Class 12 arrow-diagram MCQ Questions

Question 1/5 Easy Mathematics Relations and Functions One-one function Class 12 Level 23

तीर आरेख में यदि सहप्रांत के एक ही तत्व पर दो तीर आ रहे हैं, तो फलन कैसा होगा?

In an arrow diagram, if two arrows arrive at the same element of the codomain, what type is the function?

Explanation opens after your attempt

Correct Answer

B. एकैकी नहींNot one-one

Step 1

Concept

Two arrows arriving at the same element means two different inputs have the same output.

Step 2

Why this answer is correct

This goes against the definition of one-one.

Step 3

Exam Tip

In diagram-based questions, decide quickly by checking incoming arrows at outputs. चरण 1: दो तीरों का एक ही तत्व पर आना बताता है कि दो अलग निवेशों का निर्गत समान है। चरण 2: यह एकैकीता की परिभाषा के विरुद्ध है। चरण 3: आरेख वाले प्रश्नों में निर्गत पर आने वाले तीरों को देखकर तुरंत निर्णय लें।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: One-one function
Difficulty: Easy
Level: 23

Question Hindi:
तीर आरेख में यदि सहप्रांत के एक ही तत्व पर दो तीर आ रहे हैं, तो फलन कैसा होगा?

Question English:
In an arrow diagram, if two arrows arrive at the same element of the codomain, what type is the function?

Options:
A. एकैकी / One-one
B. एकैकी नहीं / Not one-one
C. हमेशा सर्वांगी / Always onto
D. हमेशा पहचान / Always identity

Correct Answer:
B. एकैकी नहीं / Not one-one

Explanation Hindi:
चरण 1: दो तीरों का एक ही तत्व पर आना बताता है कि दो अलग निवेशों का निर्गत समान है। चरण 2: यह एकैकीता की परिभाषा के विरुद्ध है। चरण 3: आरेख वाले प्रश्नों में निर्गत पर आने वाले तीरों को देखकर तुरंत निर्णय लें।

Explanation English:
Step 1: Two arrows arriving at the same element means two different inputs have the same output. Step 2: This goes against the definition of one-one. Step 3: In diagram-based questions, decide quickly by checking incoming arrows at outputs.

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Question 2/5 Easy Mathematics Relations and Functions One-one function Class 12 Level 23

यदि \(f:A\to B\) एकैकी है, तो (B) के किसी एक तत्व पर (A) के कितने तत्व जा सकते हैं?

If \(f:A\to B\) is one-one, how many elements of (A) can map to one element of (B)?

Explanation opens after your attempt

Correct Answer

A. अधिकतम एकAt most one

Step 1

Concept

In a one-one function, two different inputs cannot map to the same output.

Step 2

Why this answer is correct

So at most one element of (A) can map to one element of (B).

Step 3

Exam Tip

In arrow diagrams, count incoming arrows at each output to test one-one. चरण 1: एकैकी फलन में एक निर्गत पर दो अलग निवेश नहीं जा सकते। चरण 2: इसलिए (B) के किसी एक तत्व पर (A) का अधिकतम एक ही तत्व जा सकता है। चरण 3: तीर आरेख में एकैकीता जाँचते समय हर निर्गत पर आने वाले तीर गिनें।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: One-one function
Difficulty: Easy
Level: 23

Question Hindi:
यदि (f:A\to B) एकैकी है, तो (B) के किसी एक तत्व पर (A) के कितने तत्व जा सकते हैं?

Question English:
If (f:A\to B) is one-one, how many elements of (A) can map to one element of (B)?

Options:
A. अधिकतम एक / At most one
B. कम-से-कम दो / At least two
C. हमेशा सभी / Always all
D. कोई सीमा नहीं / No limit

Correct Answer:
A. अधिकतम एक / At most one

Explanation Hindi:
चरण 1: एकैकी फलन में एक निर्गत पर दो अलग निवेश नहीं जा सकते। चरण 2: इसलिए (B) के किसी एक तत्व पर (A) का अधिकतम एक ही तत्व जा सकता है। चरण 3: तीर आरेख में एकैकीता जाँचते समय हर निर्गत पर आने वाले तीर गिनें।

Explanation English:
Step 1: In a one-one function, two different inputs cannot map to the same output. Step 2: So at most one element of (A) can map to one element of (B). Step 3: In arrow diagrams, count incoming arrows at each output to test one-one.

