यदि \(A=\{1,2,4\}\) और \(R=\{(a,b):a=b^2\}\) है, तो कौन-सा ordered pair (R) में है?
If \(A=\{1,2,4\}\) and \(R=\{(a,b):a=b^2\}\), which ordered pair is in (R)?
#relations
#ordered-pair
#set-builder
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A ( (1,2) )
B ( (4,2) )
C ( (2,4) )
D ( (4,1) )
Explanation opens after your attempt
Correct Answer
B. ( (4,2) )
Step 1
Concept
Since \(4=2^2\), \((4,2)\in R\). In such questions, check the first and second components in the correct order.
Step 2
Why this answer is correct
The correct answer is B. ( (4,2) ). Since \(4=2^2\), \((4,2)\in R\). In such questions, check the first and second components in the correct order.
Step 3
Exam Tip
क्योंकि \(4=2^2\), इसलिए \((4,2)\in R\) है। ऐसे प्रश्नों में ordered pair के पहले और दूसरे घटक को सही स्थान पर रखकर जांचें।
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यदि \(A=\{a,b\}\) है, तो (A) पर खाली संबंध कौन-सा है?
If \(A=\{a,b\}\), which one is the empty relation on (A)?
#relations
#empty-relation
#class11
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A \(R=A\times A\)
B \(R=\varnothing\)
C \(R=\{(a,a)\}\)
D \(R=\{(a,b)\}\)
Explanation opens after your attempt
Correct Answer
B. \(R=\varnothing\)
Step 1
Concept
An empty relation has no ordered pair. Remember that \(R=\varnothing\) is also a valid relation.
Step 2
Why this answer is correct
The correct answer is B. \(R=\varnothing\). An empty relation has no ordered pair. Remember that \(R=\varnothing\) is also a valid relation.
Step 3
Exam Tip
खाली संबंध में कोई ordered pair नहीं होता। याद रखें \(R=\varnothing\) भी एक वैध संबंध है।
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यदि \(A=\{1,2,3\}\) है, तो (A) पर सार्वत्रिक संबंध कौन-सा है?
If \(A=\{1,2,3\}\), which is the universal relation on (A)?
#relations
#universal-relation
#basics
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A \(R=\varnothing\)
B (R=A)
C \(R=A\times A\)
D \(R=\{1,2,3\}\)
Explanation opens after your attempt
Correct Answer
C. \(R=A\times A\)
Step 1
Concept
The universal relation contains all ordered pairs of \(A\times A\). In exams, think of it as the total relation.
Step 2
Why this answer is correct
The correct answer is C. \(R=A\times A\). The universal relation contains all ordered pairs of \(A\times A\). In exams, think of it as the total relation.
Step 3
Exam Tip
सार्वत्रिक संबंध \(A\times A\) के सभी ordered pairs लेता है। परीक्षा में इसे total relation भी समझें।
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यदि \(A=\{1,2\}\) है, तो \(A\times A\) में कितने ordered pairs होंगे?
If \(A=\{1,2\}\), how many ordered pairs are there in \(A\times A\)?
#relations
#ordered-pairs
#counting
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A (2)
B (3)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
If (n(A)=2), then (n\(A\times A\)=22 =4). Use (n(A)2 ) while counting.
Step 2
Why this answer is correct
The correct answer is C. (4). If (n(A)=2), then (n\(A\times A\)=22 =4). Use (n(A)2 ) while counting.
Step 3
Exam Tip
यदि (n(A)=2), तो (n\(A\times A\)=22 =4)। संख्या गिनते समय (n(A)2 ) का प्रयोग करें।
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यदि \(A=\{1,2\}\) और \(R=\{(1,1),(2,2)\}\) है, तो (R) किस प्रकार का संबंध है?
If \(A=\{1,2\}\) and \(R=\{(1,1),(2,2)\}\), what type of relation is (R)?
#relations
#identity-relation
#easy
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A रिक्त संबंध / Empty relation
B सर्वत्र संबंध / Universal relation
C तुल्यता जैसा पहचान संबंध / Identity relation
D अमान्य संबंध / Invalid relation
Explanation opens after your attempt
Correct Answer
C. तुल्यता जैसा पहचान संबंध / Identity relation
Step 1
Concept
Each element is related only to itself. Such a relation is called the identity relation.
Step 2
Why this answer is correct
The correct answer is C. तुल्यता जैसा पहचान संबंध / Identity relation. Each element is related only to itself. Such a relation is called the identity relation.
Step 3
Exam Tip
इसमें हर तत्व केवल अपने साथ जुड़ा है। ऐसे संबंध को पहचान संबंध कहते हैं।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3)\}\) है, तो (R) में कौन-सा ordered pair अवश्य है?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3)\}\), which ordered pair is definitely in (R)?
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#ordered-pair
#recognition
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A ( (1,2) )
B ( (2,2) )
C ( (3,1) )
D ( (2,3) )
Explanation opens after your attempt
Correct Answer
B. ( (2,2) )
Step 1
Concept
The pair ( (2,2) ) is clearly present in the given relation. In MCQs, match the listed pair carefully.
Step 2
Why this answer is correct
The correct answer is B. ( (2,2) ). The pair ( (2,2) ) is clearly present in the given relation. In MCQs, match the listed pair carefully.
Step 3
Exam Tip
दिए गए संबंध में ( (2,2) ) साफ लिखा है। MCQ में सीधे दिए गए pair को ध्यान से मिलाएं।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,2),(2,3)\}\) है, तो (R) किसका उपसमुच्चय है?
If \(A=\{1,2,3\}\) and \(R=\{(1,2),(2,3)\}\), then (R) is a subset of what?
