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

Mathematics Permutations And Combinations Derivations of formulas and their connections Hard Class 11 Level 60

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Question 1/2 Hard Mathematics Permutations and Combinations Permutations Class 11 Level 60

शब्द (QUESTION) के अक्षरों की व्यवस्थाओं में व्यंजन अपने मूल सापेक्ष क्रम में रहें, ऐसी कितनी व्यवस्थाएं हैं?

In arrangements of (QUESTION), how many have the consonants in their original relative order?

Explanation opens after your attempt
Correct Answer

B. (1680)

Step 1

Concept

In the total (8!) arrangements, the (4!) relative orders of consonants are equally likely, so the count is (8!/4!). For original-order conditions, divide by relative orders.

Step 2

Why this answer is correct

The correct answer is B. (1680). In the total (8!) arrangements, the (4!) relative orders of consonants are equally likely, so the count is (8!/4!). For original-order conditions, divide by relative orders.

Step 3

Exam Tip

कुल (8!) व्यवस्थाओं में (4) व्यंजनों के (4!) सापेक्ष क्रम बराबर हैं, इसलिए (8!/4!) है। मूल क्रम वाली शर्त में सापेक्ष क्रमों से भाग दें।

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Question 2/2 Hard Mathematics Permutations and Combinations Permutations Class 11 Level 60

(7) अलग-अलग पुस्तकों को शेल्फ पर कितने तरीकों से लगाया जा सकता है यदि तीन निश्चित पुस्तकें अपने आपसी वर्णक्रम में रहें?

In how many ways can (7) distinct books be arranged on a shelf if three specified books remain in their mutual alphabetical order?

Explanation opens after your attempt
Correct Answer

D. (840)

Step 1

Concept

Among the (3!) relative orders of the three specified books, only one is valid, so the count is (7!/3!). For relative-order restrictions, divide directly.

Step 2

Why this answer is correct

The correct answer is D. (840). Among the (3!) relative orders of the three specified books, only one is valid, so the count is (7!/3!). For relative-order restrictions, divide directly.

Step 3

Exam Tip

तीन निश्चित पुस्तकों के (3!) सापेक्ष क्रमों में केवल एक क्रम मान्य है, इसलिए (7!/3!) है। सापेक्ष क्रम की शर्त में सीधे भाग दें।

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