Search: nonconsecutive

Question 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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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations
Difficulty: Expert
Level: 63

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

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

Options:
A. (10626)
B. (15504)
C. (17710)
D. (20349)

Correct Answer:
D. (20349)

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

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

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Question 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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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations
Difficulty: Expert
Level: 62

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

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

Options:
A. (462)
B. (495)
C. (540)
D. (600)

Correct Answer:
A. (462)

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

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

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
2. 2-8 sec: Show question in large readable text. Keep Hindi and English clean, no overlap.
3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 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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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Combinations
Difficulty: Expert
Level: 62

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

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

Options:
A. (2380)
B. (3060)
C. (3876)
D. (4845)

Correct Answer:
C. (3876)

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

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

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Question 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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AI Video Prompt 16:9 + 9:16

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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Fundamental principle of counting
Difficulty: Expert
Level: 52

Question Hindi:
(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?

Question English:
(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?

Options:
A. (54)
B. (60)
C. (66)
D. (72)

Correct Answer:
C. (66)

Explanation Hindi:
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।

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

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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3. 8-15 sec: Animate A/B/C/D option cards one by one.
4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
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Question 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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MCQ Data:
Class: Class 11
Subject: Mathematics
Chapter: Permutations and Combinations
Topic: Fundamental principle of counting
Difficulty: Hard
Level: 54

Question Hindi:
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?

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

Options:
A. (35)
B. (42)
C. (56)
D. (70)

Correct Answer:
A. (35)

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

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

Video Structure:
1. 0-2 sec: Premium Muft Shiksha intro with logo glow and title: "MCQ Challenge".
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4. 15-18 sec: Add countdown/timer effect: "Socho... correct answer kya hoga?"
5. 18-23 sec: Reveal correct answer with green glow and subtle success sound.
6. 23-30 sec: Show short explanation with one exam tip.
7. 30-35 sec: CTA: "More free MCQs ke liye visit karein MuftShiksha.com".

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Search Class 10 Questions

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

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

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

Concept

Why this answer is correct

Exam Tip

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