List of top Questions asked in MET

If \(b<0\), then the roots \(x_1\) and \(x_2\) of the equation \(2x^2 + 6x + b = 0\) satisfy the condition \(\left(\frac{x_1}{x_2}\right) + \left(\frac{x_2}{x_1}\right)<K\), where \(K\) is equal to

Sum of the series to \(n\) terms \(5 + 7 + 13 + 31 + 85 + \ldots\) is

The sum of \(n\) terms of the series \(1 + \frac{4}{5} + \frac{7}{5^2} + \frac{10}{5^3} + \dots\) is

The sum to \(n\) terms of the series \(\sum_{r=1}^n \frac{r}{1+r^2+r^4}\) is

The least positive integer \(n\) for which \(n!<\left(\frac{n+1}{2}\right)^n\) holds is

Nylon threads are made of

Determine the relative size of \(\mathrm{Cs}\) atom compared to a \(\mathrm{Li}\) atom, if their densities are \(1.87\mathrm{\ g/cc}\) and \(0.53\mathrm{\ g/cc}\) respectively.

Which of the following forms cationic micelles above a certain minimum concentration?

Determine solubility of \(\mathrm{AgBr}\) in a \(0.1\mathrm{\ M\ KCN}\) solution. \([K_f \text{ of } [\mathrm{Ag(CN)_2}]^- = 5.6 \times 10^8; K_{sp} \text{ of } \mathrm{AgBr} = 7.7 \times 10^{-13}]\)

Determine the \(\mathrm{pH}\) of \(0.024\mathrm{\ M}\) hydroxylamine hydrochloride solution. (\(K_b\) of hydroxyl amine is \(10^{-8}\))

Consider the following reaction in an aqueous solution \[ \mathrm{I}^-(aq) + \mathrm{OCl}^- \rightarrow \mathrm{IO}^-(aq) + \mathrm{Cl}^-(aq) \] and the following initial concentration and initial rate data for this reaction.

Which of the following is the correct rate law for this reaction?

A certain reaction rate increases \(1000\) folds in the presence of a catalyst at \(27^\circ\mathrm{C}\). The activation energy of the original pathway is \(98\mathrm{\ kJ/mol}\). What is the activation energy of the new pathway?

Which one of the following reaction energy diagrams best represents a reaction in the reverse direction; that it is the most endothermic?

\(10\mathrm{g}\) of non-volatile solute is dissolved in \(180\mathrm{g}\) of \(\mathrm{H_2O}\) resulting in lowering of vapour pressure by \(0.5%\). Determine the boiling point of solution if \(K_b\) of water is \(0.52\mathrm{\ K\ kg\ mol^{-1}}\).

A \(0.15\) molal solution of \(\mathrm{K_4[Fe(CN)_6]}\) in water freezes at \(-0.65^\circ\mathrm{C}\). What is the apparent percentage of dissociation of this compound in this solution? (\(K_f\) for water \(= 1.86^\circ\mathrm{C\ mol}^{-1}\))

The spontaneous reaction that takes place in this cell is

Consider the following redox reaction occurring in acidic medium

The unknown standard reduction potential is

Choose the correct statement.

\(p\)-cresol reacts with chloroform in alkaline medium to give the compound \(A\) which adds hydrogen cyanide to form the compound \(B\). The latter on acidic hydrolysis gives chiral carboxylic acid '\(C\)' which is

Mixture can be of:

Which polysaccharide has \(\alpha\)-glycoside linkage?

Which gives only glucose by hydrolysis?

Alanine forms Zwitter ion which exists as

Which A gives red colour in the reaction \[ A \xrightarrow[(ii)\ \mathrm{NaOH}]{(i)\ \mathrm{HNO_2}} \text{red colour} \]