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

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Question 421/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(8) people में से president, secretary और treasurer चुनने की count किस सूत्र से जुड़ेगी?

Which formula gives the count for choosing a president, secretary, and treasurer from (8) people?

Explanation opens after your attempt
Correct Answer

B. \(^{8}P_3\)

Explanation

Simple Explanation

तीनों पद अलग हैं, इसलिए order of selection meaningful है। परीक्षा में different posts हों तो permutation लगाएं। / The three posts are different, so the order of selection is meaningful. In exams use permutation for different posts.

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Question 422/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(8) people में से (3) members की बिना पद वाली committee बनानी हो, तो \(^{8}P_3\) क्यों गलत है?

If a (3)-member committee without posts is formed from (8) people, why is \(^{8}P_3\) wrong?

Explanation opens after your attempt
Correct Answer

A. क्योंकि committee में क्रम का महत्व नहीं हैBecause order has no importance in a committee

Explanation

Simple Explanation

बिना पद वाली committee में केवल group गिना जाता है। परीक्षा में पद न हों तो combination उपयोग करें। / A committee without posts counts only the group. In exams use combination when there are no posts.

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Question 423/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(12) points में से कोई (3) collinear नहीं हैं। Triangles की संख्या कौन-सी है?

Among (12) points, no (3) are collinear. What is the number of triangles?

Explanation opens after your attempt
Correct Answer

B. \(^{12}C_3\)

Explanation

Simple Explanation

कोई भी (3) points एक triangle बनाते हैं और order important नहीं है। परीक्षा में geometry selection में combination लगाएं। / Any (3) points form a triangle and order is not important. In exams use combination in geometry selection.

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Question 424/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(10) points में से (4) points collinear हैं और बाकी कोई (3) collinear नहीं हैं। Triangles की count कौन-सी है?

Among (10) points, (4) points are collinear and no other (3) are collinear. Which count gives the triangles?

Explanation opens after your attempt
Correct Answer

A. \(^{10}C_3-{}^{4}C_3\)

Explanation

Simple Explanation

Total (3)-point selections से collinear (3)-point selections हटते हैं। परीक्षा में invalid selections घटाएं। / Subtract collinear (3)-point selections from total (3)-point selections. In exams subtract invalid selections.

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Question 425/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(n)-भुज के vertices से quadrilaterals की संख्या कौन-सी है, यदि कोई (3) vertices collinear नहीं हैं?

What is the number of quadrilaterals formed from vertices of an (n)-gon if no (3) vertices are collinear?

Explanation opens after your attempt
Correct Answer

A. \(^{n}C_4\)

Explanation

Simple Explanation

चार vertices का selection एक quadrilateral तय करता है। परीक्षा में polygon से shapes बनें तो vertices का combination लें। / A selection of four vertices determines a quadrilateral. In exams use combinations of vertices when shapes are formed from polygons.

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Question 426/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(n) लोगों में handshakes की count \(^{n}C_2\) क्यों है, \(^{n}P_2\) क्यों नहीं?

Why is the number of handshakes among (n) people \(^{n}C_2\), not \(^{n}P_2\)?

Explanation opens after your attempt
Correct Answer

A. क्योंकि handshake में pair unordered होता हैBecause a handshake pair is unordered

Explanation

Simple Explanation

(A) का (B) से handshake और (B) का (A) से handshake same है। परीक्षा में mutual relation को combination मानें। / A handshake of (A) with (B) and (B) with (A) is the same. In exams treat mutual relations as combinations.

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Question 427/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(n) teams की tournament में हर team हर दूसरी team से एक match खेले, तो matches की संख्या क्या होगी?

In a tournament of (n) teams, if each team plays one match with every other team, what is the number of matches?

Explanation opens after your attempt
Correct Answer

B. \(^{n}C_2\)

Explanation

Simple Explanation

एक match दो teams के unordered pair से तय होता है। परीक्षा में one-to-one pair events में \(^{n}C_2\) लगाएं। / A match is determined by an unordered pair of two teams. In exams use \(^{n}C_2\) for one-to-one pair events.

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Question 428/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(7) distinct books को shelf पर रखना है और (3) special books साथ रहें। Count कौन-सी है?

(7) distinct books are arranged on a shelf and (3) special books stay together. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. \(5!\cdot3!\)

Explanation

Simple Explanation

(3) special books को one block मानने पर (5) objects arrange होते हैं। परीक्षा में block के अंदर (3!) arrangements भी गिनें। / Treating the (3) special books as one block gives (5) objects to arrange. In exams also count (3!) arrangements inside the block.

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Question 429/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(9) people को line में arrange करना है और (A) तथा (B) together न हों। Count कौन-सी है?

(9) people are arranged in a line and (A) and (B) are not together. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. \(9!-8!\cdot2!\)

Explanation

Simple Explanation

Total arrangements से (A) और (B) together block arrangements घटते हैं। परीक्षा में not together को complement से करना आसान है। / Subtract the arrangements where (A) and (B) are together as a block from total arrangements. In exams use complement for not together.

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Question 430/600 Hard Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

(6) boys और (5) girls को row में बैठाना है ताकि कोई दो girls साथ न बैठें। Girls placement factor क्या होगा?

(6) boys and (5) girls are seated in a row so that no two girls sit together. What is the girls placement factor?

Explanation opens after your attempt
Correct Answer

B. \(^{7}C_5\cdot5!\)

Explanation

Simple Explanation

(6) boys के बाद (7) gaps बनते हैं, जिनमें (5) girls arrange होती हैं। परीक्षा में no two together में gap method लगाएं। / After (6) boys, (7) gaps are formed, and (5) girls are arranged in them. In exams use the gap method for no two together.

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