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strings MCQ Questions for Class 11

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8 questions tagged with strings.

Question 1/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

Length (9) strings (6) symbols से बनती हैं और exactly (4) distinct symbols use हों। सही count कौन-सी है?

Length (9) strings are formed from (6) symbols and exactly (4) distinct symbols are used. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. (^{6}C_4\sum_{i=0}^{4}(-1)^i{}^{4}C_i(4-i)9)

Step 1

Concept

First choose (4) symbols and then form onto strings on them. In exams use choose set plus onto count for exactly distinct symbols.

Step 2

Why this answer is correct

The correct answer is A. (^{6}C_4\sum_{i=0}^{4}(-1)^i{}^{4}C_i(4-i)9). First choose (4) symbols and then form onto strings on them. In exams use choose set plus onto count for exactly distinct symbols.

Step 3

Exam Tip

पहले (4) symbols चुनें और फिर उन पर onto strings बनाएं। परीक्षा में exactly distinct symbols में choose set plus onto count करें।

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Question 2/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 66

Length (8) strings (5) symbols से बनती हैं और हर symbol कम से कम एक बार आए। Count का inclusion-exclusion form कौन-सा है?

Length (8) strings are formed from (5) symbols and every symbol appears at least once. Which inclusion-exclusion form gives the count?

Explanation opens after your attempt
Correct Answer

A. (\sum_{i=0}^{5}(-1)^i{}^{5}C_i(5-i)8)

Step 1

Concept

Every symbol appearing is an onto condition and missing symbols are removed. In exams solve at least once by inclusion-exclusion.

Step 2

Why this answer is correct

The correct answer is A. (\sum_{i=0}^{5}(-1)^i{}^{5}C_i(5-i)8). Every symbol appearing is an onto condition and missing symbols are removed. In exams solve at least once by inclusion-exclusion.

Step 3

Exam Tip

हर symbol का आना onto condition है और missing symbols हटते हैं। परीक्षा में at least once को inclusion-exclusion से करें।

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Question 3/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

(n) distinct symbols से length (r) strings में exactly one repeated symbol और बाकी all distinct हों, तो count का core expression क्या होगा?

For length (r) strings from (n) distinct symbols with exactly one repeated symbol and all others distinct, what is the core expression?

Explanation opens after your attempt
Correct Answer

A. \(n\cdot{}^{n-1}C_{r-2}\cdot\frac{r!}{2!}\)

Step 1

Concept

Choose the repeated symbol, choose the remaining (r-2) distinct symbols, then arrange the multiset. In exams fix the repeated item first for exactly one repeat.

Step 2

Why this answer is correct

The correct answer is A. \(n\cdot{}^{n-1}C_{r-2}\cdot\frac{r!}{2!}\). Choose the repeated symbol, choose the remaining (r-2) distinct symbols, then arrange the multiset. In exams fix the repeated item first for exactly one repeat.

Step 3

Exam Tip

Repeated symbol चुनें, बाकी (r-2) distinct symbols चुनें, फिर multiset arrange करें। परीक्षा में exactly one repeat में repeated item पहले fix करें।

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Question 4/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 65

Length (6) strings (4) symbols से बनती हैं और हर symbol कम से कम एक बार आए। Count कौन-सी है?

Length (6) strings are formed from (4) symbols and every symbol appears at least once. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. (\sum_{i=0}^{4}(-1)^i{}^{4}C_i(4-i)6)

Step 1

Concept

Every symbol appearing is an onto condition, so missing symbols are removed by inclusion-exclusion. In exams treat at least once as onto mapping.

Step 2

Why this answer is correct

The correct answer is A. (\sum_{i=0}^{4}(-1)^i{}^{4}C_i(4-i)6). Every symbol appearing is an onto condition, so missing symbols are removed by inclusion-exclusion. In exams treat at least once as onto mapping.

Step 3

Exam Tip

हर symbol का आना onto condition है, इसलिए missing symbols को inclusion-exclusion से हटाते हैं। परीक्षा में at least once को onto mapping समझें।

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Question 5/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(n) distinct symbols से length (r) strings बनती हैं और exactly (s) distinct symbols use हों। सही count कौन-सा है?

