CUET · MATHS · PYQ PAPER 2025

The function \(f(x)=4-3 x+3 x^2-x^3\) is (Here \(R\) is the set of real numbers)

A decreasing on \(R\)
B increasing on \(R\)
C increasing on \((0, \infty)\)
D neither increasing nor decreasing on \((-\infty, 0)\)

Verified Solution

Answer & Solution

Correct Answer

(A) decreasing on \(R\)

Step-by-step Solution

Detailed explanation

\(f'(x) = -3 + 6x - 3x^2\) \(f'(x) = -3(1-x)^2\) \(f'(x) \le 0\) for all \(x \in R\). Decreasing on \(R\).

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

A machine costing Rs. \(25000\) has a useful life of \(4\) years. The estimated scrap value is Rs. \(5000\) . The annual depreciation by linear method is:

CUET 2025 Hard

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=\| x \|\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=\|x+2\|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left\|x^2-4\right\|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=\|x-2\|\)	(IV) Not differentiable at \(x=2,-2\) only

Choose the correct answer from the options given below:

CUET 2025 Easy

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