The relation R = \(a, b) : a ≤ b^2\ on the set of real numbers is: Option 1: Reflexive and symmetric Option 2: Neither reflexive nor symmetric Option 3: Transitive Option 4: Reflexive but not symmetric

Answer: Neither reflexive nor symmetric. Solution: Reflexive: take a = 1/2. Then a ≤ a^2 becomes 1/2 ≤ 1/4, which is false. Not reflexive. Symmetric: take a = 1, b = 2. Then 1 ≤ 4 true, but 2 ≤ 1 false. Not symmetric. Hence neither reflexive nor symmetric.

Algebra

Relations & Functions

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The relation $R = \{(a, b) : a \leq b^2\}$ on the set of real numbers is:

Reflexive and symmetric

Neither reflexive nor symmetric

Transitive

Reflexive but not symmetric

✅ Correct Option: 2

Reflexive: take $a = 1/2$ . Then $a \le a^2$ becomes $1/2 \le 1/4$ , which is false. Not reflexive. Symmetric: take $a = 1, b = 2$ . Then $1 \le 4$ true, but $2 \le 1$ false. Not symmetric. Hence neither reflexive nor symmetric.

2023: 22 May Shift 3

If $f(x) = \sqrt{x}$ , $g(x) = 2x - 3$ , then domain of $fog(x)$ is :

2026: 21 May Shift 1

If $A = R - \{2\}$ and $B = R - \{1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \frac{x-1}{x-2}$ , then $f$ is

2026: 18 May Shift 2

For the relation R defined below, where $\mathbb{R}$ 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. $R=\{(a,b): a,b\in \mathbb{R}; a^2+b^2=4\}$	I. Neither reflexive, nor symmetric, nor transitive
B. $R=\{(a,b): a,b\in \mathbb{R}; 1+ab>0\}$	II. Equivalence relation
C. $R=\{(a,b): a,b\in N; a+2b=8\}$	III. Symmetric but neither reflexive nor transitive
D. On N×N, relation R defined by $(a,b)R(c,d) \Leftrightarrow a+d=b+c$	IV. Reflexive and symmetric, but not transitive

Choose the correct answer from the options given below:

2026: 12 May Shift 2

Let $A$ be set of all real numbers and $R$ be a relation on $A$ defined by $R=\{(a,b): 1+ab>0\}$ , then relation $R$ is

2026: 25 May Shift 1

For the relations $R_1, R_2, R_3, R_4$ defined on the set $A = \{1,2,3\}$ ,

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. $R_1 = \{(1,2),(2,1),(3,3)\}$	I. Transitive only
B. $R_2 = \{(1,1),(2,2),(3,3)\}$	II. Neither reflexive nor symmetric nor transitive
C. $R_3 = \{(1,2),(2,3),(1,3)\}$	III. Symmetric but neither reflexive nor transitive
D. $R_4 = \{(3,3),(3,1),(1,2)\}$	IV. Equivalence

Choose the correct answer from the options given below:

2026: 22 May Shift 1

Let X be a non empty set and S be the collection of all subsets of X. A relation R in S is defined by $R=\{(A,B): A\subseteq B\}$ , where $X\subseteq Y$ means $X$ is proper subset of $Y$ . Then R is:

The relation R={(a,b):a≤b2}R = \{(a, b) : a \leq b^2\}R={(a,b):a≤b2} on the set of real numbers is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

The relation $R = \{(a, b) : a \leq b^2\}$ on the set of real numbers is: