Class 12 one one onto MCQ Questions

Question 1/1 Easy Mathematics Relations and Functions Functions Class 12 Level 21

यदि \(A=\{1,2,3\}\), \(B=\{a,b,c\}\), और \(f=\{(1,a),(2,b),(3,c)\}\), तो (f) कैसा है?

If \(A=\{1,2,3\}\), \(B=\{a,b,c\}\), and \(f=\{(1,a),(2,b),(3,c)\}\), what type of function is (f)?

Explanation opens after your attempt

Correct Answer

A. उभयैकBijective

Step 1

Concept

The three inputs have distinct images, so the function is one-one.

Step 2

Why this answer is correct

All elements of (B) appear as images, so it is onto.

Step 3

Exam Tip

Since it is both one-one and onto, it is bijective. चरण 1: तीनों आगतों की छवियाँ अलग-अलग हैं, इसलिए फलन एक-एकी है। चरण 2: (B) के सभी अवयव छवि के रूप में आए हैं, इसलिए आच्छादक है। चरण 3: एक-एकी और आच्छादक दोनों होने से यह उभयैक है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Functions
Difficulty: Easy
Level: 21

Question Hindi:
यदि (A={1,2,3}), (B={a,b,c}), और (f={(1,a),(2,b),(3,c)}), तो (f) कैसा है?

Question English:
If (A={1,2,3}), (B={a,b,c}), and (f={(1,a),(2,b),(3,c)}), what type of function is (f)?

Options:
A. उभयैक / Bijective
B. केवल बहु-एकी / Only many-one
C. आच्छादक नहीं / Not onto
D. फलन नहीं / Not a function

Correct Answer:
A. उभयैक / Bijective

Explanation Hindi:
चरण 1: तीनों आगतों की छवियाँ अलग-अलग हैं, इसलिए फलन एक-एकी है। चरण 2: (B) के सभी अवयव छवि के रूप में आए हैं, इसलिए आच्छादक है। चरण 3: एक-एकी और आच्छादक दोनों होने से यह उभयैक है।

Explanation English:
Step 1: The three inputs have distinct images, so the function is one-one. Step 2: All elements of (B) appear as images, so it is onto. Step 3: Since it is both one-one and onto, it is bijective.

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यदि \(A=\{1,2,3\}\), \(B=\{a,b,c\}\), और \(f=\{(1,a),(2,b),(3,c)\}\), तो (f) कैसा है?

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यदि \(A=\{1,2,3\}\), \(B=\{a,b,c\}\), और \(f=\{(1,a),(2,b),(3,c)\}\), तो (f) कैसा है?

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