One end each of a resistance \(r\) capacitor \(C\) and resistance \(2 r\) are connected together. The other ends are respectively connected to the positive terminals of batteries, \(P, Q, R\) having respectively emf's \(E, E\) and \(2 E\). The negative terminals of the batteries are then connected together. In this circuit, with steady current the potential drop across the capacitor is :

The maximum magnetic field produced by a current of 12 A passing through a copper wire of diameter 1.2 mm is

Magnetic field induction at the centre of a circular coil of radius \(5 \mathrm{~cm}\) and carrying a current \(0.9 \mathrm{~A}\) is (in SI units) \(\left(\varepsilon_0=\right.\) absolute permittivity of air in SI units, velocity of light \(=3 \times 10^8 \mathrm{~ms}^{-1}\) )

A body is made to move up along an inclined plane of inclination \(30^{\circ}\) and the coefficient of friction is 0.5 , then its retardation is
( \(\mathrm{g}\) - acceleration due to gravity)

Match the following lists.
\begin{array}{|c|c|c|c|}
\hline & List I & & List II \\
\hline A & \begin{array}{l}\text { Zeroth law of } \\
\text { thermodynamics }\end{array} & 1 & \begin{array}{l}\text { Direction of flow of } \\
\text { heat }\end{array} \\
\hline B & \begin{array}{l}\text { First law of } \\
\text { thermodynamics }\end{array} & \| & Work done is zero \\
\hline\underline{\mathrm{C}} & Free expansion of a gas & III & Thermal equilibrium \\
\hline D & \begin{array}{l}\text { Second law of } \\
\text { Thermodynamics }\end{array} & IV & \begin{array}{l}\text { Law of conservation } \\
\text { of energy }\end{array} \\
\hline
\end{array}
The correct answer is
\(\begin{array}{lccccccccc} & \text { A } & \text { B } & \text { C } & \text { D } \end{array}\)

The principle quantum number ' \(n\) ' corresponding to the exited state of \(\mathrm{He}^{+}\)ion, if on transition to the ground state two photons in succession with wavelength \(1026 \mathrm{~A}^{\circ}\) and \(304 \mathrm{~A}^{\circ}\) are emitted ( \(\mathrm{R}=1.097 \times 10^7 \mathrm{~m}^{-1}\) )

Ionisation potential of hydrogen atom is \(13.6 \mathrm{eV}\). When hydrogen atoms in ground state are excited by a supply of \(12.1 \mathrm{eV}\), then the number of spectral lines emitted by hydrogen atoms according to Bohr's theory is

Which of the following statements are correct?
a) \(\mathrm{F}^{-}\)ion concentration above \(2 \mathrm{ppm}\) causes brown mottling of teeth
b) The maximum limit of nitrate in drinking water is \(400 \mathrm{ppm}\)
c) Depletion of ozone layer leads to cataract and skin cancer
d) The irritant red haze in the traffic is due to oxides of sulphur

The angle between the curves \(y^2=2 x\) and \(x^2+y^2=8\) is

If \(l\) and \(b\) are respectively the length and breadth of the rectangle of greatest area that can be inscribed in the ellipse \(x^2+4 y^2=64\), then \((l, b)=\)

\(\lim _{x \rightarrow \infty}\left[\left(1+\frac{1}{n^3}\right)^{\frac{1}{n^3}}\left(1+\frac{8}{n^3}\right)^{\frac{4}{n^3}}\left(1+\frac{27}{n^3}\right)^{\frac{9}{n^3}} \ldots . .(2)^{\frac{1}{n}}\right]=\)

\(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\ldots\) upto \(n\) terms \(=\)

Which of the following reactions are correct with respect to the formation of products?
I. \(2 \mathrm{NaOH}+\mathrm{SO}_2 \longrightarrow \mathrm{Na}_2 \mathrm{SO}_4+\mathrm{H}_2\)
II. \(2 \mathrm{XeF}_4+3 \mathrm{O}_2 \mathrm{~F}_2 \stackrel{143 \mathrm{~K}}{\longrightarrow} 2 \mathrm{XeO}_3+7 \mathrm{~F}_2\)
III. \(\mathrm{PCl}_5+4 \mathrm{H}_2 \mathrm{O} \longrightarrow \mathrm{H}_3 \mathrm{PO}_4+5 \mathrm{HCl}\)
IV. \(2 \mathrm{NaNO}_2+2 \mathrm{HCl} \longrightarrow 2 \mathrm{NaCl}+\mathrm{NO}\)
\(+\mathrm{NO}_2+\mathrm{H}_2 \mathrm{O}\)