The most acidic carboxylic acid is

The mole fractions of glucose and water in aqueous glucose solution are 0.0244 and 0.9756 respectively. What is the weight percentage ( \(\mathrm{w} / \mathrm{w}\) ) of glucose in this solution?

The \(\Delta_0\) of a coordination complex of a metal ion \(\left(3 d^1\right)\) is \(1000 \mathrm{~kJ} \mathrm{~mol}^{-1}\). If the energy of \(t_{2 g}\) orbitals is \(-400 \mathrm{~kJ} \mathrm{~mol}^{-1}\), the energy (in \(\mathrm{kJ} \mathrm{mol}^{-1}\) ) of \(e_g\) orbitals is

What are ' \(\mathrm{X}\) ' and ' \(\mathrm{Y}\) ' respectively in the following reaction sequence?
\(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_3 \stackrel{\mathrm{X}}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}_2 \mathrm{H} \stackrel{\mathrm{Y}}{\longrightarrow} \mathrm{C}_6 \mathrm{H}_5 \mathrm{CH}_2 \mathrm{OH}\)

The linear shape of \(\mathrm{CO}_2\) is due to

Match the item given in Column-I (method used for determining colligative property) and Column-II (for the corresponding colligative property) and find the correct order.
\(\begin{array}{|c|c|c|}
\hline & \text { Column I } & \text { Column II } \\
\hline \text { A. } & \text { Beckmann method } & \text { 1. Osmotic pressure } \\
\hline \text { B. } & \begin{array}{l}
\text { Ostwald-Walker method }
\end{array} & \text { 2. Elevation in B.P } \\
\hline \text { C. } & \begin{array}{l}
\text { Berkeley-Hartley method }
\end{array} & \text { 3. Depression in F.P. } \\
\hline \text { D. } & \text { Landsberger method } & \begin{array}{l}
\text { 4. Relative lowering of vapour pressure }
\end{array} \\
\hline
\end{array}\)

\(10 \mathrm{~g}\) of \(\mathrm{NaOH}\) is dissolved in \(500 \mathrm{~mL}\) of aqueous solution. Calculate the molarity of this solution? (Given, formula weight of \(\mathrm{NaOH}=40\) )

\(\lim _{x \rightarrow 0} \frac{1-\cos x \cos 2 x}{\sin ^2 x}=\)

Let \(a, b\) and \(c\) be the lengths of the sides of a triangle with its opposite angles \(A, B\) and \(C\) respectively. If \(\angle C=60^{\circ}\), then the value of \(\frac{c(a+b)+\left(a^2+b^2\right)}{(b+c)(c+a)}\) is

The rate of change of \(x^{\sin x}\) with respect to \((\sin x)^{\mathrm{x}}\) is

The resonant frequency of an LC circuit is \(f_0\). If a dielectric slab of constant 16 is inserted completely between the plates of the capacitor, then the resonant frequency is

The centripetal acceleration ' \(a\) ' of an electron in an orbit of hydrogen and the principal quantum number ' \(n\) ' of the orbit are related by

Which gas among the following is the easiest to liquify?