P&C Formula Capsule 10 | Counting Functions (One-One, Onto) | All Formulas | Shortnotes | JEE, NDA

Welcome to Formula Capsule No. 10! This session connects Sets with P&C. Learn how to count Total Functions, One-to-One, Onto, and Bijective mappings. This is essential for Calculus in JEE Mains, WBJEE, and NDA.

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🚀 Formula Cheat Sheet (Covered in this Video):

Variables: Domain A has m elements. Codomain B has n elements.

1. Total Number of Functions: Formula: n^m (Size of Codomain ^ Size of Domain)


2. One-to-One Functions (Injective):



3. Onto Functions (Surjective):


Sum [ (-1)^r * nCr * (n-r)^m ]

4. Bijective Functions:

Only possible if m = n.

Formula: n!








Broad Topics:
Permutations and Combinations, Combinatorics
P&C JEE Mains, Counting Principles, Selection and Arrangement.

Exam Focus: JEE Mains 2026
JEE Advanced Maths
IIT JEE Preparation
NDA Maths
MHCET
WBJEE
BITSAT
CUCET.

Content Type: Maths
Short Tricks
Formula Revision
JEE Maths PYQ
Problem Solving Techniques
One Shot Revision.

Key Concepts:
nCr and nPr
Inclusion Exclusion Principle
Division and Distribution
Geometrical Problems,
Number Theory in P&C
Beggar's Method
Derangement
Rank of Word.

Branding:
Integron Maths
Shubham Sir
Best Maths Teacher for JEE.

Target Exams:

Engineering: JEE Mains, JEE Advanced, BITSAT, WBJEE, MHCET, VITEEE.

Defense: NDA, CDS.

University: CUCET (CUET), ISI.


🔑 Tags: #functions #calculus #permutationsandcombinations #settheory #jeemains #integronmaths #mapping #InjectiveSurjective #wbjee #mhcet #ndaexam