Mathematics · 2023
JEE Main · 1 February 2023, Shift 1 · Q61
Let R be a relation on R, given by R={(a, b): 3 a-3 b+√ 7 is an irrational number }. Then R is
Let $\displaystyle R$ be a relation on $\displaystyle \mathbb{R}$, given by $\displaystyle R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\displaystyle \}$.Then $\displaystyle R$ is
Official answer
From NTA’s final answer key for this paper.
(1)
reflexive but neither symmetric nor transitive
More from Relations and Functions
- Let for some α ∈ R, f: R → R be a function satisfying f(x+y)=f(x)+2 y^2+y+α x y for all x, y ∈ R. If f(0)=-1 and f(1)=2, then the value of…2026
- Let the sets A and B denote the domain and range respectively of the function f(x)=1/(√(x -x)), where x denotes the smallest integer greater than or…2023
- Consider two sets A={x ∈ Z:|(|x-3|-3)| ≤ 1} and B={x ∈ R-{1,2}: ((x-2)(x-4))/(x-1) log_e(|x-2|)=0}. Then the number of onto functions f: A → B is…2026
- Let f: R-{0} → R be a function such that f(x)-6 f(1/x)=35/(3 x)-5/2. If the lim_x → 0(1/(α x)+f(x))=β; α, β ∈ R, then α+2 β is equal to2025
- If the domain of the function log_5(18 x-x^2-77) is (α, β) and the domain of the function log_(x-1)((2 x^2+3 x-2)/(x^2-3 x-4)) is (γ, δ), then…2025
- Let A={1,2,3,4, …., 10} and B={0,1,2,3,4}. The number of elements in the relation R={(a, b) ∈ A × A: 2(a-b)^2+3(a-b) ∈ B} is ____2023
- The function f:(-∞, ∞) →(-∞, 1), defined by f(x)=(2^x-2^-x)/(2^x+2^-x) is:2025
- Let f: R-{2,6} → R be real valued function defined as f(x)=(x^2+2 x+1)/(x^2-8 x+12). Then range of f is2023
JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.