\(50 \mathrm{~mL}\) of \(\mathrm{H}_2 \mathrm{O}\) is added to \(50 \mathrm{~mL}\) of \(1 \times 10^{-3} \mathrm{M}\) barium hydroxide solution. What is the \(\mathrm{pH}\) of the resulting solution?

Match the following

List-I (Reaction)	List-II (Catalyst)
A) Hydrogenation of vegetable oils	I. Ni
B) Decomposition of potassium chlorate	II. \(\mathrm{MnO}_2\)
C) Oxidation of \(\mathrm{SO}_2\) in lead chamber process	III. Pt
D) Oxidation of ammonia in Ostwald's process	IV. \(\mathrm{NO}(\mathrm{g})\)

The correct answer is

The ratio of ground state energy of \(\mathrm{Li}^{2+}, \mathrm{He}^{+}, \mathrm{H}\) is

The masses of an electron, a proton and a neutron respectively will be in the ratio

Match the following
\(\begin{array}{ll}
\text{List - I} & \text{List - II} \\
\text{A) } \mathrm{Al}_2 \mathrm{O}_3+2 \mathrm{NaOH}+3 \mathrm{H}_2 \mathrm{O} \rightarrow 2 \mathrm{Na}\left[\mathrm{Al}(\mathrm{OH})_4\right] & \text{I) Roasting} \\
\text{B) } \mathrm{Ni}(\mathrm{CO})_4 \xrightarrow{230^{\circ} \mathrm{C}} \mathrm{Ni}+4 \mathrm{CO} & \text{II) Calcination} \\
\text{C) } \mathrm{Fe}_2 \mathrm{O}_3 \cdot 3 \mathrm{H}_2 \mathrm{O} \xrightarrow{\Delta} \mathrm{Fe}_2 \mathrm{O}_3+3 \mathrm{H}_2 \mathrm{O} & \text{II) Vapour phase refining} \\
\text{D) } 2 \mathrm{PbS}+3 \mathrm{O}_2 \rightarrow 2 \mathrm{PbO}+2 \mathrm{SO}_2 & \text{IV) Electrolysis} \\
& \text{V) Leaching}
\end{array}\)
The correct answer is

When ethyl bromide and n-propyl bromide are allowed to react with Na metal in dry ether, the number of different alkanes formed is

The molar mass of a solute \(X\) in \(\mathrm{g} \mathrm{mol}^{-1}\), if its \(1 \%\) solution is isotonic with a \(5 \%\) solution of cane sugar (molar mass \(=342 \mathrm{~g} \mathrm{~mol}^{-1}\) ), is

Two objects of masses \(200 \mathrm{~g}\) and \(500 \mathrm{~g}\) possess velocities \(10 \hat{\mathbf{i}} \mathrm{m} / \mathrm{s}\) and \(3 \hat{\mathbf{i}}+5 \hat{\mathbf{j}} \mathrm{m} / \mathrm{s}\) respectively. The velocity of their centre of mass in \(\mathrm{m} / \mathrm{s}\) is :

If \(\int \frac{d x}{2 \cos x+3 \sin x+4}=\frac{2}{\sqrt{3}} f(x)+c\), then \(f\left(\frac{2 \pi}{3}\right)=\)

A graph drawn between absolute temperature and volume of 3 moles of helium gas as shown in the figure. If \(5 \mathrm{cal}\) of heat is used in the process, then the work done is

The current and emf through an inductance differ by phase by

The \(\mathrm{O}-\mathrm{H}\) bond length in \(\mathrm{H}_2 \mathrm{O}\) in gas phase is

The domain of defined of the function \(f(x)=\sqrt{\frac{1-|x|}{2-|x|}}\) is