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#subset
#cartesian-square
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A (A)
B \(A\times A\)
C \(\varnothing\)
D \(R\times A\)
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Correct Answer
B. \(A\times A\)
Step 1
Concept
Both components of the ordered pairs are from (A). Hence \(R\subseteq A\times A\).
Step 2
Why this answer is correct
The correct answer is B. \(A\times A\). Both components of the ordered pairs are from (A). Hence \(R\subseteq A\times A\).
Step 3
Exam Tip
दोनों ordered pairs के घटक (A) से हैं। इसलिए \(R\subseteq A\times A\) है।
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यदि \(A=\{1,2,3\}\) है, तो (A) पर कुल कितने भिन्न संबंध बन सकते हैं?
If \(A=\{1,2,3\}\), how many different relations can be formed on (A)?
#relations
#total-relations
#counting
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A \(2^3\)
B \(2^6\)
C \(2^9\)
D \(3^2\)
Explanation opens after your attempt
Correct Answer
C. \(2^9\)
Step 1
Concept
There are \(3^2=9\) pairs in \(A\times A\), so it has \(2^9\) subsets. The number of relations is \(2^{n(A)^2}\).
Step 2
Why this answer is correct
The correct answer is C. \(2^9\). There are \(3^2=9\) pairs in \(A\times A\), so it has \(2^9\) subsets. The number of relations is \(2^{n(A)^2}\).
Step 3
Exam Tip
\(A\times A\) में \(3^2=9\) pairs हैं और उसके \(2^9\) उपसमुच्चय होंगे। संबंधों की संख्या \(2^{n(A)^2}\) होती है।
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यदि \(A=\{1,2\}\) और \(B=\{x,y,z\}\) हैं, तो (A) से (B) तक कुल कितने संबंध हो सकते हैं?
If \(A=\{1,2\}\) and \(B=\{x,y,z\}\), how many relations can exist from (A) to (B)?
#relations
#counting
#from-A-to-B
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A \(2^5\)
B \(2^6\)
C (6)
D \(3^2\)
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Correct Answer
B. \(2^6\)
Step 1
Concept
Here (n\(A\times B\)=2\cdot3=6), so the number of relations is \(2^6\). Count the pairs in \(A\times B\) first.
Step 2
Why this answer is correct
The correct answer is B. \(2^6\). Here (n\(A\times B\)=2\cdot3=6), so the number of relations is \(2^6\). Count the pairs in \(A\times B\) first.
Step 3
Exam Tip
(n\(A\times B\)=2\cdot3=6), इसलिए संबंधों की संख्या \(2^6\) है। पहले \(A\times B\) के pairs गिनें।
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यदि \(R=\{(1,2),(2,4),(3,6)\}\) है, तो (R) को set-builder रूप में कैसे लिखा जा सकता है?
If \(R=\{(1,2),(2,4),(3,6)\}\), how can (R) be written in set-builder form?
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#set-builder
#pattern
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A \(R=\{(x,y):y=x\}\)
B \(R=\{(x,y):y=2x\}\)
C \(R=\{(x,y):x=2y\}\)
D \(R=\{(x,y):x+y=2\}\)
Explanation opens after your attempt
Correct Answer
B. \(R=\{(x,y):y=2x\}\)
Step 1
Concept
In every pair, the second component is (2) times the first. Therefore, the rule is (y=2x).
Step 2
Why this answer is correct
The correct answer is B. \(R=\{(x,y):y=2x\}\). In every pair, the second component is (2) times the first. Therefore, the rule is (y=2x).
Step 3
Exam Tip
हर pair में दूसरा घटक पहले का (2) गुना है। इसलिए नियम (y=2x) है।
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यदि \(R=\{(a,b):a-b=0\}\) है, तो (R) में किस प्रकार के pairs होंगे?
If \(R=\{(a,b):a-b=0\}\), what type of pairs will be in (R)?
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#condition
#equality
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A जहाँ (a>b) / where (a>b)
B जहाँ (a<b) / where (a<b)
C जहाँ (a=b) / where (a=b)
D जहाँ (a+b=0) / where (a+b=0)
Explanation opens after your attempt
Correct Answer
C. जहाँ (a=b) / where (a=b)
Step 1
Concept
From (a-b=0), we get (a=b). In such questions, simplify the equation.
Step 2
Why this answer is correct
The correct answer is C. जहाँ (a=b) / where (a=b). From (a-b=0), we get (a=b). In such questions, simplify the equation.
Step 3
Exam Tip
(a-b=0) से (a=b) मिलता है। ऐसे प्रश्न में समीकरण को सरल करें।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a<b\}\) है, तो ( (2,4) ) के बारे में सही कथन क्या है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a<b\}\), what is true about ( (2,4) )?
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#inequality
#membership
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A \((2,4)\in R\)
B \((2,4)\notin R\)
C \((4,2)\in R\)
D (2=4)
Explanation opens after your attempt
Correct Answer
A. \((2,4)\in R\)
Step 1
Concept
Since (2<4), \((2,4)\in R\). Check a pair by substituting it in the relation condition.
Step 2
Why this answer is correct
The correct answer is A. \((2,4)\in R\). Since (2<4), \((2,4)\in R\). Check a pair by substituting it in the relation condition.
Step 3
Exam Tip
क्योंकि (2<4), इसलिए \((2,4)\in R\) है। relation की condition में pair को रखकर जांचें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a+b=4\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a+b=4\}\), which pair is in (R)?
#relations
#sum-condition
#ordered-pairs
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A ( (1,1) )
B ( (1,3) )
C ( (2,3) )
D ( (3,3) )
Explanation opens after your attempt
Correct Answer
B. ( (1,3) )
Step 1
Concept
Here (1+3=4), so ( (1,3) ) belongs to the relation. The pair satisfying the condition is correct.
