CUET · CHEMISTRY · PYQ PAPER 2023

The order of a reaction where half life changes from 150 min to 75 min when the concentration of reactant is changed from 0.4 M to 1.6 M respectively is :

A \(\frac{3}{2}\)
B 3
C \(\frac{1}{2}\)
D 2

Verified Solution

Answer & Solution

Correct Answer

(A) \(\frac{3}{2}\)

Step-by-step Solution

Detailed explanation

\(t_{1/2} \propto C_0^{1-n}\) \(\frac{150}{75} = \left(\frac{0.4}{1.6}\right)^{1-n}\) \(2 = \left(\frac{1}{4}\right)^{1-n}\) \(2 = 4^{n-1}\) \(2^1 = (2^2)^{n-1}\) \(1 = 2(n-1)\) \(1 = 2n - 2\) \(3 = 2n\) \(n = \frac{3}{2}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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List-I(Name of Amino Acid)	List-II(One letter code)
(A) Phenylalanine	(I) F
(B) Tyrosine	(II) Y
(C) Asparagine	(III) N
(D) Arginine	(IV) R

List-l (Type of hybridisation)	List-II (Geometry)
(A) \(s p^3\)	(I) Trigonal bipyramidal
(B) \(d s p^2\)	(II) Octahedral
(C) \(s p^3 d\)	(III) Square planar
(D) \(s p^3 d^2\)	(IV) Tetrahedral

List - I	List - II
(A) Point of minima of \(f(x)=\|x+1\|\)	(I) 1
(B) Minimum value of \(f(x)=\|x\|\)	(II) -1
(C) Maximum value of \(f(x)=1-x^2\)	(III) 2
(D) Minimum value of \(f(x)=2+\sin ^2 x\)	(IV) 0