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CUET Mathematics 2026 PYQs18 May Shift 2. Free, no login required.

Algebra

past year questions, CUET Mathematics 2026 18 May Shift 2

Relations & Functions

past year questions, Algebra, CUET Mathematics 2026 18 May Shift 2

Hard

core

For the relation R defined below, where R\mathbb{R} and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II

LIST-I RelationLIST-II Properties of relation hold by R
A. R={(a,b):a,b∈R;a2+b2=4}R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}I. Neither reflexive, nor symmetric, nor transitive
B. R={(a,b):a,b∈R;1+ab>0}R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}II. Equivalence relation
C. R={(a,b):a,b∈N;a+2b=8}R=\{(a,b): a,b\in N; a+2b=8\}III. Symmetric but neither reflexive nor transitive
D. On N×N, relation R defined by (a,b)R(c,d)⇔a+d=b+c(a,b)R(c,d) \Leftrightarrow a+d=b+cIV. Reflexive and symmetric, but not transitive

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 1

A: a2+b2=4a^2+b^2=4 is symmetric but (1,1)(1,1) fails reflexivity and (0,2),(2,0)(0,2),(2,0) break transitivity, so III.

B: 1+a2>01+a^2>0 always, and the condition is symmetric, but a=1,b=0,c=−1a=1,b=0,c=-1 breaks transitivity, so IV.

C: pairs are (6,1),(4,2),(2,3)(6,1),(4,2),(2,3); none of the three properties holds, so I.

D: a+d=b+ca+d=b+c is an equivalence relation, so II.

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