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

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Question 281/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(12) points में से (5) points चुनकर pentagon बनाना हो और कोई (3) collinear न हों, तो formula कौन-सा है?

If a pentagon is formed by choosing (5) points from (12) points and no (3) are collinear, which formula is used?

Explanation opens after your attempt
Correct Answer

C. \(^{12}C_5\)

Explanation

Simple Explanation

Pentagon के लिए (5) points का unordered selection चाहिए। परीक्षा में shape बनाते समय points का order न गिनें। / A pentagon needs an unordered selection of (5) points. In exams do not count the order of points when forming a shape.

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Question 282/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(12) points से directed segments बनाने हों, तो formula कौन-सा होगा?

Which formula is used to form directed segments from (12) points?

Explanation opens after your attempt
Correct Answer

D. \(^{12}P_2\)

Explanation

Simple Explanation

Directed segment में start और end बदलने से object बदलता है। परीक्षा में direction हो तो permutation लगाएँ। / In a directed segment, changing start and end changes the object. In exams use permutation when direction exists.

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Question 283/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(12) points से सामान्य segments बनाने हों, तो formula कौन-सा होगा?

Which formula is used to form ordinary segments from (12) points?

Explanation opens after your attempt
Correct Answer

C. \(^{12}C_2\)

Explanation

Simple Explanation

सामान्य segment में endpoints का order नहीं बदलता। परीक्षा में unordered pair के लिए \(^{n}C_2\) लगाएँ। / In an ordinary segment, the order of endpoints does not matter. In exams use \(^{n}C_2\) for unordered pairs.

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Question 284/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (9) distinct objects को circle में arrange करना हो, तो linear arrangements से relation क्या है?

If (9) distinct objects are arranged in a circle, what is the relation with linear arrangements?

Explanation opens after your attempt
Correct Answer

A. Circular count \(=\frac{9!}{9}\)

Explanation

Simple Explanation

हर circular arrangement linear count में (9) rotations से गिनी जाती है। परीक्षा में circle में rotations को extra count मानें। / Each circular arrangement is counted (9) times in the linear count due to rotations. In exams treat rotations as extra count in a circle.

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Question 285/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(8) distinct beads की necklace में reflection same हो, तो count कौन-सा है?

What is the count for a necklace of (8) distinct beads when reflection is considered same?

Explanation opens after your attempt
Correct Answer

B. \(\frac{7!}{2}\)

Explanation

Simple Explanation

पहले rotations हटाकर (7!) मिलता है, फिर mirror images same होने से (2) से भाग देते हैं। परीक्षा में necklace में reflection जरूर जाँचें। / First removing rotations gives (7!), then mirror images being the same makes us divide by (2). In exams always check reflection in necklace problems.

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Question 286/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (10)-letter word में (A) (4) बार और (B) (2) बार है, तो arrangements का divisor क्या होगा?

If a (10)-letter word has (A) (4) times and (B) (2) times, what will be the divisor for arrangements?

Explanation opens after your attempt
Correct Answer

A. (4!2!)

Explanation

Simple Explanation

Repeated letters की अंदरूनी अदला-बदली नई arrangement नहीं बनाती। परीक्षा में हर repeated group के factorial से भाग दें। / Internal interchanges of repeated letters do not create new arrangements. In exams divide by the factorial of each repeated group.

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Question 287/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि (10) letters में (4) letters एक जैसे और (3) letters दूसरे प्रकार के एक जैसे हों, तो arrangements formula कौन-सा है?

If among (10) letters (4) letters are identical of one type and (3) letters are identical of another type, which is the arrangement formula?

Explanation opens after your attempt
Correct Answer

B. \(\frac{10!}{4!3!}\)

Explanation

Simple Explanation

दो identical groups के internal orders अलग नहीं दिखते इसलिए (4!3!) से भाग देते हैं। परीक्षा में factorial denominator को multiply करें। / Internal orders of two identical groups are not different, so divide by (4!3!). In exams multiply the factorials in the denominator.

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Question 288/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(^{n}P_r=^{n}C_r\) और (r>1) हो, तो कौन-सा निष्कर्ष सही है?

If \(^{n}P_r=^{n}C_r\) and (r>1), which conclusion is correct?

Explanation opens after your attempt
Correct Answer

B. यह असंभव है क्योंकि (r!>1)This is impossible because (r!>1)

Explanation

Simple Explanation

\(^{n}P_r=^{n}C_r r!\) और (r>1) पर (r!>1) होता है। परीक्षा में (P) और (C) की equality को factorial से जाँचें। / \(^{n}P_r=^{n}C_r r!\), and for (r>1), (r!>1). In exams verify equality of (P) and (C) using factorials.

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Question 289/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(^{n}C_r=\frac{^{n}P_r}{5040}\) हो, तो (r) का मान क्या होगा?

If \(^{n}C_r=\frac{^{n}P_r}{5040}\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

B. (7)

Explanation

Simple Explanation

\(^{n}C_r=\frac{^{n}P_r}{r!}\) और (7!=5040) है। परीक्षा में divisor को (r!) से मिलाएँ। / \(^{n}C_r=\frac{^{n}P_r}{r!}\), and (7!=5040). In exams match the divisor with (r!).

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Question 290/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

यदि \(^{n}P_r=120\times{}^{n}C_r\) हो, तो (r) का मान क्या है?

If \(^{n}P_r=120\times{}^{n}C_r\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

संबंध \(^{n}P_r=^{n}C_r r!\) है और (5!=120) है। परीक्षा में multiplier को (r!) की तरह पहचानें। / The relation is \(^{n}P_r=^{n}C_r r!\), and (5!=120). In exams identify the multiplier as (r!).

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