CUET · MATHS · PYQ PAPER 2025

The area of the region bounded by the line \(y = 2 x\) and the \(x\)-axis between \(x = - 2\) and \(x = 2\) is

A 8 sq.units
B 4 sq.units
C 16 sq.units
D 0 sq.units

Verified Solution

Answer & Solution

Correct Answer

(A) 8 sq.units

Step-by-step Solution

Detailed explanation

Area \( = \int_{-2}^{0} |-2x| \, dx + \int_{0}^{2} |2x| \, dx \) \( = \int_{-2}^{0} (-2x) \, dx + \int_{0}^{2} (2x) \, dx \) \( = 4 + 4 \) \( = 8 \) sq.units

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

Which of the following is the range of the principal value of \(\sec ^{-1} x\) ?

CUET 2023 Easy

Match List I with List II and choose the correct answer from the options given below:

List - I	List - II
(A) \(\int \frac{\sin x}{1+\cos x} d x\)	(I) \(e^{\tan ^{-1} z}+C\)
(B) \(\int \frac{1}{1-\tan x} d x\)	(II) \(\log (\log x+1)+C\)
(C) \(\int \frac{e^{\tan ^{-1} x}}{1+x^2} d x\)	(III) \(-\log \|1+\cos x\|+C\)
(D) \(\int \frac{1}{x+x \log x} d x\)	(IV) \(\frac{x}{2}-\frac{1}{2} \log \|\cos x-\sin x\|+C\)

CUET 2023 Medium

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