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$A$ galvanometer of resistance $G$ is connected in a circuit. Now,a resistance $R$ is connected in series with the galvanometer. To keep the main current in the circuit unchanged,the resistance $S$ to be put in parallel with the series combination of $G$ and $R$ is:

The integral $\int \frac{3x^{13} + 2x^{11}}{(2x^4 + 3x^2 + 1)^4} dx$ is equal to (where $C$ is a constant of integration)

$\int_0^2 \frac{2x-2}{2x-x^2} dx$ is equal to

Electrons ejected from the surface of a metal,when light of certain frequency is incident on it,are stopped fully by a retarding potential of $3 \ V$. Photoelectric effect in this metallic surface begins at a frequency $6 \times 10^{14} \ s^{-1}$. The frequency of the incident light in $s^{-1}$ is : [Planck's constant $= 6.4 \times 10^{-34} \ J \ s$,charge on the electron $= 1.6 \times 10^{-19} \ C$]

How many $ATP$ molecules are released when one molecule of glucose is oxidized in our liver cells?

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