For the relation R defined below, where R and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II | LIST-I Relation | LIST-II Properties of relation hold by R | |---|---| | A. R=\(a,b): a,b R; a^2+b^2=4\ | I. Neither reflexive, nor symmetric, nor transitive | | B. R=\(a,b): a,b R; 1+ab0\ | II. Equivalence relation | | C. R=\(a,b): a,b 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 | IV. Reflexive and symmetric, but not transitive | Choose the correct answer from the options given below:

Question

For the relation R defined below, where R and N denotes set of real numbers and set of natural numbers respectively, Match the LIST-I with LIST-II | LIST-I Relation | LIST-II Properties of relation hold by R | |---|---| | A. R=\(a,b): a,b R; a^2+b^2=4\ | I. Neither reflexive, nor symmetric, nor transitive | | B. R=\(a,b): a,b R; 1+ab>0\ | II. Equivalence relation | | C. R=\(a,b): a,b 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 | IV. Reflexive and symmetric, but not transitive | Choose the correct answer from the options given below:

Option 1: A-III, B-IV, C-I, D-II

Option 2: A-III, B-I, C-IV, D-II

Option 3: A-IV, B-III, C-I, D-II

Option 4: A-IV, B-II, C-III, D-I

AfterBoards · Accepted Answer

The answer is 'A-III, B-IV, C-I, D-II'. View full solution:

List-I	List-II
Domain and Co-domain	Kind
(A) $A = \mathbb{R}$ and $B = \mathbb{R}$	(I) $f$ is both one-one and onto
(B) $A = \mathbb{R}$ and $B = [0, \infty]$	(II) $f$ is one-one but not onto
(C) $A = B = [0, \infty]$	(III) $f$ is not one-one but onto
(D) $A = [0, \infty]$ and $B = \mathbb{R}$	(IV) $f$ is neither one-one nor onto

CUET Mathematics 2026 18th May Shift 2 PYQs

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