Step 2
Why this answer is correct
The correct answer is B. ( (1,3) ). Here (1+3=4), so ( (1,3) ) belongs to the relation. The pair satisfying the condition is correct.
Step 3
Exam Tip
(1+3=4), इसलिए ( (1,3) ) relation में है। जो pair condition पूरी करे वही सही होता है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3)\}\) है, तो (R) reflexive है या नहीं?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3)\}\), is (R) reflexive?
#relations
#reflexive
#easy
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A हाँ / Yes
B नहीं / No
C केवल (1) के लिए / only for (1)
D निर्धारित नहीं / Cannot be decided
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
For every \(a\in A\), \((a,a)\in R\). To check reflexive, look for all diagonal pairs.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. For every \(a\in A\), \((a,a)\in R\). To check reflexive, look for all diagonal pairs.
Step 3
Exam Tip
हर \(a\in A\) के लिए \((a,a)\in R\) है। Reflexive जांच में सभी diagonal pairs देखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2)\}\) है, तो (R) reflexive क्यों नहीं है?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2)\}\), why is (R) not reflexive?
#relations
#reflexive
#missing-pair
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A क्योंकि ( (1,1) ) है / because ( (1,1) ) is present
B क्योंकि ( (2,2) ) है / because ( (2,2) ) is present
C क्योंकि ( (3,3) ) नहीं है / because ( (3,3) ) is absent
D क्योंकि ( (1,2) ) नहीं है / because ( (1,2) ) is absent
Explanation opens after your attempt
Correct Answer
C. क्योंकि ( (3,3) ) नहीं है / because ( (3,3) ) is absent
Step 1
Concept
For reflexive relation, ( (3,3) ) must also be present. If one diagonal pair is missing, the relation is not reflexive.
Step 2
Why this answer is correct
The correct answer is C. क्योंकि ( (3,3) ) नहीं है / because ( (3,3) ) is absent. For reflexive relation, ( (3,3) ) must also be present. If one diagonal pair is missing, the relation is not reflexive.
Step 3
Exam Tip
Reflexive होने के लिए ( (3,3) ) भी होना चाहिए। एक diagonal pair missing हो तो relation reflexive नहीं होता।
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यदि \(R=\{(1,2),(2,1)\}\) है, तो symmetric property के लिए कौन-सा कारण सही है?
If \(R=\{(1,2),(2,1)\}\), which reason supports symmetric property?
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#symmetric
#property
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A ( (1,2) ) के साथ ( (2,1) ) भी है / ( (2,1) ) is present with ( (1,2) )
B ( (1,1) ) missing है / ( (1,1) ) is missing
C ( (2,2) ) missing है / ( (2,2) ) is missing
D कोई pair नहीं है / no pair is present
Explanation opens after your attempt
Correct Answer
A. ( (1,2) ) के साथ ( (2,1) ) भी है / ( (2,1) ) is present with ( (1,2) )
Step 1
Concept
In symmetric relation, if \((a,b)\in R\), then \((b,a)\in R\) must also be present. Here both ( (1,2) ) and ( (2,1) ) are present.
Step 2
Why this answer is correct
The correct answer is A. ( (1,2) ) के साथ ( (2,1) ) भी है / ( (2,1) ) is present with ( (1,2) ). In symmetric relation, if \((a,b)\in R\), then \((b,a)\in R\) must also be present. Here both ( (1,2) ) and ( (2,1) ) are present.
Step 3
Exam Tip
Symmetric में \((a,b)\in R\) हो तो \((b,a)\in R\) भी चाहिए। यहाँ ( (1,2) ) और ( (2,1) ) दोनों हैं।
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यदि \(R=\{(1,2)\}\) है, तो (R) symmetric क्यों नहीं है?
If \(R=\{(1,2)\}\), why is (R) not symmetric?
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#symmetric
#reverse-pair
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A ( (1,1) ) missing है / ( (1,1) ) is missing
B ( (2,1) ) missing है / ( (2,1) ) is missing
C ( (2,2) ) missing है / ( (2,2) ) is missing
D ( (1,2) ) present है / ( (1,2) ) is present
Explanation opens after your attempt
Correct Answer
B. ( (2,1) ) missing है / ( (2,1) ) is missing
Step 1
Concept
Here \((1,2)\in R\), but the reverse pair ( (2,1) ) is absent. A reverse pair is necessary for symmetry.
Step 2
Why this answer is correct
The correct answer is B. ( (2,1) ) missing है / ( (2,1) ) is missing. Here \((1,2)\in R\), but the reverse pair ( (2,1) ) is absent. A reverse pair is necessary for symmetry.
Step 3
Exam Tip
\((1,2)\in R\) है लेकिन उल्टा pair ( (2,1) ) नहीं है। Symmetric के लिए reverse pair जरूरी है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,2),(2,3),(1,3)\}\) है, तो कौन-सी बात transitive property को दिखाती है?
If \(A=\{1,2,3\}\) and \(R=\{(1,2),(2,3),(1,3)\}\), which fact shows transitive property?
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#transitive
#property
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A ( (1,2) ) और ( (2,3) ) से ( (1,3) ) है / ( (1,2) ) and ( (2,3) ) give ( (1,3) )
B ( (1,1) ) है / ( (1,1) ) is present
C ( (3,1) ) है / ( (3,1) ) is present
D ( (2,2) ) है / ( (2,2) ) is present
Explanation opens after your attempt
Correct Answer
A. ( (1,2) ) और ( (2,3) ) से ( (1,3) ) है / ( (1,2) ) and ( (2,3) ) give ( (1,3) )
Step 1
Concept
In transitive relation, if ( (a,b) ) and ( (b,c) ) are present, then ( (a,c) ) is needed. Here ( (1,3) ) is present.
