CUET · MATHS · PYQ PAPER 2025

Let \(f(x)=x^2+\frac{250}{x}\) be any function defined on \(R -\{0\}\), where \(R\) is the set of real numbers. Then which of the following are FALSE?

A \(f^{\prime}(x)=2 x-\frac{250}{x^2}\)
B \(x=5\) is the only critical point of \(f(x)\)
C Minimum value of \(f(x)\) is 75
D Maximum value of \(f(x)\) is 50

Verified Solution

Answer & Solution

Correct Answer

(D) Maximum value of \(f(x)\) is 50

Step-by-step Solution

Detailed explanation

A) First Derivative \((f(x))\) :To find the derivative, we apply the power rule: \(f^{\prime}(x)=\frac{d}{d x}\left(x^2\right)+\frac{d}{d x}\left(250 x^{-1}\right)=2 x-\frac{250}{x^2}\) Statement A is TRUE. B) Critical Points:Set \(f^{\prime}(x)=0\) to find critical points:…

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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