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Question 3/5 Expert Mathematics Relations and Functions Symmetric relation Class 12 Level 11

निर्देशित आरेख में सममित संबंध पहचानने का सही तरीका कौन-सा है?

What is the correct way to identify a symmetric relation in a directed graph?

Explanation opens after your attempt

Correct Answer

A. हर तीर के साथ विपरीत दिशा का तीर भी होEvery arrow has a reverse arrow

Step 1

Concept

In a directed graph, ((a,b)) is shown by an arrow from (a) to (b).

Step 2

Why this answer is correct

Symmetry requires the reverse arrow from (b) to (a).

Step 3

Exam Tip

In graph questions, carefully check every two-way pair. चरण 1: निर्देशित आरेख में ((a,b)) को (a) से (b) की ओर तीर से दिखाते हैं। चरण 2: सममितता के लिए (b) से (a) की ओर विपरीत तीर भी चाहिए। चरण 3: चित्र वाले प्रश्नों में हर दो-तरफा जोड़ी को ध्यान से जाँचें।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Symmetric relation
Difficulty: Expert
Level: 11

Question Hindi:
निर्देशित आरेख में सममित संबंध पहचानने का सही तरीका कौन-सा है?

Question English:
What is the correct way to identify a symmetric relation in a directed graph?

Options:
A. हर तीर के साथ विपरीत दिशा का तीर भी हो / Every arrow has a reverse arrow
B. हर बिंदु पर केवल स्वयं-चक्र हो / Every vertex has only a loop
C. किसी भी दो बिंदुओं के बीच तीर न हो / There is no arrow between any two vertices
D. सभी तीर केवल एक ही दिशा में हों / All arrows are in only one direction

Correct Answer:
A. हर तीर के साथ विपरीत दिशा का तीर भी हो / Every arrow has a reverse arrow

Explanation Hindi:
चरण 1: निर्देशित आरेख में ((a,b)) को (a) से (b) की ओर तीर से दिखाते हैं। चरण 2: सममितता के लिए (b) से (a) की ओर विपरीत तीर भी चाहिए। चरण 3: चित्र वाले प्रश्नों में हर दो-तरफा जोड़ी को ध्यान से जाँचें।

Explanation English:
Step 1: In a directed graph, ((a,b)) is shown by an arrow from (a) to (b). Step 2: Symmetry requires the reverse arrow from (b) to (a). Step 3: In graph questions, carefully check every two-way pair.

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Question 4/5 Medium Mathematics Relations and Functions Symmetric relation Class 12 Level 12

यदि किसी संबंध का आलेखीय चित्र हर तीर के साथ उल्टा तीर भी दिखाता है, तो वह संबंध किस गुण को दर्शाता है?

If the arrow diagram of a relation shows a reverse arrow for every arrow, which property does the relation show?

Explanation opens after your attempt

Correct Answer

A. सममितताSymmetry

Step 1

Concept

An arrow from (a) to (b) represents ((a,b)).

Step 2

Why this answer is correct

A reverse arrow for every arrow means ((b,a)) is also present, which is symmetry.

Step 3

Exam Tip

In diagram-based questions, observe arrow directions carefully. चरण 1: तीर ((a,b)) को दिखाता है। चरण 2: हर तीर के साथ उल्टा तीर होना ((b,a)) की उपस्थिति बताता है, यही सममितता है। चरण 3: आलेखीय प्रश्नों में तीरों की दिशा देखकर गुण पहचानें।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Symmetric relation
Difficulty: Medium
Level: 12

Question Hindi:
यदि किसी संबंध का आलेखीय चित्र हर तीर के साथ उल्टा तीर भी दिखाता है, तो वह संबंध किस गुण को दर्शाता है?

Question English:
If the arrow diagram of a relation shows a reverse arrow for every arrow, which property does the relation show?

Options:
A. सममितता / Symmetry
B. स्वतुल्यता / Reflexivity
C. संक्रामकता / Transitivity
D. एकैकीपन / One-one property

Correct Answer:
A. सममितता / Symmetry

Explanation Hindi:
चरण 1: तीर ((a,b)) को दिखाता है। चरण 2: हर तीर के साथ उल्टा तीर होना ((b,a)) की उपस्थिति बताता है, यही सममितता है। चरण 3: आलेखीय प्रश्नों में तीरों की दिशा देखकर गुण पहचानें।

Explanation English:
Step 1: An arrow from (a) to (b) represents ((a,b)). Step 2: A reverse arrow for every arrow means ((b,a)) is also present, which is symmetry. Step 3: In diagram-based questions, observe arrow directions carefully.