Step 2
Why this answer is correct
The correct answer is A. ( (1,2) ) और ( (2,3) ) से ( (1,3) ) है / ( (1,2) ) and ( (2,3) ) give ( (1,3) ). In transitive relation, if ( (a,b) ) and ( (b,c) ) are present, then ( (a,c) ) is needed. Here ( (1,3) ) is present.
Step 3
Exam Tip
Transitive में ( (a,b) ) और ( (b,c) ) हों तो ( (a,c) ) चाहिए। यहाँ ( (1,3) ) मौजूद है।
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यदि \(R=\{(1,2),(2,3)\}\) है, तो (R) transitive क्यों नहीं है?
If \(R=\{(1,2),(2,3)\}\), why is (R) not transitive?
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#transitive
#missing-pair
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A ( (1,3) ) missing है / ( (1,3) ) is missing
B ( (2,1) ) missing है / ( (2,1) ) is missing
C ( (3,2) ) missing है / ( (3,2) ) is missing
D ( (1,1) ) missing है / ( (1,1) ) is missing
Explanation opens after your attempt
Correct Answer
A. ( (1,3) ) missing है / ( (1,3) ) is missing
Step 1
Concept
From ( (1,2) ) and ( (2,3) ), ( (1,3) ) is required. Without it, the relation is not transitive.
Step 2
Why this answer is correct
The correct answer is A. ( (1,3) ) missing है / ( (1,3) ) is missing. From ( (1,2) ) and ( (2,3) ), ( (1,3) ) is required. Without it, the relation is not transitive.
Step 3
Exam Tip
( (1,2) ) और ( (2,3) ) से ( (1,3) ) जरूरी है। उसके बिना relation transitive नहीं है।
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यदि \(A=\{1,2\}\) और \(R=A\times A\) है, तो (R) में कौन-सा pair होगा?
If \(A=\{1,2\}\) and \(R=A\times A\), which pair will be in (R)?
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#membership
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A ( (1,3) )
B ( (2,1) )
C ( (3,1) )
D ( (2,3) )
Explanation opens after your attempt
Correct Answer
B. ( (2,1) )
Step 1
Concept
In \(A\times A\), both components must come from (A). Both components of ( (2,1) ) are in (A).
Step 2
Why this answer is correct
The correct answer is B. ( (2,1) ). In \(A\times A\), both components must come from (A). Both components of ( (2,1) ) are in (A).
Step 3
Exam Tip
\(A\times A\) में दोनों घटक (A) से होने चाहिए। ( (2,1) ) के दोनों घटक (A) में हैं।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(1,2),(2,2)\}\) है, तो (R) में कितने ordered pairs हैं?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(1,2),(2,2)\}\), how many ordered pairs are in (R)?
#relations
#counting-pairs
#basic
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A (2)
B (3)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
There are three ordered pairs listed in (R). While counting, count pairs and not repeated elements.
Step 2
Why this answer is correct
The correct answer is B. (3). There are three ordered pairs listed in (R). While counting, count pairs and not repeated elements.
Step 3
Exam Tip
दिए गए (R) में तीन ordered pairs लिखे हैं। गिनती करते समय repeated elements नहीं बल्कि pairs गिनें।
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\(यदि (R={(x,y):x+y\) is even\(}) है और (x=1), (y=3) हैं, तो ( (1,3) ) के बारे में सही क्या है\)?
\(If (R={(x,y):x+y\) is even\(}) and (x=1), (y=3), what is true about ( (1,3) )\)?
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A \((1,3)\in R\)
B \((1,3)\notin R\)
C \(R=\varnothing\)
D (x=y)
Explanation opens after your attempt
Correct Answer
A. \((1,3)\in R\)
Step 1
Concept
Since (1+3=4) is even, \((1,3)\in R\). Substitute the values in the condition to decide.
Step 2
Why this answer is correct
The correct answer is A. \((1,3)\in R\). Since (1+3=4) is even, \((1,3)\in R\). Substitute the values in the condition to decide.
Step 3
Exam Tip
(1+3=4) सम है, इसलिए \((1,3)\in R\) है। condition में मान रखकर निर्णय लें।
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यदि \(R={(x,y):x\) divides (y}) है, तो कौन-सा pair (R) में है?
If \(R={(x,y):x\) divides (y}), which pair is in (R)?
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A ( (2,5) )
B ( (3,8) )
C ( (2,6) )
D ( (5,2) )
Explanation opens after your attempt
Correct Answer
C. ( (2,6) )
Step 1
Concept
The number (2) divides (6). In a divisibility relation, order is very important.
Step 2
Why this answer is correct
The correct answer is C. ( (2,6) ). The number (2) divides (6). In a divisibility relation, order is very important.
Step 3
Exam Tip
(2) संख्या (6) को divide करती है। divisibility relation में order बहुत महत्वपूर्ण होता है।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a=b\}\) है, तो (R) में कितने pairs होंगे?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a=b\}\), how many pairs will be in (R)?
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
When (a=b), the pairs are ( (1,1),(2,2),(3,3),(4,4) ). In identity relation, the number of pairs is (n(A)).
Step 2
Why this answer is correct
The correct answer is C. (4). When (a=b), the pairs are ( (1,1),(2,2),(3,3),(4,4) ). In identity relation, the number of pairs is (n(A)).
