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group_division MCQ Questions for Class 11

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

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11 questions tagged with group_division.

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

यदि (10) objects को (5) और (5) के दो unlabelled groups में बाँटना हो, तो expression क्या होगा?

If (10) objects are divided into two unlabelled groups of (5) and (5), what is the expression?

Explanation opens after your attempt
Correct Answer

A. \(\frac{^{10}C_5}{2!}\)

Explanation

Simple Explanation

पहला (5)-group चुनने पर दूसरा तय है और दोनों groups interchange होने से duplicate count आता है। परीक्षा में equal groups हों तो (2!) से भाग दें। / After choosing the first (5)-group the second is fixed, and interchanging the two groups creates duplicate count. In exams divide by (2!) for equal groups.

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

यदि (n) objects को (3) labelled groups में sizes (a), (b), (c) में बाँटना हो, तो formula कौन-सा है?

If (n) objects are divided into (3) labelled groups of sizes (a), (b), (c), which formula is correct?

Explanation opens after your attempt
Correct Answer

A. \(\frac{n!}{a!b!c!}\)

Explanation

Simple Explanation

हर labelled group के अंदर order महत्वहीन है इसलिए (a!b!c!) से भाग दिया जाता है। परीक्षा में labelled groups को आपस में extra divide न करें। / Order inside each labelled group is irrelevant, so divide by (a!b!c!). In exams do not divide extra among labelled groups themselves.

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

यदि (8) objects को (4) और (4) के दो unlabelled groups में बाँटना हो तो expression क्या होगा?

If (8) objects are divided into two unlabelled groups of (4) and (4), what is the expression?

Explanation opens after your attempt
Correct Answer

A. \(\frac{^{8}C_4}{2!}\)

Explanation

Simple Explanation

पहला (4)-group चुनने पर दूसरा तय है और दोनों groups interchange होने से duplicate count आता है। परीक्षा में equal groups हों तो (2!) से भाग दें। / After choosing the first (4)-group the second is fixed, and interchanging the two groups creates duplicate count. In exams divide by (2!) for equal groups.

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Question 4/11 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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Question 5/11 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (n) objects को (3) labelled groups में sizes (a), (b), (c) में बाँटना हो तो denominator का रूप क्या होगा?

If (n) objects are divided into (3) labelled groups of sizes (a), (b), (c), what is the form of the denominator?

Explanation opens after your attempt
Correct Answer

A. (a!b!c!)

Explanation

Simple Explanation

हर group के अंदर order महत्वहीन है इसलिए (a!b!c!) से भाग दिया जाता है। परीक्षा में labelled groups में groups को आपस में divide न करें। / Order inside each group is irrelevant, so divide by (a!b!c!). In exams do not divide among labelled groups themselves.

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

यदि (11) objects को (4) selected और (7) rejected में बाँटा जाए तो selected group count कौन-सा है?

If (11) objects are divided into (4) selected and (7) rejected objects, what is the selected group count?

Explanation opens after your attempt
Correct Answer

A. \(^{11}C_4\)

Explanation

Simple Explanation

(4) selected चुनते ही (7) rejected तय हो जाते हैं। परीक्षा में selected-rejected split को combination से जोड़ें। / Once (4) selected objects are chosen, the (7) rejected objects are fixed. In exams connect selected-rejected split with combination.

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

यदि (n) अलग वस्तुओं को (r) और (n-r) के दो unlabelled groups में बाँटना हो तो formula कौन-सा है?

If (n) distinct objects are divided into two unlabelled groups of sizes (r) and (n-r), what is the formula?

Explanation opens after your attempt
Correct Answer

B. \(^{n}C_r\)

Explanation

Simple Explanation

एक group चुनते ही दूसरा group तय हो जाता है इसलिए \(^{n}C_r\) पर्याप्त है। परीक्षा में complement fixed हो तो एक ही selection गिनें। / Once one group is chosen, the other group is fixed, so \(^{n}C_r\) is enough. In exams count only one selection when the complement is fixed.

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

\(^{n}C_r\) की व्युत्पत्ति में (r!(n-r)!) से भाग देने का grouped meaning क्या है?

What is the grouped meaning of dividing by (r!(n-r)!) in the derivation of \(^{n}C_r\)?

Explanation opens after your attempt
Correct Answer

A. दो groups के अंदर के क्रम हटानाRemoving orders inside two groups

Explanation

Simple Explanation

(n!) में चुने और न चुने groups के internal orders अलग गिने जाते हैं। परीक्षा में group division में internal order हटाएँ। / In (n!), internal orders of chosen and unchosen groups are counted separately. In exams remove internal order in group division.

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Question 9/11 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(12) विद्यार्थियों में से (5) की समिति और (7) का बाकी समूह बनाने की संख्या कौन-सी है?

What is the number of ways to make a committee of (5) and a remaining group of (7) from (12) students?

Explanation opens after your attempt
Correct Answer

A. \(^{12}C_5\)

Explanation

Simple Explanation

(5) की समिति चुनते ही बाकी (7) विद्यार्थी तय हो जाते हैं। परीक्षा में complement group खुद तय हो तो केवल एक combination लगाएँ। / Once the committee of (5) is chosen the remaining (7) students are fixed. In exams use only one combination when the complement group is fixed automatically.

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Question 10/11 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(^{n}C_r\) को group division से समझाने पर (n) वस्तुएँ किन दो sizes में बँटती हैं?

When \(^{n}C_r\) is explained by group division into what two sizes are (n) objects divided?

Explanation opens after your attempt
Correct Answer

C. (r) और (n-r)

Explanation

Simple Explanation

एक समूह में (r) चुनी वस्तुएँ और दूसरे में (n-r) बाकी वस्तुएँ होती हैं। परीक्षा में group sizes का योग (n) जाँचें। / One group has (r) chosen objects and the other has (n-r) remaining objects. In exams check that group sizes add to (n).

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

कौन-सा विचार \(^{n}C_r\) को (n) वस्तुओं को दो समूहों (r) और (n-r) में बाँटने से जोड़ता है?

Which idea connects \(^{n}C_r\) with dividing (n) objects into two groups (r) and (n-r)?

Explanation opens after your attempt
Correct Answer

A. पहले (r) का समूह चुनते ही दूसरा समूह अपने आप तय हो जाता हैOnce the group of (r) is chosen the other group is automatically fixed

Explanation

Simple Explanation

(r) वस्तुओं का चयन बाकी (n-r) वस्तुओं को तय कर देता है। परीक्षा में group division को combination से जोड़ें। / Choosing (r) objects fixes the remaining (n-r) objects. In exams connect group division with combination.

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