CUET · MATHS · PYQ PAPER 2025

The area (in sq. units) of the region enclosed by the curve \(9 x^2+4 y^2=36\) is

A \(10 \pi\)
B \(8 \pi\)
C \(6 \pi\)
D \(4 \pi\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(6 \pi\)

Step-by-step Solution

Detailed explanation

\(\frac{9 x^2}{36} + \frac{4 y^2}{36} = 1 \implies \frac{x^2}{4} + \frac{y^2}{9} = 1\) \(a^2=4, b^2=9 \implies a=2, b=3\) \(Area = \pi ab = \pi (2)(3) = 6\pi\)

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 a 200 m race, Rohan completes the race in 8 seconds and Vivan completes the race in 10 seconds. By how much distance Rohan beats Vivan?

CUET 2025 Medium

Match List - I with List - II

List - I	List - II
(A) Line: x = 2y + 1 = z - 1	(I) Crosses xz-plane at (1,0,1)
(B) Line: x + 1 = 2y + 1 = z	(II) Crosses xz-plane at (0,0,1)
(C) Line: x - 1 = 2y = z + 1	(III) Crosses xz-plane at (1,0,-1)
(D) Line: x - 1 = 2y = z - 1	(IV) Crosses xz-plane at (1,0,2)

Choose the correct answer from the options given below:

CUET 2025 Hard

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Year	2016	2017	2018	2019	2020	2021
Production (thousand tonnes)	200	220	231	254	202	243