The ratio of de-Broglie wavelength of two particles \(A\) and \(B\) is \(2: 1\). If the velocities of \(A\) and \(B\) are \(0.05 \mathrm{~ms}^{-1}\) and \(0.02 \mathrm{~ms}^{-1}\), respectively, then the ratio of their masses \(m_A: m_B\) must be

Identify the conditions at which van der Waals equation of state changes to ideal gas equation.

Consider the following.
Statement-I \(\quad: \mathrm{CCl}_4\) does not undergo hydrolysis. But \(\mathrm{SiCl}_4\) undergoes hydrolysis.
\(\begin{array}{ll}\text { Statement-II } \quad: & \text { Thermal and chemical stability of } \mathrm{GeX}_4 \text { is more than } \\ & \mathrm{GeX}_2\end{array}\)
The correct answer is

The reagent used for converting acetylene to oxalic acid is

\(100 \mathrm{~mL}\) of \(0.2 \mathrm{M}\) acetic acid is completely neutralised using a standard solution of \(\mathrm{NaOH}\). The volume of ethane obtained at STP after complete electrolysis of the resulting solution is

In which of the following reactions, hydrogen is one of the products?
i. \(\mathrm{NaBH}_4+\mathrm{I}_2 \longrightarrow\)
ii. \(\mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm{~K}}\)
iii. \(\mathrm{BF}_3+\mathrm{LiAlH}_4 \longrightarrow\)
iv. \(\mathrm{B}_2 \mathrm{H}_6+\mathrm{NH}_3 \xrightarrow{\text { heat }}\)

From the following data at \(25^{\circ} \mathrm{C}\), calculate the \(\Delta_{\mathrm{r}} \mathrm{H}^0\) for \(\mathrm{H}_2 \mathrm{O}(\mathrm{g}) \rightarrow 2 \mathrm{H}(\mathrm{g})+\mathrm{O}(\mathrm{g})\)
reaction: \(\Delta_{\mathrm{r}} \mathrm{H}^0\left(\mathrm{~kJ} \mathrm{~mol}^{-1}\right)\)
\[
\begin{array}{ll}
\frac{1}{2} \mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{OH}(\mathrm{g}) & 42.09 \\
\mathrm{H}_2(\mathrm{~g})+\frac{1}{2} \mathrm{O}_2(\mathrm{~g}) \rightarrow \mathrm{H}_2 \mathrm{O}(\mathrm{g}) & -242 \\
\mathrm{H}_2(\mathrm{~g}) \rightarrow 2 \mathrm{H}(\mathrm{g}) & 436 \\
\mathrm{O}_2(\mathrm{~g}) \rightarrow 2 \mathrm{O}(\mathrm{g}) & 496
\end{array}
\]

Let \(S_n=\sum_{k=1}^n(-1)^{k-1} \cdot k^2\) for \(n \geq 1\). Given that \(S_{2 n}=-n(2 n+1)\) for \(n=1,2,3, \ldots\). then \(S_{77}=\)

Ethylene on reaction with Baeyer's reagent gives the compound \(\underline{\underline{A}}\). In the preparation of co-polymer X, compound A is used as monomer. What is X?

The ratio of the efficiencies of two Carnot engines A and B is 1.25 and the temperature difference between the source and the sink is same in both the engines. The ratio of the absolute temperature of the sources of the engines \(A\) and \(B\) is

If \(y^2=a x^2+2 x+c\), then \(y^3 \frac{d^2 y}{d x^2}\) is

\(\sin A+\sin B=\sqrt{3}(\cos B-\cos A)\)
\(\Rightarrow \sin 3 A+\sin 3 B\) is equal to

The efficiency of a heat engine that works between the temperatures where Celsius-Fahrenheit scales coincides and Kelvin-Fahrenheit scales coincides is (approximately)