Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2024
Exam
NDA
Year
2024
Subject
Mathematics
Chapter
Functions

NDA 2024 · Mathematics · Functions

Let A=\ 1,2,3,4,5\ and B=\ 6,7\ . What is the number of onto...

Let A={1,2,3,4,5}\mathrm{A}=\{1,2,3,4,5\} and B={6,7}\mathrm{B}=\{6,7\}. What is the number of onto functions from A to B ?

Options

  1. A10
  2. B20
  3. C30
  4. D32

Correct answer

C. 30

Step-by-step solution

n(A)=5n(\mathrm{ A})=5 and n(B)=2 Number of onto functions =25−2C1(2−1)5=32−2=30.n(\mathrm{ B})=2\begin{gathered}\text{ Number of onto functions }=2^5-{ }^2 \mathrm{C}_1(2-1)^5 \\ =32-2=30.\end{gathered}
Practice Functions on Quantrex Academy →

More from Functions

Consider the following statements in respect of the function f(x)=x in the interval… NDA 2026Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of… NDA 2026If 2f(x)+f(1-x)=x , then what is f(x) equal to ? NDA 2026For the following two (02) items: Consider the function f(x) = 1 - [3] (x-1)^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let the function y = (1 - x)^… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let the curve f(x) = |x - 3| .… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: The function f(x) satisfies… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025For the following two (02) items: Consider the function f(x) = (x)/(1 - x) (x > 0 , x ≠ 1… NDA 2025For the following two (02) items: Consider the function f(x) = 10^x - 10^ -x 10^x + 10^… NDA 2025Consider the following for the two (02) items that follow: Let f = \ (1,1), (2,4), (3,7)… NDA 2025Consider the following for the two (02) items that follow: A function f is such that… NDA 2025 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs