Class 11 Mathematics - Permutations And Combinations - Derivations of formulas and their connections Expert Quiz

Mathematics Permutations And Combinations Derivations of formulas and their connections Expert Class 11 Level 52

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This level needs 47 more active questions. Admin panel me same class, subject, difficulty aur level_no 52 par question add karein.
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Question 1/3 Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(1) से (12) तक के पूर्णांकों में से (4) संख्याएँ चुननी हैं। कोई दो संख्याएँ लगातार न हों और उनका योग सम हो। कुल कितने चयन होंगे?

(4) integers are to be selected from (1) to (12). No two selected integers should be consecutive, and their sum must be even. How many selections are possible?

Explanation opens after your attempt
Correct Answer

C. (66)

Step 1

Concept

First consider non-consecutive selections of (4) numbers and then separate those with even sum. Parity classification helps in such questions.

Step 2

Why this answer is correct

The correct answer is C. (66). First consider non-consecutive selections of (4) numbers and then separate those with even sum. Parity classification helps in such questions.

Step 3

Exam Tip

पहले गैर-लगातार (4) संख्याओं के चयन पर विचार करें और फिर सम योग वाले चयन अलग करें। सम-विषम वर्गीकरण ऐसे प्रश्नों में सहायक है।

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Question 2/3 Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(1) से (20) तक की संख्याओं में से (3) संख्याएँ चुननी हैं। उनका गुणनफल सम और योग विषम होना चाहिए। कुल कितने चयन होंगे?

(3) numbers are to be selected from (1) to (20). Their product must be even and their sum must be odd. How many selections are possible?

Explanation opens after your attempt
Correct Answer

C. (450)

Step 1

Concept

For the sum to be odd and the product to be even, exactly (1) odd and (2) even numbers must be chosen. Classify parity conditions first.

Step 2

Why this answer is correct

The correct answer is C. (450). For the sum to be odd and the product to be even, exactly (1) odd and (2) even numbers must be chosen. Classify parity conditions first.

Step 3

Exam Tip

योग विषम और गुणनफल सम होने के लिए ठीक (1) विषम और (2) सम संख्याएँ चुनी जानी चाहिए। सम-विषम शर्तों को पहले वर्गीकृत करें।

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Question 3/3 Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(5) बच्चों को (5) निश्चित कुर्सियों पर बैठाना है। ठीक (2) बच्चे अपनी निर्धारित कुर्सियों पर बैठें। कुल कितनी व्यवस्थाएँ होंगी?

(5) children are to be seated on (5) assigned chairs. Exactly (2) children must sit on their assigned chairs. How many arrangements are possible?

Explanation opens after your attempt
Correct Answer

A. (20)

Step 1

Concept

First choose the (2) children who sit correctly, then derange the remaining (3) children. Exact fixed-position conditions use derangements.

Step 2

Why this answer is correct

The correct answer is A. (20). First choose the (2) children who sit correctly, then derange the remaining (3) children. Exact fixed-position conditions use derangements.

Step 3

Exam Tip

पहले सही बैठने वाले (2) बच्चे चुनें, फिर बाकी (3) बच्चों को पूर्ण अव्यवस्था में बैठाएँ। ठीक सही स्थान की शर्त में अव्यवस्था का प्रयोग करें।

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