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Mathematics Derivations of formulas and their connections MCQ Questions for Class 11 General

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Derivations of formulas and their connections Practice Questions

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Question 131/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

एक जैसे (3) लाल और अलग (4) नीले balls की line arrangements में कौन-सा divisor आएगा?

What divisor appears in line arrangements of identical (3) red balls and distinct (4) blue balls?

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Correct Answer

A. (3!)

Explanation

Simple Explanation

तीन लाल balls समान हैं इसलिए उनके (3!) अंदरूनी क्रम अलग नहीं हैं। परीक्षा में केवल repeated group के factorial से भाग दें। / The three red balls are identical so their (3!) internal orders are not different. In exams divide by the factorial of the repeated group only.

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Question 132/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि कुल (8) अक्षरों में (A) (2) बार और (B) (3) बार समान हों तो arrangements का formula क्या होगा?

If among (8) letters (A) is identical (2) times and (B) is identical (3) times what is the formula for arrangements?

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Correct Answer

B. \(\frac{8!}{2!3!}\)

Explanation

Simple Explanation

दो repeated groups के internal orders हटाने के लिए (2!3!) से भाग देते हैं। परीक्षा में हर repeated letter का factorial denominator में रखें। / To remove internal orders of two repeated groups divide by (2!3!). In exams put the factorial of each repeated letter in the denominator.

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Question 133/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

गोल मेज पर (6) अलग लोगों को बैठाने में ((6-1)!) क्यों आता है?

Why does ((6-1)!) appear in seating (6) distinct people around a round table?

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Correct Answer

A. क्योंकि एक व्यक्ति को fixed मानकर rotations हटाते हैंBecause one person is fixed to remove rotations

Explanation

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वृत्त में केवल घूमना नई seating नहीं बनाता। परीक्षा में circular arrangement में one fixed method लगाएँ। / A mere rotation in a circle does not make a new seating. In exams use the one fixed method in circular arrangement.

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Question 134/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि clockwise और anticlockwise arrangements को same माना जाए तो (n) अलग beads की necklace count किस रूप से जुड़ती है?

If clockwise and anticlockwise arrangements are considered same the necklace count of (n) distinct beads is connected with which form?

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Correct Answer

C. (\frac{(n-1)!}{2})

Explanation

Simple Explanation

पहले rotations हटाकर ((n-1)!) मिलता है फिर reflection same होने से (2) से भाग देते हैं। परीक्षा में necklace में rotation और reflection दोनों देखें। / First removing rotations gives ((n-1)!) and then same reflection makes us divide by (2). In exams check both rotation and reflection in necklaces.

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Question 135/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(^{n}P_r\) और \(^{n}C_r\) कब बराबर होते हैं?

When are \(^{n}P_r\) and \(^{n}C_r\) equal?

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Correct Answer

A. जब (r=0) या (r=1) होWhen (r=0) or (r=1)

Explanation

Simple Explanation

क्योंकि (r!) केवल (r=0) और (r=1) पर (1) होता है। परीक्षा में equality के लिए relation \(^{n}P_r=^{n}C_r r!\) देखें। / Because (r!) is (1) only for (r=0) and (r=1). In exams check \(^{n}P_r=^{n}C_r r!\) for equality.

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Question 136/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(^{n}P_r\) से \(^{n}C_r\) छोटा क्यों होता है जब (r>1)?

Why is \(^{n}C_r\) smaller than \(^{n}P_r\) when (r>1)?

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Correct Answer

A. क्योंकि combination में (r!) orders को एक ही selection माना जाता हैBecause in combination (r!) orders are treated as one selection

Explanation

Simple Explanation

Permutation एक ही group के कई orders गिनता है। परीक्षा में (r>1) पर (P) और (C) का अंतर साफ रखें। / Permutation counts many orders of the same group. In exams keep the difference between (P) and (C) clear when (r>1).

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Question 137/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(^{n}C_r\) की derivation में division principle कब उपयोग होता है?

When is the division principle used in the derivation of \(^{n}C_r\)?

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Correct Answer

A. जब extra repeated orders हटाने होंWhen extra repeated orders must be removed

Explanation

Simple Explanation

Permutation से combination बनाते समय एक ही selection (r!) बार गिना जाता है। परीक्षा में overcounting दिखे तो division principle लगाएँ। / When making combination from permutation the same selection is counted (r!) times. In exams use division principle when overcounting appears.

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Question 138/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (3) shirts और (4) pants में से outfit बनाना हो तो कौन-सा सिद्धांत formula connection दिखाता है?

If an outfit is made from (3) shirts and (4) pants which principle shows the formula connection?

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Correct Answer

B. गुणन सिद्धांतMultiplication principle

Explanation

Simple Explanation

हर shirt के साथ (4) pants जुड़ सकते हैं इसलिए \(3\times4\) choices हैं। परीक्षा में independent choices साथ चाहिए तो multiply करें। / Each shirt can pair with (4) pants so there are \(3\times4\) choices. In exams multiply when independent choices are needed together.

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Question 139/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (5) red pens या (6) blue pens में से एक pen चुनना हो तो कौन-सा सिद्धांत लगेगा?

If one pen is to be chosen from (5) red pens or (6) blue pens which principle is used?

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Correct Answer

B. जोड़ सिद्धांतAddition principle

Explanation

Simple Explanation

यह या वाली स्थिति है इसलिए (5+6) choices मिलते हैं। परीक्षा में or शब्द पर addition principle देखें। / This is an or situation so there are (5+6) choices. In exams look for the addition principle when the word or appears.

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Question 140/600 Easy Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

\(^{n}C_r\) को unordered selection मानने का सबसे अच्छा संकेत कौन-सा शब्द है?

Which word is the best signal to treat \(^{n}C_r\) as unordered selection?

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Correct Answer

C. समितिCommittee

Explanation

Simple Explanation

समिति में सदस्यों का क्रम नहीं बदलता। परीक्षा में committee या group पर combination लगाएँ। / In a committee the order of members does not change the committee. In exams use combination for committee or group.

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