List of top Questions asked in KEAM

Let \( S \) denote the set of all subsets of integers containing more than two numbers. A relation \( R \) on \( S \) is defined by:

\[ R = \{ (A, B) : \text{the sets } A \text{ and } B \text{ have at least two numbers in common} \}. \]

Then the relation \( R \) is:

Let \( f(x) = \log_e(x) \) and let \( g(x) = \frac{x - 2}{x^2 + 1} \). Then the domain of the composite function \( f \circ g \) is:

The IUPAC name of the complex \( [\text{Cr(NH}_3)_3(\text{H}_2\text{O})_3]\text{Cl}_3 \) is:

Coordination compounds exhibit different types of isomerism. Some complexes are given in Column I, and the type of isomerism is given in Column II.

\[ \begin{array}{|l|l|} \hline \textbf{Column I} & \textbf{Column II} \\ \hline (a) [\text{Pt(NH}_3)_2\text{Cl}_2] & (i) \text{Ionisation isomerism} \\ \hline (b) [\text{Co(en)}_3]^{3+} & (ii) \text{Linkage isomerism} \\ \hline (c) [\text{Cr(NH}_3)_5(\text{SO}_4)]\text{Br} & (iii) \text{Optical isomerism} \\ \hline (d) [\text{Co(NH}_3)_5(\text{NO}_2)]\text{Cl}_2 & (iv) \text{Geometrical isomerism} \\ \hline \end{array} \]

The standard molar entropies of \( \text{SO}_2(g) \), \( \text{SO}_3(g) \), and \( \text{O}_2(g) \) are:

• \( S^\circ_{\text{SO}_2} = 250 \) J/K·mol
• \( S^\circ_{\text{SO}_3} = 257 \) J/K·mol
• \( S^\circ_{\text{O}_2} = 205 \) J/K·mol

Calculate the standard molar entropy change for the reaction:

\[ 2\text{SO}_2(g) + \text{O}_2(g) \rightarrow 2\text{SO}_3(g) \]

The standard entropy change (\( \Delta S^\circ \)) is given by:

\[ \Delta S^\circ = \sum S^\circ_{\text{products}} - \sum S^\circ_{\text{reactants}} \]