Step 3
Exam Tip
(a=b) होने पर pairs ( (1,1),(2,2),(3,3),(4,4) ) हैं। पहचान relation में pairs की संख्या (n(A)) होती है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a>b\}\) है, तो कौन-सा pair (R) में नहीं है?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a>b\}\), which pair is not in (R)?
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A ( (2,1) )
B ( (3,1) )
C ( (3,2) )
D ( (1,3) )
Explanation opens after your attempt
Correct Answer
D. ( (1,3) )
Step 1
Concept
The statement (1>3) is false, so \((1,3)\notin R\). Do not change the order in an inequality relation.
Step 2
Why this answer is correct
The correct answer is D. ( (1,3) ). The statement (1>3) is false, so \((1,3)\notin R\). Do not change the order in an inequality relation.
Step 3
Exam Tip
(1>3) असत्य है, इसलिए \((1,3)\notin R\)। inequality relation में ordered pair का क्रम न बदलें।
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यदि \(R=\{(1,2),(2,1),(2,3),(3,2)\}\) है, तो (R) में कौन-सा reverse pair ( (2,3) ) के साथ है?
If \(R=\{(1,2),(2,1),(2,3),(3,2)\}\), which reverse pair is present with ( (2,3) )?
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#reverse
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A ( (3,2) )
B ( (2,1) )
C ( (1,2) )
D ( (3,3) )
Explanation opens after your attempt
Correct Answer
A. ( (3,2) )
Step 1
Concept
The reverse pair of ( (2,3) ) is ( (3,2) ). In symmetry questions, check the reversed ordered pair.
Step 2
Why this answer is correct
The correct answer is A. ( (3,2) ). The reverse pair of ( (2,3) ) is ( (3,2) ). In symmetry questions, check the reversed ordered pair.
Step 3
Exam Tip
( (2,3) ) का reverse pair ( (3,2) ) होता है। Symmetry questions में उल्टा ordered pair देखें।
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यदि \(A=\{1,2\}\) है, तो (A) पर reflexive relation में कौन-से pairs अनिवार्य हैं?
If \(A=\{1,2\}\), which pairs are compulsory in a reflexive relation on (A)?
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A ( (1,2),(2,1) )
B ( (1,1),(2,2) )
C ( (1,1),(1,2) )
D ( (2,1),(2,2) )
Explanation opens after your attempt
Correct Answer
B. ( (1,1),(2,2) )
Step 1
Concept
A reflexive relation must contain the diagonal pair of every element. For \(A=\{1,2\}\), ( (1,1) ) and ( (2,2) ) are compulsory.
Step 2
Why this answer is correct
The correct answer is B. ( (1,1),(2,2) ). A reflexive relation must contain the diagonal pair of every element. For \(A=\{1,2\}\), ( (1,1) ) and ( (2,2) ) are compulsory.
Step 3
Exam Tip
Reflexive relation में हर तत्व का diagonal pair होना चाहिए। \(A=\{1,2\}\) के लिए ( (1,1) ) और ( (2,2) ) अनिवार्य हैं।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\) है, तो (R) reflexive है या नहीं?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\), is (R) reflexive?
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A हाँ / Yes
B नहीं / No
C केवल symmetric / only symmetric
D केवल empty / only empty
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
It contains all ( (1,1),(2,2),(3,3) ). Extra pairs do not spoil reflexive property.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. It contains all ( (1,1),(2,2),(3,3) ). Extra pairs do not spoil reflexive property.
Step 3
Exam Tip
इसमें ( (1,1),(2,2),(3,3) ) सभी हैं। Extra pairs reflexive property को खराब नहीं करते।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,2),(2,1),(2,3)\}\) है, तो (R) symmetric क्यों नहीं है?
If \(A=\{1,2,3\}\) and \(R=\{(1,2),(2,1),(2,3)\}\), why is (R) not symmetric?
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A ( (3,2) ) missing है / ( (3,2) ) is missing
B ( (1,2) ) missing है / ( (1,2) ) is missing
C ( (2,1) ) missing है / ( (2,1) ) is missing
D ( (1,1) ) missing है / ( (1,1) ) is missing
Explanation opens after your attempt
Correct Answer
A. ( (3,2) ) missing है / ( (3,2) ) is missing
Step 1
Concept
Here \((2,3)\in R\), but \((3,2)\notin R\). One missing reverse pair breaks symmetry.
Step 2
Why this answer is correct
The correct answer is A. ( (3,2) ) missing है / ( (3,2) ) is missing. Here \((2,3)\in R\), but \((3,2)\notin R\). One missing reverse pair breaks symmetry.
Step 3
Exam Tip
\((2,3)\in R\) है लेकिन \((3,2)\notin R\) है। एक reverse pair missing होने से symmetry टूट जाती है।
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यदि \(R=\{(1,1),(1,2),(2,2)\}\) है, तो transitive check में ( (1,2) ) और ( (2,2) ) से कौन-सा pair चाहिए?
If \(R=\{(1,1),(1,2),(2,2)\}\), which pair is needed from ( (1,2) ) and ( (2,2) ) in transitive check?
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A ( (1,2) )
B ( (2,1) )
C ( (1,1) )
D ( (2,2) )
Explanation opens after your attempt
Correct Answer
A. ( (1,2) )
Step 1
Concept
From ( (a,b)=(1,2) ) and ( (b,c)=(2,2) ), we need ( (a,c)=(1,2) ). This pair is already present.
Step 2
Why this answer is correct
The correct answer is A. ( (1,2) ). From ( (a,b)=(1,2) ) and ( (b,c)=(2,2) ), we need ( (a,c)=(1,2) ). This pair is already present.
Step 3
Exam Tip
( (a,b)=(1,2) ) और ( (b,c)=(2,2) ) से ( (a,c)=(1,2) ) चाहिए। यह pair पहले से मौजूद है।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):b=a+1\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):b=a+1\}\), which pair is in (R)?
