Step 1: Understanding geometrical isomerism
Geometrical isomerism (cis-trans or E-Z isomerism) arises due to restricted rotation around a double bond. The presence of two different groups on each carbon of the double bond is required.
Step 2: Understanding optical isomerism Optical isomerism occurs when a compound has a chiral center (a carbon attached to four different groups). The presence of a chiral center leads to non-superimposable mirror images (enantiomers).
Step 3: Analyzing each option \({2-chloropent-2-ene}\): Lacks a chiral center.
\({5-chloropent-2-ene}\): No chiral center.
\({4-chloropent-2-ene}\): - Double bond at C2-C3 ensures geometrical isomerism.
- The chiral center at C4 (\(-{Cl}, -{H}, -{CH}_3, -{CH}_2CH_3\)) leads to optical isomerism.
\({3-chloropent-1-ene}\): No geometrical isomerism due to terminal double bond.
\({3-chloropent-2-ene}\): No chiral center.
Step 4: Conclusion Only \({4-chloropent-2-ene}\) satisfies both conditions. Thus, it exhibits both geometrical and optical isomerism.
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 given compound

Kepler's second law (law of areas) of planetary motion leads to law of conservation of