Benzene reacts with propyl chloride in presence of \(AlCl_3\) to give product \(X\). Mark correct statement(s) for the given reaction. 
(a) One of the intermediate is formed due to rearrangement.
(b) Major product is n-propylbenzene.
(c) Polysubstitution of substrate is also possible.
(d) Electron releasing group decreases rate of reaction.
Concept:
This reaction is an example of Friedel–Crafts alkylation. In this reaction, an alkyl halide reacts with benzene in presence of a Lewis acid catalyst such as \(AlCl_3\) to generate a carbocation intermediate which then attacks the benzene ring. 
Step 1: Formation of carbocation intermediate. \[ CH_3CH_2CH_2Cl + AlCl_3 \rightarrow CH_3CH_2CH_2^+ + AlCl_4^- \] The primary carbocation formed is unstable and rearranges to a more stable secondary carbocation. \[ CH_3CH_2CH_2^+ \rightarrow (CH_3)_2CH^+ \] Thus, rearrangement occurs. Step 2: Electrophilic substitution on benzene. The rearranged secondary carbocation attacks benzene to form isopropylbenzene (cumene) as the major product. \[ \text{Benzene} + (CH_3)_2CH^+ \rightarrow \text{Isopropylbenzene} \] Therefore, the major product is not n-propylbenzene. Step 3: Polysubstitution possibility. The alkyl group introduced into benzene is electron-donating and activates the ring toward further substitution. Hence polysubstitution can occur. Step 4: Effect of substituents. Electron-releasing groups increase the rate of electrophilic substitution rather than decrease it. Step 5: Final evaluation of statements. (a) True — rearrangement occurs.
(b) False — major product is isopropylbenzene.
(c) True — polysubstitution is possible.
(d) False — electron releasing groups increase reaction rate. \[ \boxed{\text{Correct statements: a and c}} \]
What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)

Cobalt chloride when dissolved in water forms pink colored complex $X$ which has octahedral geometry. This solution on treating with cone $HCl$ forms deep blue complex, $\underline{Y}$ which has a $\underline{Z}$ geometry $X, Y$ and $Z$, respectively, are


What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,