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A ( (1,3) )
B ( (2,3) )
C ( (3,2) )
D ( (4,1) )
Explanation opens after your attempt
Correct Answer
B. ( (2,3) )
Step 1
Concept
Since (3=2+1), ( (2,3) ) satisfies the condition. Keep the first and second components in the correct order.
Step 2
Why this answer is correct
The correct answer is B. ( (2,3) ). Since (3=2+1), ( (2,3) ) satisfies the condition. Keep the first and second components in the correct order.
Step 3
Exam Tip
(3=2+1), इसलिए ( (2,3) ) condition पूरी करता है। पहले और दूसरे घटक को सही क्रम में रखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a+b=5\}\) है, तो (R) में कितने pairs हैं?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a+b=5\}\), how many pairs are in (R)?
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#sum-condition
#counting
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The pairs from the given set are ( (2,3) ) and ( (3,2) ). In ordered pairs, ( (2,3) ) and ( (3,2) ) are different.
Step 2
Why this answer is correct
The correct answer is B. (2). The pairs from the given set are ( (2,3) ) and ( (3,2) ). In ordered pairs, ( (2,3) ) and ( (3,2) ) are different.
Step 3
Exam Tip
दिए गए set से pairs ( (2,3) ) और ( (3,2) ) बनते हैं। ordered pairs में ( (2,3) ) और ( (3,2) ) अलग होते हैं।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a\le b\}\) है, तो कौन-सा pair (R) में नहीं है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a\le b\}\), which pair is not in (R)?
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A ( (1,1) )
B ( (2,4) )
C ( (3,3) )
D ( (4,2) )
Explanation opens after your attempt
Correct Answer
D. ( (4,2) )
Step 1
Concept
The statement \(4\le2\) is false, so \((4,2)\notin R\). Watch the direction of the inequality carefully.
Step 2
Why this answer is correct
The correct answer is D. ( (4,2) ). The statement \(4\le2\) is false, so \((4,2)\notin R\). Watch the direction of the inequality carefully.
Step 3
Exam Tip
\(4\le2\) असत्य है, इसलिए \((4,2)\notin R\)। inequality में direction ध्यान से देखें।
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यदि \(R=\{(x,y):x=y+1\}\) है, तो कौन-सा ordered pair (R) में होगा?
If \(R=\{(x,y):x=y+1\}\), which ordered pair will be in (R)?
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A ( (2,1) )
B ( (1,2) )
C ( (3,5) )
D ( (1,1) )
Explanation opens after your attempt
Correct Answer
A. ( (2,1) )
Step 1
Concept
Since (2=1+1), ( (2,1) ) belongs to the relation. Substitute the correct components for (x) and (y).
Step 2
Why this answer is correct
The correct answer is A. ( (2,1) ). Since (2=1+1), ( (2,1) ) belongs to the relation. Substitute the correct components for (x) and (y).
Step 3
Exam Tip
(2=1+1), इसलिए ( (2,1) ) relation में है। condition में (x) और (y) की जगह सही घटक रखें।
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यदि \(A=\{1,2,3\}\) है, तो पहचान संबंध \(I_A\) क्या होगा?
If \(A=\{1,2,3\}\), what is the identity relation \(I_A\)?
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A (I_A={(1,2),(2,3)})
B (I_A={(1,1),(2,2),(3,3)})
C \(I_A=\varnothing\)
D \(I_A=A\)
Explanation opens after your attempt
Correct Answer
B. (I_A={(1,1),(2,2),(3,3)})
Step 1
Concept
The identity relation contains only pairs of the form ( (a,a) ). Pair each element with itself.
Step 2
Why this answer is correct
The correct answer is B. (I_A={(1,1),(2,2),(3,3)}). The identity relation contains only pairs of the form ( (a,a) ). Pair each element with itself.
Step 3
Exam Tip
पहचान संबंध में केवल ( (a,a) ) प्रकार के pairs होते हैं। हर element को अपने साथ pair करें।
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यदि \(A=\{1,2,3\}\) और \(R=\varnothing\) है, तो (R) symmetric है या नहीं?
If \(A=\{1,2,3\}\) and \(R=\varnothing\), is (R) symmetric?
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#empty-relation
#symmetric
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A हाँ / Yes
B नहीं / No
C केवल reflexive / only reflexive
D केवल universal / only universal
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
In an empty relation, there is no pair that can break symmetry. Hence the empty relation is considered symmetric.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. In an empty relation, there is no pair that can break symmetry. Hence the empty relation is considered symmetric.
Step 3
Exam Tip
खाली relation में symmetry तोड़ने वाला कोई pair नहीं है। इसलिए empty relation symmetric माना जाता है।
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यदि \(A=\{1,2\}\) और \(R=\varnothing\) है, तो (R) reflexive है या नहीं?
If \(A=\{1,2\}\) and \(R=\varnothing\), is (R) reflexive?
#relations
#empty-relation
#reflexive
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A हाँ / Yes
B नहीं / No
C सिर्फ (1) के लिए / only for (1)
D निर्धारित नहीं / Cannot be decided
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Step 1
Concept
For reflexive relation, ( (1,1) ) and ( (2,2) ) are needed. These pairs are absent in the empty relation.
Step 2
Why this answer is correct
The correct answer is B. नहीं / No. For reflexive relation, ( (1,1) ) and ( (2,2) ) are needed. These pairs are absent in the empty relation.
