CUET · MATHS · PYQ PAPER 2023

The function \(f(x) = x^2 - 2x\) has a critical point at:

A x = 0
B x = 1
C x = 2
D x = -1

Verified Solution

Answer & Solution

Correct Answer

(B) x = 1

Step-by-step Solution

Detailed explanation

\(f'(x) = 2x - 2\) \(2x - 2 = 0\) \(x = 1\)

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.

Same subject

Match List-I with List-II

List-I (Function f(x))	List-II (Interval)
(A) \(f(x)=x\|x\|\)	(I) Decreases on \((0, \infty)\)
(B) \(f(x)=x^2+2 x-5\)	(II) Increases on \((3, \infty)\)
(C) \(f(x)=x^2-6 x+9\)	(III) Decreases on \((-\infty,-1)\)
(D) \(f(x)=-x^2\)	(IV) Increases on \((-\infty, \infty)\)

Choose the correct answer from the options given below:

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List-I	List-II
(A) Amino acids linked in a specific sequence.	(I) Primary structure of proteins.
(B) Regular folding of a specific sequence of amino acids due to H-bonding.	(II) Secondary structure of proteins.
(C) Fibrous proteins.	(III) Quaternary structure of proteins.
(D) Spatial arrangement of two or more polypeptide chains.	(IV) Tertiary structure of proteins.

Choose the correct answer from the options given below :

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