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compulsory digits MCQ Questions for Class 11

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2 questions tagged with compulsory digits.

Question 1/2 Hard Mathematics Permutations and Combinations Permutations Class 11 Level 59

(1,2,3,4,5,6,7,8,9) से बिना पुनरावृत्ति कितनी (5)-अंकीय संख्याएं बनेंगी जिनमें अंक (1) और (2) दोनों शामिल हों?

How many (5)-digit numbers can be formed from (1,2,3,4,5,6,7,8,9) without repetition if both digits (1) and (2) are included?

Explanation opens after your attempt
Correct Answer

A. (2520)

Step 1

Concept

Include (1,2), choose (3) more digits from the remaining (7), then arrange the (5) digits in (5!) ways. For compulsory objects, include them first and choose the rest.

Step 2

Why this answer is correct

The correct answer is A. (2520). Include (1,2), choose (3) more digits from the remaining (7), then arrange the (5) digits in (5!) ways. For compulsory objects, include them first and choose the rest.

Step 3

Exam Tip

(1,2) के साथ शेष (7) अंकों में से (3) चुनकर (5!) तरीकों से व्यवस्थित करें। अनिवार्य वस्तुओं को पहले शामिल मानकर बाकी चुनें।

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Question 2/2 Hard Mathematics Permutations and Combinations Permutations Class 11 Level 58

अंकों (1,2,3,4,5,6,7,8) से बिना पुनरावृत्ति (4) अंकों की कितनी संख्याएं बनेंगी जिनमें (2) और (3) दोनों शामिल हों?

How many (4)-digit numbers can be formed from (1,2,3,4,5,6,7,8) without repetition and containing both (2) and (3)?

Explanation opens after your attempt
Correct Answer

A. (720)

Step 1

Concept

Choose the other (2) digits from (6) digits in \(\binom{6}{2}\) ways and arrange the (4) digits in (4!) ways. The total is \(15\cdot24=360\).

Step 2

Why this answer is correct

The correct answer is A. (720). Choose the other (2) digits from (6) digits in \(\binom{6}{2}\) ways and arrange the (4) digits in (4!) ways. The total is \(15\cdot24=360\).

Step 3

Exam Tip

बाकी (2) अंक (6) अंकों में से \(\binom{6}{2}\) तरीकों से चुनें और (4) अंकों को (4!) तरीकों से सजाएं। कुल \(15\cdot24=360\) है।

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