Step 3
Exam Tip
Reflexive के लिए ( (1,1) ) और ( (2,2) ) चाहिए। Empty relation में ये pairs नहीं हैं।
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यदि \(A=\{1,2\}\) और \(R=A\times A\) है, तो (R) reflexive है या नहीं?
If \(A=\{1,2\}\) and \(R=A\times A\), is (R) reflexive?
#relations
#universal-relation
#reflexive
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A हाँ / Yes
B नहीं / No
C केवल ( (1,2) ) के कारण / only due to ( (1,2) )
D निर्भर करता है / Depends
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
The set \(A\times A\) includes both ( (1,1) ) and ( (2,2) ). A universal relation is always reflexive.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. The set \(A\times A\) includes both ( (1,1) ) and ( (2,2) ). A universal relation is always reflexive.
Step 3
Exam Tip
\(A\times A\) में ( (1,1) ) और ( (2,2) ) दोनों शामिल हैं। Universal relation हमेशा reflexive होता है।
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यदि \(A=\{1,2\}\) और \(R=A\times A\) है, तो (R) symmetric है या नहीं?
If \(A=\{1,2\}\) and \(R=A\times A\), is (R) symmetric?
#relations
#universal-relation
#symmetric
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A हाँ / Yes
B नहीं / No
C केवल empty relation / only empty relation
D केवल identity relation / only identity relation
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
In \(A\times A\), every pair has its reverse pair too. Hence the universal relation is symmetric.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. In \(A\times A\), every pair has its reverse pair too. Hence the universal relation is symmetric.
Step 3
Exam Tip
\(A\times A\) में हर pair के साथ उसका reverse pair भी होता है। इसलिए universal relation symmetric है।
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यदि \(A=\{1,2\}\) और \(R=A\times A\) है, तो (R) transitive है या नहीं?
If \(A=\{1,2\}\) and \(R=A\times A\), is (R) transitive?
#relations
#universal-relation
#transitive
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A हाँ / Yes
B नहीं / No
C केवल symmetric / only symmetric
D केवल reflexive / only reflexive
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
The set \(A\times A\) contains all possible pairs, so the transitive condition is satisfied. The universal relation is also transitive.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. The set \(A\times A\) contains all possible pairs, so the transitive condition is satisfied. The universal relation is also transitive.
Step 3
Exam Tip
\(A\times A\) में सभी possible pairs होते हैं, इसलिए transitive condition पूरी होती है। Universal relation transitive भी होता है।
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यदि \(R=\{(1,1),(2,2)\}\) है, तो (R) symmetric क्यों है?
If \(R=\{(1,1),(2,2)\}\), why is (R) symmetric?
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A हर pair अपना reverse खुद है / each pair is its own reverse
B कोई diagonal pair नहीं है / no diagonal pair exists
C ( (1,2) ) मौजूद है / ( (1,2) ) is present
D ( (2,1) ) missing है / ( (2,1) ) is missing
Explanation opens after your attempt
Correct Answer
A. हर pair अपना reverse खुद है / each pair is its own reverse
Step 1
Concept
The reverse of a diagonal pair ( (a,a) ) is the same pair ( (a,a) ). Hence a relation with only diagonal pairs is symmetric.
Step 2
Why this answer is correct
The correct answer is A. हर pair अपना reverse खुद है / each pair is its own reverse. The reverse of a diagonal pair ( (a,a) ) is the same pair ( (a,a) ). Hence a relation with only diagonal pairs is symmetric.
Step 3
Exam Tip
Diagonal pair ( (a,a) ) का reverse भी ( (a,a) ) ही होता है। इसलिए केवल diagonal pairs वाला relation symmetric है।
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यदि \(A=\{1,2,3,4,5\}\) और \(R={(a,b):a\) is one less than (b}) है, तो कौन-सा pair सही है?
If \(A=\{1,2,3,4,5\}\) and \(R={(a,b):a\) is one less than (b}), which pair is correct?
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A ( (4,3) )
B ( (3,4) )
C ( (5,5) )
D ( (2,4) )
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Correct Answer
B. ( (3,4) )
Step 1
Concept
The number (3) is one less than (4), so ( (3,4) ) is correct. Convert word conditions into equations.
Step 2
Why this answer is correct
The correct answer is B. ( (3,4) ). The number (3) is one less than (4), so ( (3,4) ) is correct. Convert word conditions into equations.
Step 3
Exam Tip
(3) संख्या (4) से एक कम है, इसलिए ( (3,4) ) सही है। शब्दों वाली condition को equation में बदलें।
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यदि \(R={(a,b):a\) and (b) have same parity(}) है, तो कौन-सा pair (R) में है?
If \(R={(a,b):a\) and (b) have same parity(}), which pair is in (R)?
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A ( (1,2) )
B ( (2,3) )
C ( (3,5) )
D ( (4,7) )
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Correct Answer
C. ( (3,5) )
Step 1
Concept
Both (3) and (5) are odd, so they have the same parity. In a parity relation, even-even or odd-odd pairs are correct.
Step 2
Why this answer is correct
The correct answer is C. ( (3,5) ). Both (3) and (5) are odd, so they have the same parity. In a parity relation, even-even or odd-odd pairs are correct.
Step 3
Exam Tip
(3) और (5) दोनों विषम हैं, इसलिए same parity है। parity relation में सम-सम या विषम-विषम pair सही होता है।
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यदि \(A=\{1,2,3\}\) और \(R={(a,b):a+b\) is odd(}) है, तो कौन-सा pair (R) में नहीं है?
If \(A=\{1,2,3\}\) and \(R={(a,b):a+b\) is odd(}), which pair is not in (R)?
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A ( (1,2) )
B ( (2,3) )
C ( (1,3) )
D ( (2,1) )
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Correct Answer
C. ( (1,3) )
Step 1
Concept
Since (1+3=4) is even, ( (1,3) ) is not in the odd-sum relation. Always check the parity of the sum.
