MHT CET 2025 20TH APRIL EVENING SHIFT

The approximate value of $\cos \left(59^{\circ} 30^{\prime}\right)$ is (given $1^{\circ}=0.0175^{\mathrm{c}}, \sin 60^{\circ}=0.8660$ )

4 gram of NaOH is added in water to form 500 mL solution at 298 K . What is pH of solution? (Molar mass of $\mathrm{NaOH}=40 \mathrm{~g} \mathrm{~mol}^{-1}$ )

The change in the internal energy of the mass of gas, when the volume changes from V to 2 V at constant pressure P is $\left(\gamma=\frac{\mathrm{Cp}}{\mathrm{Cv}}\right)$

If the projection of $\bar{a}$ on $\bar{b}+\bar{c}$ is twice the projection of $\bar{b}+\bar{c}$ on $\bar{a}$ also if $|\bar{b}|=2 \sqrt{2},|\bar{c}|=4$ and the angle between $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ is $\frac{\pi}{4}$ then $|\overline{\mathrm{a}}|=$

Calculate work done if 1 mole of an ideal gas compressed isothermally and reversibly from 12 $\mathrm{dm}^3$ to $6 \mathrm{dm}^3$ at $300 \mathrm{~K} .\left[\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right]$

The density of a cube is measured by measuring its mass and length of its sides. The \% error in the measurement of mass and length are $5 \%$ and $6 \%$ respectively. The percentage error in the measurement of density is