Length (r) strings are formed from (n) distinct symbols and exactly (s) distinct symbols are used. Which count is correct?

Explanation opens after your attempt
Correct Answer

A. (^{n}C_s s! S(r,s))

Step 1

Concept

First choose (s) symbols, then map the (r) positions onto those (s) symbols. In exams use the onto idea for exactly distinct symbols.

Step 2

Why this answer is correct

The correct answer is A. (^{n}C_s s! S(r,s)). First choose (s) symbols, then map the (r) positions onto those (s) symbols. In exams use the onto idea for exactly distinct symbols.

Step 3

Exam Tip

पहले (s) symbols चुनें, फिर (r) positions को उन (s) symbols पर onto map करें। परीक्षा में exactly distinct symbols में onto idea उपयोग करें।

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Question 6/8 Expert Mathematics Permutations and Combinations Derivations of formulas and their connections Class 11 Level 64

(n) distinct symbols से length (r) strings बनती हैं जिनमें repetition allowed है लेकिन कम से कम एक symbol repeat हो। Count क्या है?

Length (r) strings are formed from (n) distinct symbols with repetition allowed, but at least one symbol repeats. What is the count?

Explanation opens after your attempt
Correct Answer

A. \(n^r-{}^{n}P_r\)

Step 1

Concept

Subtract all-distinct strings from total repetition-allowed strings. In exams solve at least repeat by the no-repeat complement.

Step 2

Why this answer is correct

The correct answer is A. \(n^r-{}^{n}P_r\). Subtract all-distinct strings from total repetition-allowed strings. In exams solve at least repeat by the no-repeat complement.

Step 3

Exam Tip

Total repeated-allowed strings से all distinct strings घटाएं। परीक्षा में at least repeat को complement no repeat से करें।

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Question 7/8 Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(A,B,C) अक्षरों और (1,2,3,4) अंकों से (5) चिह्नों की कितनी श्रेणियाँ बनेंगी यदि पुनरावृत्ति मान्य हो, पहला चिह्न अक्षर हो और अंतिम चिह्न अंक हो?

Using letters (A,B,C) and digits (1,2,3,4), how many strings of (5) symbols can be formed if repetition is allowed, the first symbol is a letter, and the last symbol is a digit?

Explanation opens after your attempt
Correct Answer

C. (4116)

Step 1

Concept

The first position has (3) choices, the last has (4), and each middle position has (7) choices. Multiply choices for independent positions.

Step 2

Why this answer is correct

The correct answer is C. (4116). The first position has (3) choices, the last has (4), and each middle position has (7) choices. Multiply choices for independent positions.

Step 3

Exam Tip

पहले स्थान के लिए (3), अंतिम के लिए (4) और बीच के प्रत्येक स्थान के लिए (7) विकल्प हैं। स्वतंत्र स्थानों के विकल्पों को गुणा करें।

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Question 8/8 Expert Mathematics Permutations and Combinations Fundamental principle of counting Class 11 Level 52

(4) स्वरों और (6) व्यंजनों से (6) अक्षरों की कितनी श्रेणियाँ बनेंगी यदि पुनरावृत्ति मान्य हो, ठीक (2) स्वर हों और कोई दो स्वर साथ-साथ न हों?

Using (4) vowels and (6) consonants, how many strings of (6) letters can be formed if repetition is allowed, exactly (2) vowels are used, and no two vowels are adjacent?

Explanation opens after your attempt
Correct Answer

C. (207360)

Step 1

Concept

First choose (2) non-adjacent vowel positions among (6), then fill vowels and consonants. With repetition allowed, each chosen position keeps the same number of choices.

Step 2

Why this answer is correct

The correct answer is C. (207360). First choose (2) non-adjacent vowel positions among (6), then fill vowels and consonants. With repetition allowed, each chosen position keeps the same number of choices.

Step 3

Exam Tip

पहले (6) स्थानों में (2) गैर-लगातार स्वर-स्थान चुनें, फिर स्वर और व्यंजन भरें। पुनरावृत्ति हो तो हर चुने स्थान पर विकल्प समान रहते हैं।

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