In the circuit shown in the following figure,the value of $Y$ is:

An electrochemical cell is fueled by the combustion of butane at $1$ bar and $298 K$ . Its cell potential is $\frac{ X }{ F } \times 10^3$ volts, where $F$ is the Faraday constant. The value of $X$ is $...$ .
Use : Standard Gibbs energies of formation at $298 K$ are : $\Delta_f G_{ CO _2}^{ o }=-394 kJ mol ^{-1}; \Delta_f G_{\text {water }}^{ o }=-237 kJ mol ^{-1} ; \Delta_f G_{\text {butane }}^{ o }=-18 kJ mol ^{-1}$

The area (in square units) of the region bounded by the curve $y=|\sin 2x|$ and the $X$-axis in the interval $[0, 2\pi]$ is:

Which one of the following pairs is correctly matched with regard to the codon and the amino acid coded by it?

When the temperature of a body increases from $T$ to $T+\Delta T$,its moment of inertia increases from $I$ to $I+\Delta I$. If $\alpha$ is the coefficient of linear expansion of the material of the body,then $\frac{\Delta I}{I}$ is (neglect higher orders of $\alpha$ ).

If $\int \frac{\sin^8 x - \cos^8 x}{1 - 2 \sin^2 x \cos^2 x} dx = A \sin 2x + B$,then $A$ is equal to