List of top Questions asked in MET- 2013

If \(m\) parallel lines in a plane are intersected by a family of \(n\) parallel lines, then the number of parallelograms that can be formed is

A person is permitted to select at least one and at most \(n\) coins from a collection of \((2n+1)\) distinct coins. If the total number of ways in which he can select coins is 255, then \(n\) equals

The value of \(x\) in the expression \((x + x^{\log_{10}x})^5\), if the third term in the expansion is 1,000,000, is

\(\sum_{k=0}^{10} {}^{20}C_k\) is equal to

If the point \((a,a)\) is placed in between the lines \(|x+y| = 4\) then

If the roots of the equation \((a-1)(x^2 + x + 1)^2 = (a+1)(x^4 + x^2 + 1)\) are real and distinct then the value of \(a \in\)

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.