यदि \(A=\{2,4,6\}\) और \(B=\{1,3\}\) हैं, तो (A) से (B) तक संबंध किसका उपसमुच्चय होगा?
If \(A=\{2,4,6\}\) and \(B=\{1,3\}\), then a relation from (A) to (B) will be a subset of what?
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#definition
#cartesian-product
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A (A)
B (B)
C \(A\times B\)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
C. \(A\times B\)
Step 1
Concept
A relation from (A) to (B) is always a subset of \(A\times B\). In exams, identify the Cartesian product first.
Step 2
Why this answer is correct
The correct answer is C. \(A\times B\). A relation from (A) to (B) is always a subset of \(A\times B\). In exams, identify the Cartesian product first.
Step 3
Exam Tip
संबंध (A) से (B) तक हमेशा \(A\times B\) का उपसमुच्चय होता है। परीक्षा में पहले कार्तीय गुणनफल पहचानें।
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यदि \(R=\{(1,3),(2,4),(3,5)\}\) है, तो (R) का परिभाषा क्षेत्र क्या है?
If \(R=\{(1,3),(2,4),(3,5)\}\), what is the domain of (R)?
#relations
#domain
#ordered-pairs
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A ( {1,2,3} )
B ( {3,4,5} )
C ( {1,2,3,4,5} )
D ( {(1,3),(2,4)} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
The domain contains the first components of the ordered pairs. Hence the domain of (R) is ( {1,2,3} ).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). The domain contains the first components of the ordered pairs. Hence the domain of (R) is ( {1,2,3} ).
Step 3
Exam Tip
परिभाषा क्षेत्र में ordered pairs के पहले घटक लिए जाते हैं। इसलिए (R) का परिभाषा क्षेत्र ( {1,2,3} ) है।
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यदि \(A=\{5,7\}\) है, तो (A) पर पहचान संबंध कौन-सा है?
If \(A=\{5,7\}\), which is the identity relation on (A)?
#relations
#identity-relation
#basic
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A \(R=\{(5,7),(7,5)\}\)
B \(R=\{(5,5),(7,7)\}\)
C \(R=\varnothing\)
D \(R=A\times A\)
Explanation opens after your attempt
Correct Answer
B. \(R=\{(5,5),(7,7)\}\)
Step 1
Concept
In the identity relation, each element is related to itself. So only ( (5,5) ) and ( (7,7) ) appear.
Step 2
Why this answer is correct
The correct answer is B. \(R=\{(5,5),(7,7)\}\). In the identity relation, each element is related to itself. So only ( (5,5) ) and ( (7,7) ) appear.
Step 3
Exam Tip
पहचान संबंध में प्रत्येक तत्व अपने साथ जुड़ता है। इसलिए केवल ( (5,5) ) और ( (7,7) ) आएंगे।
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यदि \(R=\{(2,5),(4,7),(6,9)\}\) है, तो (R) का परिसर क्या है?
If \(R=\{(2,5),(4,7),(6,9)\}\), what is the range of (R)?
#relations
#range
#ordered-pairs
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A ( {2,4,6} )
B ( {5,7,9} )
C ( {2,5,6,9} )
D ( {(5,2),(7,4),(9,6)} )
Explanation opens after your attempt
Correct Answer
B. ( {5,7,9} )
Step 1
Concept
The range contains the second components of the ordered pairs. Hence the range of (R) is ( {5,7,9} ).
Step 2
Why this answer is correct
The correct answer is B. ( {5,7,9} ). The range contains the second components of the ordered pairs. Hence the range of (R) is ( {5,7,9} ).
Step 3
Exam Tip
परिसर में ordered pairs के दूसरे घटक लिए जाते हैं। इसलिए (R) का परिसर ( {5,7,9} ) है।
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यदि \(A=\{p,q,r\}\) है, तो (A) पर सार्वत्रिक संबंध में कितने ordered pairs होंगे?
If \(A=\{p,q,r\}\), how many ordered pairs will be in the universal relation on (A)?
#relations
#universal-relation
#counting
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A (3)
B (6)
C (9)
D \(2^3\)
Explanation opens after your attempt
Step 1
Concept
The universal relation is \(A\times A\), and (n\(A\times A\)=32 =9). A universal relation contains all possible pairs.
Step 2
Why this answer is correct
The correct answer is C. (9). The universal relation is \(A\times A\), and (n\(A\times A\)=32 =9). A universal relation contains all possible pairs.
Step 3
Exam Tip
सार्वत्रिक संबंध \(A\times A\) होता है और (n\(A\times A\)=32 =9)। universal relation में सभी possible pairs शामिल होते हैं।
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यदि \(A=\{1,3,5\}\) और \(R=\{(1,3),(3,5)\}\) है, तो (R) किसका संबंध है?
If \(A=\{1,3,5\}\) and \(R=\{(1,3),(3,5)\}\), then (R) is a relation on what?
