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divisor function MCQ Questions for Class 12

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2 questions tagged with divisor function.

Question 1/2 Hard Mathematics Relations and Functions Equivalence relation Class 12 Level 17

समुच्चय \(A=\{1,2,3,4,5,6,7,8,9,10\}\) पर (\tau(a)=\tau(b)) से बने संबंध में कुल कितने तुल्यता वर्ग हैं?

On \(A=\{1,2,3,4,5,6,7,8,9,10\}\), how many equivalence classes are formed by the relation (\tau(a)=\tau(b))?

Explanation opens after your attempt
Correct Answer

A. (4)

Step 1

Concept

The divisor-count values appearing are (1,2,3,4).

Step 2

Why this answer is correct

The classes are ({1}), ({2,3,5,7}), ({4,9}), and ({6,8,10}).

Step 3

Exam Tip

The number of distinct \(\tau\)-values gives the number of classes. चरण 1: भाजक-संख्या के मान (1,2,3,4) मिलते हैं। चरण 2: वर्ग ({1}), ({2,3,5,7}), ({4,9}), ({6,8,10}) बनते हैं। चरण 3: अलग-अलग \(\tau\) मानों की संख्या ही वर्गों की संख्या है।

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Question 2/2 Hard Mathematics Relations and Functions Equivalence relation Class 12 Level 17

समुच्चय \(A=\{1,2,3,4,5,6,7,8,9,10\}\) पर (aRb) तब है जब (\tau(a)=\tau(b)), जहाँ (\tau(n)) धनात्मक भाजकों की संख्या है। (6) का तुल्यता वर्ग कौन सा है?

On \(A=\{1,2,3,4,5,6,7,8,9,10\}\), (aRb) holds when (\tau(a)=\tau(b)), where (\tau(n)) is the number of positive divisors. Which is the equivalence class of (6)?

Explanation opens after your attempt
Correct Answer

A. ({6,8,10})

Step 1

Concept

The divisors of (6) are (1,2,3,6), so (\tau(6)=4).

Step 2

Why this answer is correct

(8) and (10) also have (4) positive divisors.

Step 3

Exam Tip

Elements with the same divisor count form one equivalence class. चरण 1: (6) के भाजक (1,2,3,6) हैं, इसलिए (\tau(6)=4)। चरण 2: (8) और (10) के भी (4) धनात्मक भाजक हैं। चरण 3: समान भाजक-संख्या वाले तत्व एक ही तुल्यता वर्ग में आते हैं।

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