KCET 2020

If the side of a cube is increased by \(5 \%\), then the surface area of a cube is increased by

A metal exists as an oxide with formula \(M_{0.96}\) O. Metal, \(M\) can exist as \(M^{2+}\) and \(M^{3+}\) in its oxide \(M_{0.96} \mathrm{O}\). The percentage of \(\mathrm{M}^{3+}\) in the oxide is nearly

A cylindrical wire has a mass \((0.3 \pm 0.003) \mathrm{g}\), radius \((0.5 \pm 0.005) \mathrm{mm}\) and length \((6 \pm 0.06) \mathrm{cm}\). The maximum percentage error in the measurement of its density is

If the sum of \(n\) terms of an AP is given by \(S_n=n^2+n\), then the common difference of the \(\mathrm{AP}\) is

A gas mixture contains \(25 \% \mathrm{~He}\) and \(75 \% \mathrm{~CH}_4\) by volume at a given temperature and pressure. The percentage by mass of methane in the mixture is approximately _________.

A thin uniform rectangular plate of mass \(2 \mathrm{~kg}\) is placed in \(x y\)-plane as shown in figure. The moment of inertial about \(x\)-axis is \(I_x=0.2 \mathrm{~kgm}^2\) and the moment of inertia about \(Y\)-axis is \(I_y=0.3 \mathrm{~kgm}^2\). The radius of gyration of the plate about the axis passing through \(O\) and perpendicular to the plane of the plate is