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 61

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Question 1/4 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 61

(1) से (8) तक की संख्याओं में से (3) संख्याएँ ऐसी चुननी हैं जिनका योग सम हो। कुल चयन कितने हैं?

From the numbers (1) to (8), (3) numbers are chosen so that their sum is even. How many selections are possible?

Explanation opens after your attempt
Correct Answer

B. (28)

Step 1

Concept

The sum is even when (3) even numbers or (2) odd and (1) even number are chosen, giving (28). Count parity cases separately.

Step 2

Why this answer is correct

The correct answer is B. (28). The sum is even when (3) even numbers or (2) odd and (1) even number are chosen, giving (28). Count parity cases separately.

Step 3

Exam Tip

योग सम तब होगा जब (3) सम या (2) विषम और (1) सम चुने जाएँ, कुल (28) हैं। सम-विषम मामलों को अलग-अलग गिनें।

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Question 2/4 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 61

(1) से (15) तक की संख्याओं में से (4) संख्याएँ चुननी हैं ताकि उनका गुणनफल विषम हो। कुल चयन कितने हैं?

From the numbers (1) to (15), (4) numbers are chosen so that their product is odd. How many selections are possible?

Explanation opens after your attempt
Correct Answer

C. (70)

Step 1

Concept

The product is odd only when all four numbers are odd, so \( \binom{8}{4}=70 \). For product parity, check every factor.

Step 2

Why this answer is correct

The correct answer is C. (70). The product is odd only when all four numbers are odd, so \( \binom{8}{4}=70 \). For product parity, check every factor.

Step 3

Exam Tip

गुणनफल विषम तभी होगा जब चारों संख्याएँ विषम हों, इसलिए \( \binom{8}{4}=70 \)। गुणनफल की सम-विषम प्रकृति में सभी कारकों पर ध्यान दें।

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Question 3/4 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 61

(1) से (20) तक की संख्याओं में से (3) संख्याएँ ऐसी चुननी हैं जिनका योग विषम हो। कुल चयन कितने हैं?

From the numbers (1) to (20), (3) numbers are chosen so that their sum is odd. How many selections are possible?

Explanation opens after your attempt
Correct Answer

B. (570)

Step 1

Concept

For an odd sum, choose (1) odd and (2) even or (3) odd numbers, giving (570). Making a parity case table reduces errors.

Step 2

Why this answer is correct

The correct answer is B. (570). For an odd sum, choose (1) odd and (2) even or (3) odd numbers, giving (570). Making a parity case table reduces errors.

Step 3

Exam Tip

योग विषम के लिए (1) विषम और (2) सम या (3) विषम चुनें, कुल (570) है। सम-विषम संयोजन तालिका बनाकर गलती घटती है।

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Question 4/4 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 61

(1) से (12) तक की संख्याओं में से (4) संख्याएँ ऐसी चुननी हैं जिनका योग सम हो। कुल चयन कितने हैं?

From the numbers (1) to (12), (4) numbers are chosen so that their sum is even. How many selections are possible?

Explanation opens after your attempt
Correct Answer

C. (255)

Step 1

Concept

For an even sum, the number of odd selected numbers can be (0,2,4), giving (255). Focus on how many odd elements are selected, not only on total selection size.

Step 2

Why this answer is correct

The correct answer is C. (255). For an even sum, the number of odd selected numbers can be (0,2,4), giving (255). Focus on how many odd elements are selected, not only on total selection size.

Step 3

Exam Tip

सम योग के लिए विषम संख्याओं की संख्या (0,2,4) हो सकती है, कुल (255) है। चयन की संख्या पर नहीं, विषम चुने गए तत्वों की संख्या पर ध्यान दें।

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