Mathematics · 2021
JEE Main · 25 July 2021, Shift 1 · Q66
Let g: N → N be defined as g(3 n+1)=3 n+2, g(3 n+2)=3 n+3, g(3 n+3)=3 n+1, for all n ≥ 0. Then which of the following statements is true?
Let $\displaystyle g: \mathbf{N} \rightarrow \mathbf{N}$ be defined as
$$\begin{aligned}
& g(3 n+1)=3 n+2, \\
& g(3 n+2)=3 n+3, \\
& g(3 n+3)=3 n+1, \text { for all } n \geqslant 0 .
\end{aligned}
$$
Then which of the following statements is true ?
Official answer
(3)
There exists an onto function $\displaystyle f: \mathbf{N} \rightarrow \mathbf{N}$ such that $\displaystyle f \circ g=f$
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
- Consider functions f: A → B and g: B → C(A, B, C ⊆ R) such that (g ° f)^-1 exists, then:2021
- Let R be a relation on R, given by R={(a, b): 3 a-3 b+√7 is an irrational number }. Then R is2023
- 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
JEE Main 2021 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.