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

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Question 231/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(10) points से directed line segment बनाने हों तो formula कौन-सा होगा?

Which formula is used to form directed line segments from (10) points?

Explanation opens after your attempt
Correct Answer

B. \(^{10}P_2\)

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 232/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(10) points से सामान्य line segments बनाने हों तो formula कौन-सा होगा?

Which formula is used to form ordinary line segments from (10) points?

Explanation opens after your attempt
Correct Answer

C. \(^{10}C_2\)

Explanation

Simple Explanation

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

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Question 233/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (8) distinct objects को circle में arrange करना हो तो linear arrangements से relation क्या है?

If (8) distinct objects are arranged in a circle, what is the relation with linear arrangements?

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Correct Answer

A. Circular count \(=\frac{8!}{8}\)

Explanation

Simple Explanation

हर circular arrangement linear count में (8) rotations से गिनी जाती है। परीक्षा में circle में rotations को extra count मानें। / Each circular arrangement is counted (8) times in the linear count due to rotations. In exams treat rotations as extra count in a circle.

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Question 234/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

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

What is the count for a necklace of (7) distinct beads when reflection is considered same?

Explanation opens after your attempt
Correct Answer

B. \(\frac{6!}{2}\)

Explanation

Simple Explanation

पहले rotation हटाकर (6!) मिलता है और फिर mirror images same होने से (2) से भाग देते हैं। परीक्षा में necklace में reflection जरूर जाँचें। / First removing rotations gives (6!), then mirror images being the same makes us divide by (2). In exams always check reflection in necklace problems.

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Question 235/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (8) letters वाले word में (A) (3) बार और (B) (2) बार है तो arrangements का divisor क्या होगा?

If an (8)-letter word has (A) (3) times and (B) (2) times, what will be the divisor for arrangements?

Explanation opens after your attempt
Correct Answer

A. (3!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 236/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि (9) letters में (3) letters एक जैसे और (2) letters दूसरे प्रकार के एक जैसे हों तो arrangements formula कौन-सा है?

If among (9) letters (3) letters are identical of one type and (2) letters are identical of another type, which is the arrangement formula?

Explanation opens after your attempt
Correct Answer

A. \(\frac{9!}{3!2!}\)

Explanation

Simple Explanation

दो identical groups के internal orders अलग नहीं दिखते इसलिए (3!2!) से भाग देते हैं। परीक्षा में factorial denominator को multiply करें। / Internal orders of two identical groups are not different, so divide by (3!2!). In exams multiply the factorials in the denominator.

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Question 237/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{n}P_r=^{n}C_r\) और (n>1) हो तो (r) के कौन-से मान संभव हैं?

If \(^{n}P_r=^{n}C_r\) and (n>1), which values of (r) are possible?

Explanation opens after your attempt
Correct Answer

A. (0) या (1)(0) or (1)

Explanation

Simple Explanation

क्योंकि \(^{n}P_r=^{n}C_r r!\) और (r!=1) केवल (r=0) या (r=1) पर होता है। परीक्षा में equality को factorial से जाँचें। / Because \(^{n}P_r=^{n}C_r r!\), and (r!=1) only for (r=0) or (r=1). In exams verify equality using factorials.

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Question 238/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{n}C_r=\frac{^{n}P_r}{120}\) हो तो (r) का मान क्या होगा?

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

Explanation opens after your attempt
Correct Answer

B. (5)

Explanation

Simple Explanation

\(^{n}C_r=\frac{^{n}P_r}{r!}\) और (5!=120) है। परीक्षा में divisor को (r!) से मिलाएँ। / \(^{n}C_r=\frac{^{n}P_r}{r!}\) and (5!=120). In exams match the divisor with (r!).

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Question 239/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{n}P_r=720\times{}^{n}C_r\) हो तो (r) का मान क्या है?

If \(^{n}P_r=720\times{}^{n}C_r\), what is the value of (r)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

संबंध \(^{n}P_r=^{n}C_r r!\) है और (6!=720) है। परीक्षा में multiplier को (r!) की तरह पहचानें। / The relation is \(^{n}P_r=^{n}C_r r!\), and (6!=720). In exams identify the multiplier as (r!).

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Question 240/600 Medium Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

यदि \(^{16}C_a=^{16}C_{a+4}\) और indices अलग हैं तो (a) क्या होगा?

If \(^{16}C_a=^{16}C_{a+4}\) and the indices are different, what is (a)?

Explanation opens after your attempt
Correct Answer

B. (6)

Explanation

Simple Explanation

पूरक indices का योग (16) होगा इसलिए (a+a+4=16) और (a=6) है। परीक्षा में equal combinations से linear equation बनाएं। / Complementary indices have sum (16), so (a+a+4=16) and (a=6). In exams form a linear equation from equal combinations.

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