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 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: