CUET · MATHS · PYQ PAPER 2025

If \(x=e^{\cos 2 t}, y=e^{\sin 2 t}\), then \(\frac{d y}{d x}\) equals to

A \(\frac{y \log _e x}{x \log _e y}\)
B \(\frac{x \log _e x}{y \log _e y}\)
C \(-\frac{y \log _e x}{x \log _e y}\)
D \(-\frac{x \log _e x}{y \log _e y}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(-\frac{y \log _e x}{x \log _e y}\)

Step-by-step Solution

Detailed explanation

\(\frac{dx}{dt} = e^{\cos 2t} \cdot (-2\sin 2t) = -2x \log y\) \(\frac{dy}{dt} = e^{\sin 2t} \cdot (2\cos 2t) = 2y \log x\) \(\frac{dy}{dx} = \frac{dy/dt}{dx/dt} = \frac{2y \log x}{-2x \log y} = -\frac{y \log x}{x \log y}\)

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-l with List-ll

List-I	List-II
(A) The measurable characteristic of a population is called	(I) sample
(B) The measurable characteristics of a sample is called	(II) Alternative hypothesis
(C) A smaller group of a population selected to represent a population is caller	(III) Parameter
(D) The assumption made opposite to the null hypothesis is called	(IV) statistic

Choose the correct answer from the options given below:

CUET 2025 Easy

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