If \(C\) be the capacitance and \(V\) be the electric potential, then the dimensional formula of \(\mathrm{CV}^2\) is

Five charges, '\(q\)' each are placed at the comers of a regular pentagon of side '\(a\)' as shown in figure. First, charge from '\(A\)' is removed with other charges intact, then charge at '\(A\)' is replaced with an equal opposite charge. The ratio of magnitudes of electric fields at \(\mathrm{O}\), without charge at \(A\) and that with equal and opposite charge at \(A\) is

The current through a conductor is '\(\mathrm{a}\)' when the temperature is \(0^{\circ} \mathrm{C}\). It is '\(\mathrm{b}\)' when the temperature is \(100^{\circ} \mathrm{C}\). The current through the conductor at \(220^{\circ} \mathrm{C}\) is

In the figure shown above, a cell of negligible internal resistance and emf 22 V is connected to a network of resistors. If the power dissipated in the whole circuit is \(\dfrac{x}{10 R}\), then the value of \(x\) is:

The instantaneous voltage of a \(50 \mathrm{~Hz}\) generator giving peak voltage as \(300 \mathrm{~V}\), The generator equation for this voltage is

The primary of a transformer when connected to a DC battery of \(10 \mathrm{~V}\) draws a current of \(1 \mathrm{~mA}\). The number of turns of the primary and secondary windings are 50 and 100 , respectively. The voltage in the secondary and the current drawn by the circuit in the secondary are respectively

A \(5.80 \mu \mathrm{~F}\) parallel plate air capacitor has a plate separation of 5 mm and is charged to a potential difference of 400 V . The energy density in the region between the plates is

\(\mathrm{Mg}\) is an important component of

Match the reaction in Column I with the major product formed given in Column II.
\(\begin{array}{|l|l|l|} \hline & \text { Column I- Reaction/conditions } & & \text { Column II- Product } \\ \hline A & \mathrm{C}_6 \mathrm{H}_6 \xrightarrow[\substack{\text{(ii) NaOH} \\ \text{(iii) H^+}}]{\text{(i) Oleum}} & P & \text { Pentan-2-ol. } \\ \hline B & \text{Butanal } \xrightarrow[\text{(ii) } \mathrm{H}^+]{\text{(i) } \text{MeMgBr/ dry ether}} & Q & \text { 2-Hydroxybenzoic acid. } \\ \hline C & \text {2-Methylpropene } \xrightarrow[\text { (ii) } \mathrm{H}_2 \mathrm{O}_2 / \mathrm{NaOH}]{\text { (i) } \mathrm{B}_2 \mathrm{H}_6} & R & \text { Phenol } \\ \hline D & \text{Phenol } \xrightarrow[\text { (ii) } \mathrm{CO}_2, 400 \mathrm{~K}, 7 \mathrm{~atm} .]{\text { (i) } \mathrm{NaOH}} & S & \text { 2-Methylpropan-1-0 I } \\ \hline \end{array}\)

An organic compound which produces a bluish green flame when heated on a copper wire is

A gaseous carbon compound is soluble in dilute \(\mathrm{HCl}\). The solution on treating with \(\mathrm{NaNO}_{2}\) gives off nitrogen leaving behind a solution, which smells of wood spirit. The carbon compound is

An aqueous solution which contains \(42 \%\) by weight ( \(\mathrm{w} / \mathrm{W}\) ) of a volatile liquid " A " of molar mass of \(140 \mathrm{~g} / \mathrm{mol}\), has a vapour pressure of 2141.4 mm of Hg at \(37^{\circ} \mathrm{C}\). What is the vapour pressure of the pure liquid "A"? Vapour pressure of water at \(37^{\circ} \mathrm{C}\) is 2019.1 mm .

The volume of \(\mathrm{H}_{2}\) obtained at \(\mathrm{STP}\), when \(\mathrm{Mg}\) obtained by passing a current of \(0.5 \mathrm{~A}\) through molten \(\mathrm{MgCl}_{2}\) for \(32.2\) min is treated with excess of dilute HCl is approximately
[Equivalent mass of \(\mathrm{Mg}=12\) ]