CUET · MATHS · PYQ PAPER 2023

Given relation \(R =\{(x, y): y=x+5, x<4, x, y \in N\}\). Where N is a set of natural numbers then :

A \(R\) is an equivalence relation.
B \(R\) is transitive but neither reflexive nor symmetric.
C \(R\) is reflexive but neither symmetric nor transitive.
D \(R\) is symmetric \(\backslash \&\) transitive but not reflexive.

Verified Solution

Answer & Solution

Correct Answer

(B) \(R\) is transitive but neither reflexive nor symmetric.

Step-by-step Solution

Detailed explanation

\(x \in N, x \(R = \{(1, 6), (2, 7), (3, 8)\}\) Reflexivity: \((1, 1) \notin R\) (as \(1 \ne 1+5\)). Not reflexive. Symmetry: \((1, 6) \in R\) but \((6, 1) \notin R\) (as \(1 \ne 6+5\)). Not symmetric. Transitivity: No \((x, y) \in R\) and…

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 - I with List - II. Evaluate the integrals.

\(List - I\)	\(List - II\)
(A) \(\int_0^{\pi / 2} \frac{\sin x-\cos x}{1+\sin x \cos x} d x\)	\((I)\) \(2 \pi\)
(B) \(\int_0^{1 / 2} \frac{d x}{\sqrt{x-x^2}}\)	\((II)\) \(\frac{\pi}{4}\)
(C) \(\int_{-\pi}^\pi x \sin x d x\)	\((III)\) \(0\)
(D) \(\int_0^1 \frac{1}{1+x^2} d x\)	\((IV)\) \(\frac{\pi}{2}\)

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