Step 2
Why this answer is correct
The correct answer is C. ( (1,3) ). Since (1+3=4) is even, ( (1,3) ) is not in the odd-sum relation. Always check the parity of the sum.
Step 3
Exam Tip
(1+3=4) सम है, इसलिए ( (1,3) ) odd-sum relation में नहीं है। sum की parity जरूर जांचें।
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यदि \(R=\{(1,1),(1,2),(2,1),(2,2)\}\) है, तो यह \(A=\{1,2\}\) पर कौन-सा संबंध है?
If \(R=\{(1,1),(1,2),(2,1),(2,2)\}\), what relation is it on \(A=\{1,2\}\)?
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A खाली संबंध / Empty relation
B पहचान संबंध / Identity relation
C सार्वत्रिक संबंध / Universal relation
D केवल symmetric नहीं / Not symmetric only
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Correct Answer
C. सार्वत्रिक संबंध / Universal relation
Step 1
Concept
It contains all pairs of \(A\times A\). Therefore, it is the universal relation.
Step 2
Why this answer is correct
The correct answer is C. सार्वत्रिक संबंध / Universal relation. It contains all pairs of \(A\times A\). Therefore, it is the universal relation.
Step 3
Exam Tip
यह \(A\times A\) के सभी pairs रखता है। इसलिए यह universal relation है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3),(1,3)\}\) है, तो (R) reflexive है या नहीं?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,3)\}\), is (R) reflexive?
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A हाँ / Yes
B नहीं / No
C सिर्फ symmetric / only symmetric
D सिर्फ transitive / only transitive
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Correct Answer
A. हाँ / Yes
Step 1
Concept
All diagonal pairs ( (1,1),(2,2),(3,3) ) are present. The extra pair ( (1,3) ) does not stop reflexivity.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. All diagonal pairs ( (1,1),(2,2),(3,3) ) are present. The extra pair ( (1,3) ) does not stop reflexivity.
Step 3
Exam Tip
सभी diagonal pairs ( (1,1),(2,2),(3,3) ) मौजूद हैं। Extra pair ( (1,3) ) reflexive होने से नहीं रोकता।
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यदि \(R=\{(1,2),(2,1),(3,3)\}\) है, तो (R) symmetric है या नहीं?
If \(R=\{(1,2),(2,1),(3,3)\}\), is (R) symmetric?
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A हाँ / Yes
B नहीं / No
C केवल reflexive / only reflexive
D निर्धारित नहीं / Cannot be decided
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Correct Answer
A. हाँ / Yes
Step 1
Concept
The pair ( (2,1) ) is present with ( (1,2) ), and ( (3,3) ) is its own reverse. Hence the relation is symmetric.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. The pair ( (2,1) ) is present with ( (1,2) ), and ( (3,3) ) is its own reverse. Hence the relation is symmetric.
Step 3
Exam Tip
( (1,2) ) के साथ ( (2,1) ) है और ( (3,3) ) अपना reverse खुद है। इसलिए relation symmetric है।
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यदि \(R=\{(1,2),(2,3),(1,3),(3,3)\}\) है, तो ( (1,2) ) और ( (2,3) ) transitive condition में क्या मांगते हैं?
If \(R=\{(1,2),(2,3),(1,3),(3,3)\}\), what do ( (1,2) ) and ( (2,3) ) require in transitive condition?
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A ( (1,3) )
B ( (3,1) )
C ( (2,1) )
D ( (2,2) )
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Correct Answer
A. ( (1,3) )
Step 1
Concept
By the transitive rule, ( (1,2) ) and ( (2,3) ) require ( (1,3) ). This pair is present in the relation.
Step 2
Why this answer is correct
The correct answer is A. ( (1,3) ). By the transitive rule, ( (1,2) ) and ( (2,3) ) require ( (1,3) ). This pair is present in the relation.
Step 3
Exam Tip
Transitive rule के अनुसार ( (1,2) ) और ( (2,3) ) से ( (1,3) ) चाहिए। यह pair relation में मौजूद है।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a+b=6\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a+b=6\}\), which pair is in (R)?
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A ( (1,4) )
B ( (2,4) )
C ( (3,2) )
D ( (4,1) )
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Correct Answer
B. ( (2,4) )
Step 1
Concept
Since (2+4=6), ( (2,4) ) is correct. Check the condition while staying inside the given set.
Step 2
Why this answer is correct
The correct answer is B. ( (2,4) ). Since (2+4=6), ( (2,4) ) is correct. Check the condition while staying inside the given set.
Step 3
Exam Tip
(2+4=6), इसलिए ( (2,4) ) सही है। दिए गए set के अंदर रहकर condition जांचें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a\ne b\}\) है, तो कौन-सा pair (R) में नहीं होगा?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a\ne b\}\), which pair will not be in (R)?
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A ( (1,2) )
B ( (2,3) )
C ( (3,1) )
D ( (2,2) )
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Correct Answer
D. ( (2,2) )
Step 1
Concept
In ( (2,2) ), both components are equal, so \(a\ne b\) is not satisfied. Diagonal pairs do not appear in a not-equal relation.
Step 2
Why this answer is correct
The correct answer is D. ( (2,2) ). In ( (2,2) ), both components are equal, so \(a\ne b\) is not satisfied. Diagonal pairs do not appear in a not-equal relation.
Step 3
Exam Tip
( (2,2) ) में दोनों घटक बराबर हैं, इसलिए \(a\ne b\) पूरी नहीं होती। Not equal relation में diagonal pairs नहीं आते।
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