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.
The compounds \( [\text{PtCl}_2(\text{NH}_3)_4]\text{Br}_2 \) and \( [\text{PtBr}_2(\text{NH}_3)_4]\text{Cl}_2 \) constitute a pair of:
For the reaction:
\[ 2A + B \rightarrow 2C + D \]
The following kinetic data were obtained for three different experiments performed at the same temperature:
\[ \begin{array}{|c|c|c|c|} \hline \text{Experiment} & [A]_0 \, (\text{M}) & [B]_0 \, (\text{M}) & \text{Initial rate} \, (\text{M/s}) \\ \hline I & 0.10 & 0.10 & 0.10 \\ II & 0.20 & 0.10 & 0.40 \\ III & 0.20 & 0.20 & 0.40 \\ \hline \end{array} \]
The total order and order in [B] for the reaction are respectively:
\[ f(x) = \begin{cases} x\left( \frac{\pi}{2} + x \right), & \text{if } x \geq 0 \\ x\left( \frac{\pi}{2} - x \right), & \text{if } x < 0 \end{cases} \]
Then \( f'(-4) \) is equal to:If \( f'(x) = 4x\cos^2(x) \sin\left(\frac{x}{4}\right) \), then \( \lim_{x \to 0} \frac{f(\pi + x) - f(\pi)}{x} \) is equal to:
Let \( f(x) = \frac{x^2 + 40}{7x} \), \( x \neq 0 \), \( x \in [4,5] \). The value of \( c \) in \( [4,5] \) at which \( f'(c) = -\frac{1}{7} \) is equal to: