CUET · MATHS · PYQ PAPER 2025

If the function \(f(x)=2 x^2-k x+7\) is increasing on \([1,2]\), then \(k\) lies in the interval

A \((-\infty, 8)\)
B \((-\infty, 4)\)
C \((4, \infty)\)
D \((8, \infty)\)

Verified Solution

Answer & Solution

Correct Answer

(B) \((-\infty, 4)\)

Step-by-step Solution

Detailed explanation

\(f'(x) = 4x - k\) For \(f(x)\) to be increasing on \([1,2]\), \(f'(x) \ge 0\) for all \(x \in [1,2]\). \(4x - k \ge 0\) \(k \le 4x\) This must hold for all \(x \in [1,2]\). The minimum value of \(4x\) on \([1,2]\) is \(4(1)=4\). \(k \le 4\) The interval for \(k\) is…

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

In the context of differential equation
Match List I with List II

LIST I	LIST II
A. \(\frac{d y}{d x}=\frac{1+y^2}{1+x^2}\)	I. Not a differential equation
B. \(x^2 \frac{d y}{d x}=x^2-2 y^2+x y\)	II. Linear first order
C. \(\sin x+y=\cos (x+y)\)	III. Variable separable
D. \((x+y) \frac{d y}{d x}=1\)	IV. Homogenous

Choose the correct answer from the options given below:

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Match List-I with List-II

Differential equation	Degree
(A) \(\frac{d^2 y}{d x^2}+\sqrt{\frac{d y}{d x}}-y=0\)	(I) 6
(B) \(\sqrt{\frac{d^3 y}{d x^3}}-\sqrt[12]{\frac{d^2 y}{d x^2}}=0\)	(II) not defined
(C) \(\left(\frac{d^2 y}{d x^2}\right)^2+\frac{d y}{d x}+e^{\frac{d y}{d x}}=x^2\)	(III) 3
(D) \(\sqrt[3]{\frac{d y}{d x}}-\frac{d^2 y}{d x^2}=e^x\)	(IV) 2

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CUET 2025 Hard

The total cost \(C(x)\) in Rupees associated with the production of \(x\) units of an item is given by
\(C(x)=0.007 x^3+26 x^2+15 x+400\)
The marginal cost when 10 items are produced is:

CUET 2025 Hard

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From CUET

Match List-l with List-ll

List-l (Term)	List-II (Explanation)
(A) Natality	(I) Number of the same species individuals that have come into the habitat
(B) Immigration	(II) Number of deaths during a given time in a population
(C) Mortality	(III) Number of the same species individuals that have left the habitat
(D) Emigration	(IV) Number of births during a given time in a population

Choose the correct answer from the options given below:

CUET 2025 Easy

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