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unlabelled_groups MCQ Questions for Class 11

unlabelled_groups se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.

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8 questions tagged with unlabelled_groups.

Question 1/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(14) distinct objects को (3,3,4,4) के unlabelled groups में बांटने का denominator कौन-सा होगा?

What is the denominator for dividing (14) distinct objects into unlabelled groups of sizes (3,3,4,4)?

Explanation opens after your attempt
Correct Answer

A. (3!3!4!4!2!2!)

Explanation

Simple Explanation

Internal orders और equal-size group swaps दोनों हटते हैं। परीक्षा में denominator में group sizes और equal-group factorials दोनों लिखें। / Both internal orders and equal-size group swaps are removed. In exams write both group sizes and equal-group factorials in the denominator.

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Question 2/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (n) distinct objects को (a,a,b) आकार के unlabelled groups में बांटा जाए और (2a+b=n), तो extra division किससे होगा?

If (n) distinct objects are divided into unlabelled groups of sizes (a,a,b) and (2a+b=n), what is the extra division?

Explanation opens after your attempt
Correct Answer

C. (2!)

Explanation

Simple Explanation

दो groups का size (a) समान है इसलिए उनकी अदला-बदली duplicate देती है। परीक्षा में equal-size unlabelled groups पर extra factorial divide करें। / Two groups have the same size (a), so interchanging them gives duplicates. In exams divide extra by factorial for equal-size unlabelled groups.

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Question 3/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(n) distinct objects को (3) non-empty unlabelled groups में बांटने की संख्या किससे जुड़ती है?

The number of ways to divide (n) distinct objects into (3) non-empty unlabelled groups is connected with which form?

Explanation opens after your attempt
Correct Answer

A. (\frac{1}{3!}\left\(3^n-3\cdot2^n+3\right\))

Explanation

Simple Explanation

पहले (3) labelled non-empty groups गिनते हैं, फिर labels की (3!) अदला-बदली हटाते हैं। परीक्षा में unlabelled groups के लिए labelled count divide करें। / First count (3) labelled non-empty groups, then remove the (3!) label permutations. In exams divide the labelled count for unlabelled groups.

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Question 4/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(15) distinct objects को (5,5,5) के unlabelled groups में बांटने का formula कौन-सा है?

What is the formula for dividing (15) distinct objects into unlabelled groups of (5,5,5)?

Explanation opens after your attempt
Correct Answer

B. (\frac{15!}{(5!)3 3!})

Explanation

Simple Explanation

तीनों groups same size और unlabelled हैं इसलिए group order (3!) भी हटता है। परीक्षा में equal unlabelled groups में extra (3!) याद रखें। / All three groups have the same size and are unlabelled, so group order (3!) is also removed. In exams remember the extra (3!) for equal unlabelled groups.

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Question 5/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (12) distinct objects को (2,2,4,4) आकार के unlabelled groups में बांटना हो, तो extra division कौन-सी होगी?

If (12) distinct objects are divided into unlabelled groups of sizes (2,2,4,4), what is the extra division?

Explanation opens after your attempt
Correct Answer

A. \(2!\cdot2!\)

Explanation

Simple Explanation

दो size (2) groups और दो size (4) groups की अदला-बदली duplicate देती है। परीक्षा में equal-size unlabelled groups के factorials से extra divide करें। / Interchanging the two size (2) groups and the two size (4) groups gives duplicates. In exams divide extra by factorials of equal-size unlabelled groups.

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Question 6/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(n) distinct objects को (2) non-empty unlabelled groups में बांटने की संख्या कौन-सी है?

What is the number of ways to divide (n) distinct objects into (2) non-empty unlabelled groups?

Explanation opens after your attempt
Correct Answer

A. \(\frac{2^n-2}{2}\)

Explanation

Simple Explanation

Labelled count में दोनों groups की अदला-बदली दो बार गिनती है। परीक्षा में unlabelled दो groups के लिए (2) से divide करें। / In the labelled count, interchanging the two groups counts each division twice. In exams divide by (2) for two unlabelled groups.

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Question 7/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(12) अलग वस्तुओं को (4,4,4) के unlabelled समूहों में बांटने का formula क्या होगा?

What is the formula for dividing (12) distinct objects into unlabelled groups of (4,4,4)?

Explanation opens after your attempt
Correct Answer

B. \(\frac{12!}{4!4!4!3!}\)

Explanation

Simple Explanation

तीनों groups equal size और unlabelled हैं, इसलिए groups की (3!) अदला-बदली भी हटती है। परीक्षा में समान unlabelled groups पर extra factorial divide करें। / All three groups have equal size and are unlabelled, so the (3!) interchange of groups is also removed. In exams divide extra by factorial for equal unlabelled groups.

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Question 8/8 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (n) objects को (2) equal unlabelled groups में बाँटना हो तो \(^{n}C_{n/2}\) के बाद किससे भाग देना होगा?

If (n) objects are divided into (2) equal unlabelled groups, by what should \(^{n}C_{n/2}\) be divided?

Explanation opens after your attempt
Correct Answer

A. (2!)

Explanation

Simple Explanation

दो equal groups unlabelled हैं इसलिए group interchange दो बार गिनता है। परीक्षा में equal unlabelled groups पर extra (2!) correction लगाएँ। / The two equal groups are unlabelled, so interchanging the groups counts twice. In exams apply the extra (2!) correction for equal unlabelled groups.

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