# Misc 4 - Chapter 1 Class 12 Relation and Functions

Last updated at April 16, 2024 by Teachoo

Miscellaneous

Misc 1
Important

Misc 2

Misc 3 Important

Misc 4 Important You are here

Misc 5

Misc 6 (MCQ) Important

Misc 7 (MCQ) Important

Question 1

Question 2

Question 3 Important

Question 4

Question 5

Question 6 Important

Question 7 (i) Important

Question 7 (ii)

Question 8

Question 9 Important

Question 10 Important

Question 11

Question 12 (MCQ) Important

Chapter 1 Class 12 Relation and Functions

Serial order wise

Last updated at April 16, 2024 by Teachoo

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Misc 4 (Introduction) Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Taking set {1, 2, 3} Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of one-one function = 3 × 2 × 1 = 6 Misc 4 Find the number of all onto functions from the set {1, 2, 3, … , n} to itself. Since f is onto, all elements of {1, 2, 3} have unique pre-image. Total number of onto functions = n × n –1 × n – 2 × …. × 2 × 1 = n!