In an electrochemicalcell, dichromate ions in aqueous acidic medium are reduced to $Cr ^{3+}$. The current $($in amperes$)$ that flows through the cell for $48.25$ minutes to produce $1$ mole of $Cr ^{3+}$ is $....$ . Use: $1$ Faraday $=96500 C mol ^{-1}$

In the circuit shown in the figure,the power developed across the $1 \Omega$,$2 \Omega$,and $3 \Omega$ resistors are in the ratio of:

If $f: R \rightarrow R$ and $g: R \rightarrow R$ are defined by $f(x)=|x|$ and $g(x)=[x-3]$ for $x \in R$,then $\{g(f(x)):-\frac{8}{5} < x < \frac{8}{5}\}$ is equal to

Jelly is a colloidal solution of

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 : $\Delta_f G_{ CO _2}^{ o }=-394 kJ mol ^{-1}; \Delta_f G_{\text {water }}^{ o }=-237 kJ mol ^{-1} ; \Delta_f G_{\text {butane }}^{ o }=-18 kJ mol ^{-1}$

$A$ plano-convex lens is made of glass with a refractive index of $1.5$. The radius of curvature of its convex surface is $R$. What is its focal length?