Solving for $l$,$$l = \frac{0.1 \times 100}{2.5} = 4 \text{ cm}$$Therefore, the relative percentage error in length is $2.5\%$ and the length of the cuboid is $4 \text{ cm}$.Answer:Option B: $2.5\%$ and $4 \text{ cm}$.