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Question 5/5 Medium Mathematics Relations and Functions Reflexive relation Class 12 Level 9

यदि किसी संबंध के तीर-चित्र में हर बिंदु पर अपने-आप की ओर तीर है, तो संबंध कैसा होगा?

If every point in the arrow diagram of a relation has an arrow to itself, what type of relation is it?

Explanation opens after your attempt

Correct Answer

A. परावर्तीReflexive

Step 1

Concept

In an arrow diagram, an arrow from a point to itself represents ((a,a)).

Step 2

Why this answer is correct

Since every point has such an arrow, every element is related to itself.

Step 3

Exam Tip

A loop at every point is the sign of reflexivity in a diagram. चरण 1: तीर-चित्र में अपने-आप की ओर तीर ((a,a)) को दिखाता है। चरण 2: हर बिंदु पर ऐसा तीर है, इसलिए हर तत्व अपने-आप से संबंधित है। चरण 3: तीर-चित्र में हर बिंदु का फंदा परावर्तिता का संकेत है।

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MCQ Data:
Class: Class 12
Subject: Mathematics
Chapter: Relations and Functions
Topic: Reflexive relation
Difficulty: Medium
Level: 9

Question Hindi:
यदि किसी संबंध के तीर-चित्र में हर बिंदु पर अपने-आप की ओर तीर है, तो संबंध कैसा होगा?

Question English:
If every point in the arrow diagram of a relation has an arrow to itself, what type of relation is it?

Options:
A. परावर्ती / Reflexive
B. केवल रिक्त / Only empty
C. परावर्ती नहीं / Not reflexive
D. केवल प्रतिलोम / Only inverse

Correct Answer:
A. परावर्ती / Reflexive

Explanation Hindi:
चरण 1: तीर-चित्र में अपने-आप की ओर तीर ((a,a)) को दिखाता है। चरण 2: हर बिंदु पर ऐसा तीर है, इसलिए हर तत्व अपने-आप से संबंधित है। चरण 3: तीर-चित्र में हर बिंदु का फंदा परावर्तिता का संकेत है।

Explanation English:
Step 1: In an arrow diagram, an arrow from a point to itself represents ((a,a)). Step 2: Since every point has such an arrow, every element is related to itself. Step 3: A loop at every point is the sign of reflexivity in a diagram.

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arrow-diagram MCQ Questions for Class 12

Practice Questions

तीर आरेख में यदि सहप्रांत के एक ही तत्व पर दो तीर आ रहे हैं, तो फलन कैसा होगा?

Concept

Why this answer is correct

Exam Tip

यदि \(f:A\to B\) एकैकी है, तो (B) के किसी एक तत्व पर (A) के कितने तत्व जा सकते हैं?

Concept

Why this answer is correct

Exam Tip

निर्देशित आरेख में सममित संबंध पहचानने का सही तरीका कौन-सा है?

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यदि किसी संबंध का आलेखीय चित्र हर तीर के साथ उल्टा तीर भी दिखाता है, तो वह संबंध किस गुण को दर्शाता है?

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यदि किसी संबंध के तीर-चित्र में हर बिंदु पर अपने-आप की ओर तीर है, तो संबंध कैसा होगा?

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तीर आरेख में यदि सहप्रांत के एक ही तत्व पर दो तीर आ रहे हैं, तो फलन कैसा होगा?

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यदि \(f:A\to B\) एकैकी है, तो (B) के किसी एक तत्व पर (A) के कितने तत्व जा सकते हैं?

Concept

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निर्देशित आरेख में सममित संबंध पहचानने का सही तरीका कौन-सा है?

Concept

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Exam Tip

यदि किसी संबंध का आलेखीय चित्र हर तीर के साथ उल्टा तीर भी दिखाता है, तो वह संबंध किस गुण को दर्शाता है?

Concept

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यदि किसी संबंध के तीर-चित्र में हर बिंदु पर अपने-आप की ओर तीर है, तो संबंध कैसा होगा?

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