यदि \(A=\{1,2,3,4\}\) और संबंध \(R=\{(a,b):a,b\in A,\ a+2=b\}\) है, तो (R) का प्रांत क्या है?
If \(A=\{1,2,3,4\}\) and the relation is \(R=\{(a,b):a,b\in A,\ a+2=b\}\), what is the domain of (R)?
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A ({1,2})
B ({3,4})
C ({1,2,3,4})
D ({2,3})
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Correct Answer
A. ({1,2})
Step 1
Concept
The condition (a+2=b) gives the ordered pairs ((1,3)) and ((2,4)). Therefore the domain is ({1,2}).
Step 2
Why this answer is correct
The correct answer is A. ({1,2}). The condition (a+2=b) gives the ordered pairs ((1,3)) and ((2,4)). Therefore the domain is ({1,2}).
Step 3
Exam Tip
शर्त (a+2=b) से ordered pairs ((1,3)) और ((2,4)) मिलते हैं। इसलिए प्रांत ({1,2}) है।
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यदि \(A=\{2,4,6\}\) और संबंध \(R=\{(2,4),(4,6),(6,2)\}\) है, तो (R) का प्रांत क्या है?
If \(A=\{2,4,6\}\) and the relation is \(R=\{(2,4),(4,6),(6,2)\}\), what is the domain of (R)?
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A ({2,4,6})
B ({4,6,2})
C ({4,6})
D ({2,6})
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Correct Answer
A. ({2,4,6})
Step 1
Concept
The domain contains all first components, so it is ({2,4,6}). In exams, look at the first place in each ordered pair.
Step 2
Why this answer is correct
The correct answer is A. ({2,4,6}). The domain contains all first components, so it is ({2,4,6}). In exams, look at the first place in each ordered pair.
Step 3
Exam Tip
प्रांत में सभी प्रथम घटक आते हैं, इसलिए ({2,4,6}) मिलेगा। परीक्षा में ordered pair का पहला स्थान देखें।
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यदि संबंध \(R=\{(1,3),(2,3),(3,5),(4,7)\}\) है, तो (R) का परिसर क्या है?
If the relation is \(R=\{(1,3),(2,3),(3,5),(4,7)\}\), what is the range of (R)?
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A ({1,2,3,4})
B ({3,5,7})
C ({3,3,5,7})
D ({1,3,5,7})
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Correct Answer
B. ({3,5,7})
Step 1
Concept
The range contains second components and repeated entries are removed. Hence ({3,5,7}) is correct.
Step 2
Why this answer is correct
The correct answer is B. ({3,5,7}). The range contains second components and repeated entries are removed. Hence ({3,5,7}) is correct.
Step 3
Exam Tip
परिसर में दूसरे घटक लिए जाते हैं और पुनरावृत्ति हटती है। इसलिए ({3,5,7}) सही है।
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यदि \(R=\{(a,b):a,b\in {1,2,3,4},\ a<b\}\), तो (R) का परिसर क्या है?
If \(R=\{(a,b):a,b\in {1,2,3,4},\ a<b\}\), what is the range of (R)?
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A ({1,2,3})
B ({2,3,4})
C ({1,2,3,4})
D ({4})
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Correct Answer
B. ({2,3,4})
Step 1
Concept
The second component can be (2,3,4). Therefore the range is ({2,3,4}).
Step 2
Why this answer is correct
The correct answer is B. ({2,3,4}). The second component can be (2,3,4). Therefore the range is ({2,3,4}).
Step 3
Exam Tip
दूसरे घटक के रूप में (2,3,4) आ सकते हैं। इसलिए परिसर ({2,3,4}) है।
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यदि \(R=\{(1,2),(2,3),(1,3)\}\), तो (R) का प्रांत क्या है?
If \(R=\{(1,2),(2,3),(1,3)\}\), what is the domain of (R)?
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A ({1,2})
B ({2,3})
C ({1,2,3})
D ({3})
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Correct Answer
A. ({1,2})
Step 1
Concept
Only first components are taken in the domain. Here the first components are (1) and (2).
Step 2
Why this answer is correct
The correct answer is A. ({1,2}). Only first components are taken in the domain. Here the first components are (1) and (2).
Step 3
Exam Tip
प्रांत में केवल प्रथम घटक लिए जाते हैं। यहां प्रथम घटक (1) और (2) हैं।
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यदि \(R=\{(1,2),(2,3),(1,3)\}\), तो (R) का परिसर क्या है?
If \(R=\{(1,2),(2,3),(1,3)\}\), what is the range of (R)?
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A ({1,2})
B ({2,3})
C ({1,3})
D ({1,2,3})
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Correct Answer
B. ({2,3})
Step 1
Concept
Second components are taken in the range. Here the second components are (2) and (3).
Step 2
Why this answer is correct
The correct answer is B. ({2,3}). Second components are taken in the range. Here the second components are (2) and (3).
Step 3
Exam Tip
परिसर में दूसरे घटक लिए जाते हैं। यहां दूसरे घटक (2) और (3) हैं।
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यदि \(A=\{1,2,3\}\), \(B=\{x,y\}\) और \(R=\{(1,x),(3,y)\}\), तो (R) का सहप्रांत क्या है?
If \(A=\{1,2,3\}\), \(B=\{x,y\}\), and \(R=\{(1,x),(3,y)\}\), what is the codomain of (R)?
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A ({x,y})
B ({1,3})
C ({x})
D ({y})
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Correct Answer
A. ({x,y})
Step 1
Concept
For a relation from (A) to (B), the codomain is the whole set (B). Here \(B=\{x,y\}\).
Step 2
Why this answer is correct
The correct answer is A. ({x,y}). For a relation from (A) to (B), the codomain is the whole set (B). Here \(B=\{x,y\}\).
Step 3
Exam Tip
(A) से (B) तक संबंध में सहप्रांत पूरा (B) होता है। यहां \(B=\{x,y\}\) है।
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यदि किसी संबंध का परिसर ({p,q}) है और सहप्रांत ({p,q,r}) है, तो कौन सा कथन सही है?
If the range of a relation is ({p,q}) and the codomain is ({p,q,r}), which statement is correct?
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A परिसर सहप्रांत का उपसमुच्चय है / Range is a subset of codomain
B सहप्रांत परिसर का उपसमुच्चय है / Codomain is a subset of range
C परिसर और सहप्रांत हमेशा बराबर होते हैं / Range and codomain are always equal
D सहप्रांत खाली है / Codomain is empty
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Correct Answer
A. परिसर सहप्रांत का उपसमुच्चय है / Range is a subset of codomain
Step 1
Concept
The range is always a subset of the codomain. They need not be equal.
Step 2
Why this answer is correct
The correct answer is A. परिसर सहप्रांत का उपसमुच्चय है / Range is a subset of codomain. The range is always a subset of the codomain. They need not be equal.
Step 3
Exam Tip
परिसर हमेशा सहप्रांत का उपसमुच्चय होता है। दोनों बराबर होना जरूरी नहीं है।
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