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nonconsecutive MCQ Questions for Class 11

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5 questions tagged with nonconsecutive.

Question 1/5 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 63

(1) से (25) तक की संख्याओं में से (5) संख्याएं चुननी हैं ताकि कोई दो लगातार न हों। कितने चयन होंगे?

Choose (5) numbers from (1) to (25) so that no two are consecutive. How many selections are possible?

Explanation opens after your attempt
Correct Answer

D. (20349)

Step 1

Concept

For non-consecutive selection, use \(^{n-r+1}C_{r}\). Here \(^{21}C_{5}=20349\).

Step 2

Why this answer is correct

The correct answer is D. (20349). For non-consecutive selection, use \(^{n-r+1}C_{r}\). Here \(^{21}C_{5}=20349\).

Step 3

Exam Tip

गैर-लगातार चयन के लिए सूत्र \(^{n-r+1}C_{r}\) है। यहां \(^{21}C_{5}=20349\)।

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Question 2/5 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 62

(1) से (15) तक की संख्याओं में से (5) संख्याएं चुननी हैं, जिनमें कोई दो लगातार न हों। कितने तरीके हैं?

Choose (5) numbers from (1) to (15) such that no two are consecutive. How many ways are possible?

Explanation opens after your attempt
Correct Answer

A. (462)

Step 1

Concept

By the gap method, the count is \(^{15-5+1}C_{5}=^{11}C_{5}=462\). In such problems identify the gap condition first.

Step 2

Why this answer is correct

The correct answer is A. (462). By the gap method, the count is \(^{15-5+1}C_{5}=^{11}C_{5}=462\). In such problems identify the gap condition first.

Step 3

Exam Tip

अलगाव विधि से संख्या \(^{15-5+1}C_{5}=^{11}C_{5}=462\)। ऐसी समस्याओं में पहले अंतर की शर्त पहचानें।

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Question 3/5 Expert Mathematics Permutations and Combinations Combinations Class 11 Level 62

(1) से (20) तक की संख्याओं में से (4) संख्याएं चुननी हैं ताकि कोई दो लगातार न हों। कितने चयन संभव हैं?

Choose (4) numbers from (1) to (20) so that no two are consecutive. How many selections are possible?

Explanation opens after your attempt
Correct Answer

C. (3876)

Step 1

Concept

If no two are consecutive, use \(^{n-r+1}C_{r}\). Here \(^{17}C_{4}=2380\), so the correct answer is (2380).

Step 2

Why this answer is correct

The correct answer is C. (3876). If no two are consecutive, use \(^{n-r+1}C_{r}\). Here \(^{17}C_{4}=2380\), so the correct answer is (2380).

Step 3

Exam Tip

कोई दो लगातार न हों तो सूत्र \(^{n-r+1}C_{r}\) है। यहां \(^{17}C_{4}=2380\), इसलिए सही विकल्प (2380) है।

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Question 4/5 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 5/5 Hard Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 54

एक विद्यार्थी (10) दिनों में से (4) दिन अभ्यास चुनता है। कोई दो चुने गए दिन लगातार नहीं होने चाहिए। चयन कितने तरीकों से होगा?

A student chooses (4) practice days from (10) days. No two selected days should be consecutive. In how many ways can this be done?

Explanation opens after your attempt
Correct Answer

A. (35)

Step 1

Concept

The number of ways to choose (4) non-consecutive days is \(\binom{10-4+1}{4}\). Remember the gap method for non-consecutive selections.

Step 2

Why this answer is correct

The correct answer is A. (35). The number of ways to choose (4) non-consecutive days is \(\binom{10-4+1}{4}\). Remember the gap method for non-consecutive selections.

Step 3

Exam Tip

लगातार न होने वाले (4) दिनों का चयन \(\binom{10-4+1}{4}\) से मिलेगा। गैर-लगातार चयन में अंतर विधि याद रखें।

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