JAMIA 2021 — Mathematics PYQ

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Question

JAMIA 2021 — Mathematics PYQ

JAMIA | Mathematics | 2021

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is:

Choose the correct answer:

Explanation

Given Information

$n(A) = 5$
$n(B) = 6$

1. One-One (Injective) Mappings

A function $f: A \to B$ is one-one if every element in $A$ maps to a distinct element in $B$ .

\text{Condition: } n(B) \geq n(A)

\text{Number of One-One Functions} = {}^6P_5 = \frac{6!}{(6-5)!} = 720

2. Onto (Surjective) Mappings

A function $f: A \to B$ is onto if every element in $B$ has at least one pre-image in $A$ .

\text{Condition: } n(A) \geq n(B)

Since $5 < 6$ , no onto function is possible.

\text{Number of Onto Functions} = 0

3. One-One and Onto (Bijective) Mappings

A function is both one-one and onto only if:

n(A) = n(B)

Since $5 \neq 6$ :

\text{Number of One-One and Onto Mappings} = 0

Final Answer:

The number of one-one and onto mappings is 0.

Choose the correct answer:

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