If $y=\mathrm{a}^x \cdot \mathrm{~b}^{2 x-1}$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ is equal to

In a culture bacteria count is $1,00,000$ initially. The number increases by $10 \%$ in first 2 hours. In how many hours will the count reach $2,00,000$, if the rate of growth of bacteria is proportional to the number present?

Error in the measurement of radius of the sphere is $2 \%$. The error in the calculated value of its volume is

In the circuit shown in the figure, $P \neq R$. The reading of the galvanometer remains the same with switch ' $S$ ' open or closed. Then