CUET · MATHS · PYQ PAPER 2023

Match List I with List II
LIST-I LIST-II
A. (AB)' I. \(B^{-1} A^{-1}\)
B. \((A B)^{-1}\) II. \(A ^{\prime}+ B ^{\prime}\)
C. \((A+B)^{\prime}\) III. B'A'
D. (A-B)' IV. A'-B'
Choose the correct answer from the options given below:

A A-III, B-I, C-II, D-IV
B A-II, B-III, C-IV, D-I
C A-I, B-II, C-III, D-IV
D A-IV, B-I, C-II, D-III

Verified Solution

Answer & Solution

Correct Answer

(A) A-III, B-I, C-II, D-IV

Step-by-step Solution

Detailed explanation

A. \((AB)'\) = III. \(B'A'\) B. \((AB)^{-1}\) = I. \(B^{-1} A^{-1}\) C. \((A+B)'\) = II. \(A' + B'\) D. \((A-B)'\) = IV. \(A' - B'\)

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-l (Mathematical Statement)	List-ll (Value)
(A) \(\hat{i} \cdot(\hat{j} \times \hat{k})\)	(I) \(-\hat{k}\)
(B) \(\hat{j} \cdot(\hat{i} \times \hat{k})\)	(II) 1
(C) \(\hat{i} \times(\hat{j} \times \hat{k})\)	(III) \(-1\)
(D) \(\hat{j} \times \hat{i}\)	(IV) \(\overrightarrow{0}\)

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List-I	List-II
(A) Williamson's synthesis.	\((I)\) \(C _6 H _5 Cl + NaOH \xrightarrow[\text { High pressure }]{350^{\circ} C }\)
(B) Reimer Tiemann reaction.	\((II)\) \(C _6 H _5 OH + C _6 H _5 COCl \xrightarrow{\text { aq. } NaOH }\)
(C) Dow's process	\((II)I\) \(CH_3 CH_2 ONa+CH_3 Cl \xrightarrow{\text { heat }}\)
(D) Schotten Baumann reaction	\((IV)\) \(C _6 H _5 OH + CHCl _3+ NaOH \xrightarrow{\text { heat }}\)

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LIST-I	LIST-II
A. (AB)'	I. \(B^{-1} A^{-1}\)
B. \((A B)^{-1}\)	II. \(A ^{\prime}+ B ^{\prime}\)
C. \((A+B)^{\prime}\)	III. B'A'
D. (A-B)'	IV. A'-B'

Match List I with List IILIST-ILIST-IIA. (AB)'I. \(B^{-1} A^{-1}\)B. \((A B)^{-1}\)II. \(A ^{\prime}+ B ^{\prime}\)C. \((A+B)^{\prime}\)III. B'A'D. (A-B)'IV. A'-B'Choose the correct answer from the options given below:

Step-by-step Solution

Match List I with List II
LIST-I LIST-II
A. (AB)' I. \(B^{-1} A^{-1}\)
B. \((A B)^{-1}\) II. \(A ^{\prime}+ B ^{\prime}\)
C. \((A+B)^{\prime}\) III. B'A'
D. (A-B)' IV. A'-B'
Choose the correct answer from the options given below: