Class 11 Mathematics - Relations And Functions - Real valued functions, domain and range of these functions Medium Quiz

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यदि \(R=\{(1,2),(2,3),(3,4)\}\) है, तो (R) का प्रांत क्या है?

If \(R=\{(1,2),(2,3),(3,4)\}\), what is the domain of (R)?

Explanation opens after your attempt
Correct Answer

B. ( {1,2,3} )

Step 1

Concept

The domain is the set of first components of the ordered pairs, so ( {1,2,3} ) is correct. In exams, look at the first entries.

Step 2

Why this answer is correct

The correct answer is B. ( {1,2,3} ). The domain is the set of first components of the ordered pairs, so ( {1,2,3} ) is correct. In exams, look at the first entries.

Step 3

Exam Tip

प्रांत ordered pairs के पहले घटकों का समुच्चय होता है, इसलिए ( {1,2,3} ) सही है। परीक्षा में पहले स्थान वाले अवयव देखें।

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यदि \(R=\{(2,5),(3,5),(4,6),(5,7)\}\) है, तो (R) का परिसर क्या है?

If \(R=\{(2,5),(3,5),(4,6),(5,7)\}\), what is the range of (R)?

Explanation opens after your attempt
Correct Answer

B. ( {5,6,7} )

Step 1

Concept

The range is the set of second components, and repeated values are written once. Hence ( {5,6,7} ) is correct.

Step 2

Why this answer is correct

The correct answer is B. ( {5,6,7} ). The range is the set of second components, and repeated values are written once. Hence ( {5,6,7} ) is correct.

Step 3

Exam Tip

परिसर ordered pairs के दूसरे घटकों का समुच्चय होता है और पुनरावृत्ति केवल एक बार लिखी जाती है। इसलिए ( {5,6,7} ) सही है।

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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a>b\}\), तो (R) का प्रांत क्या है?

If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a>b\}\), what is the domain of (R)?

Explanation opens after your attempt
Correct Answer

B. ( {2,3,4} )

Step 1

Concept

The first component must be greater than some smaller (b), so (2,3,4) appear. (1) is not greater than any \(b\in A\).

Step 2

Why this answer is correct

The correct answer is B. ( {2,3,4} ). The first component must be greater than some smaller (b), so (2,3,4) appear. (1) is not greater than any \(b\in A\).

Step 3

Exam Tip

पहला घटक ऐसा होना चाहिए जो किसी छोटे (b) से बड़ा हो, इसलिए (2,3,4) आते हैं। (1) किसी भी \(b\in A\) से बड़ा नहीं है।

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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a>b\}\), तो (R) का परिसर क्या है?

If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a>b\}\), what is the range of (R)?

Explanation opens after your attempt
Correct Answer

A. ( {1,2,3} )

Step 1

Concept

The second component must have some greater \(a\in A\), so (1,2,3) appear. There is no element in (A) greater than (4).

Step 2

Why this answer is correct

The correct answer is A. ( {1,2,3} ). The second component must have some greater \(a\in A\), so (1,2,3) appear. There is no element in (A) greater than (4).

Step 3

Exam Tip

दूसरा घटक ऐसा होना चाहिए जिससे बड़ा कोई \(a\in A\) मिले, इसलिए (1,2,3) आते हैं। (4) से बड़ा कोई अवयव (A) में नहीं है।

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यदि \(R=\{(1,4),(2,5),(3,6)\}\) है, तो (R) का प्रांत और परिसर कौन सा है?

If \(R=\{(1,4),(2,5),(3,6)\}\), what are the domain and range of (R)?

Explanation opens after your attempt
Correct Answer

A. प्रांत ( {1,2,3} ), परिसर ( {4,5,6} )Domain ( {1,2,3} ), range ( {4,5,6} )

Step 1

Concept

The domain is formed from first components and the range from second components. Therefore domain is ( {1,2,3} ) and range is ( {4,5,6} ).

Step 2

Why this answer is correct

The correct answer is A. प्रांत ( {1,2,3} ), परिसर ( {4,5,6} ) / Domain ( {1,2,3} ), range ( {4,5,6} ). The domain is formed from first components and the range from second components. Therefore domain is ( {1,2,3} ) and range is ( {4,5,6} ).

Step 3

Exam Tip

प्रांत पहले घटक और परिसर दूसरे घटक से बनता है। इसलिए domain ( {1,2,3} ) और range ( {4,5,6} ) हैं।

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यदि \(A=\{2,3,4,5\}\) पर \(R=\{(a,b):a-b=1\}\), तो (R) का परिसर क्या है?

If \(R=\{(a,b):a-b=1\}\) on \(A=\{2,3,4,5\}\), what is the range of (R)?

Explanation opens after your attempt
Correct Answer

A. ( {2,3,4} )

Step 1

Concept

The pairs are ( (3,2),(4,3),(5,4) ), so the range is ( {2,3,4} ). In exams, take second components for range.

Step 2

Why this answer is correct

The correct answer is A. ( {2,3,4} ). The pairs are ( (3,2),(4,3),(5,4) ), so the range is ( {2,3,4} ). In exams, take second components for range.

Step 3

Exam Tip

युग्म ( (3,2),(4,3),(5,4) ) हैं, इसलिए परिसर ( {2,3,4} ) है। परीक्षा में range के लिए दूसरे घटक लें।

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यदि \(A=\{2,3,4,5\}\) पर \(R=\{(a,b):a-b=1\}\), तो (R) का प्रांत क्या है?

If \(R=\{(a,b):a-b=1\}\) on \(A=\{2,3,4,5\}\), what is the domain of (R)?

Explanation opens after your attempt
Correct Answer

B. ( {3,4,5} )

Step 1

Concept

The condition gives pairs ( (3,2),(4,3),(5,4) ), so the domain is ( {3,4,5} ). In exams, take first components for domain.

Step 2

Why this answer is correct

The correct answer is B. ( {3,4,5} ). The condition gives pairs ( (3,2),(4,3),(5,4) ), so the domain is ( {3,4,5} ). In exams, take first components for domain.

Step 3

Exam Tip

शर्त से युग्म ( (3,2),(4,3),(5,4) ) बनते हैं, इसलिए प्रांत ( {3,4,5} ) है। परीक्षा में domain के लिए पहले घटक लें।

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