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#relation-on-set
#subset
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A (A) पर / on (A)
B (R) पर / on (R)
C \(\varnothing\) पर / on \(\varnothing\)
D \(A\cup R\) पर / on \(A\cup R\)
Explanation opens after your attempt
Correct Answer
A. (A) पर / on (A)
Step 1
Concept
Both components of the ordered pairs are taken from (A). Hence \(R\subseteq A\times A\).
Step 2
Why this answer is correct
The correct answer is A. (A) पर / on (A). Both components of the ordered pairs are taken from (A). Hence \(R\subseteq A\times A\).
Step 3
Exam Tip
दोनों ordered pairs के घटक (A) से लिए गए हैं। इसलिए \(R\subseteq A\times A\) है।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a+b=7\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a+b=7\}\), which pair is in (R)?
#relations
#sum-condition
#membership
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A ( (1,4) )
B ( (3,4) )
C ( (2,4) )
D ( (2,3) )
Explanation opens after your attempt
Correct Answer
B. ( (3,4) )
Step 1
Concept
Since (3+4=7), \((3,4)\in R\). In such questions, test the pair in the condition.
Step 2
Why this answer is correct
The correct answer is B. ( (3,4) ). Since (3+4=7), \((3,4)\in R\). In such questions, test the pair in the condition.
Step 3
Exam Tip
क्योंकि (3+4=7), इसलिए \((3,4)\in R\) है। ऐसे प्रश्नों में pair को condition में रखकर जांचें।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a+b=7\}\) है, तो (R) में कुल कितने ordered pairs हैं?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a+b=7\}\), how many ordered pairs are in (R)?
#relations
#counting-pairs
#sum
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From the given set, ( (3,4) ) and ( (4,3) ) are formed. In ordered pairs, changing the order changes the pair.
Step 2
Why this answer is correct
The correct answer is B. (2). From the given set, ( (3,4) ) and ( (4,3) ) are formed. In ordered pairs, changing the order changes the pair.
Step 3
Exam Tip
दिए गए set से ( (3,4) ) और ( (4,3) ) बनते हैं। ordered pair में क्रम बदलने से pair बदल जाता है।
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यदि \(R=\{(2,4),(3,9),(4,16)\}\) है, तो (R) का सही नियम कौन-सा है?
If \(R=\{(2,4),(3,9),(4,16)\}\), which is the correct rule for (R)?
#relations
#rule-identification
#set-builder
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A (y=x+2)
B (y=2x)
C \(y=x^2\)
D \(x=y^2\)
Explanation opens after your attempt
Correct Answer
C. \(y=x^2\)
Step 1
Concept
In every pair, the second component is the square of the first component. Therefore, the rule is \(y=x^2\).
Step 2
Why this answer is correct
The correct answer is C. \(y=x^2\). In every pair, the second component is the square of the first component. Therefore, the rule is \(y=x^2\).
Step 3
Exam Tip
हर pair में दूसरा घटक पहले घटक का वर्ग है। इसलिए नियम \(y=x^2\) है।
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यदि \(R=\{(x,y):y=x+3\}\) है, तो कौन-सा ordered pair (R) में आएगा?
If \(R=\{(x,y):y=x+3\}\), which ordered pair will belong to (R)?
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#linear-rule
#membership
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A ( (2,5) )
B ( (5,2) )
C ( (3,3) )
D ( (1,3) )
Explanation opens after your attempt
Correct Answer
A. ( (2,5) )
Step 1
Concept
Since (5=2+3), ( (2,5) ) satisfies the condition. Substitute the correct components for (x) and (y).
Step 2
Why this answer is correct
The correct answer is A. ( (2,5) ). Since (5=2+3), ( (2,5) ) satisfies the condition. Substitute the correct components for (x) and (y).
Step 3
Exam Tip
(5=2+3), इसलिए ( (2,5) ) condition पूरी करता है। (x) और (y) की जगह सही घटक रखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a<b\}\) है, तो कौन-सा pair (R) में नहीं होगा?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a<b\}\), which pair will not belong to (R)?
#relations
#inequality
#nonmembership
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A ( (1,2) )
B ( (1,3) )
C ( (2,3) )
D ( (3,1) )
Explanation opens after your attempt
Correct Answer
D. ( (3,1) )
Step 1
Concept
The statement (3<1) is false, so \((3,1)\notin R\). Order is very important in an inequality relation.
Step 2
Why this answer is correct
The correct answer is D. ( (3,1) ). The statement (3<1) is false, so \((3,1)\notin R\). Order is very important in an inequality relation.
Step 3
Exam Tip
(3<1) असत्य है, इसलिए \((3,1)\notin R\)। inequality relation में order बहुत महत्वपूर्ण है।
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यदि \(A=\{2,3,4,5\}\) और \(R=\{(a,b):a\ge b\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{2,3,4,5\}\) and \(R=\{(a,b):a\ge b\}\), which pair is in (R)?
#relations
#greater-equal
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A ( (2,5) )
B ( (3,5) )
C ( (5,3) )
D ( (2,4) )
Explanation opens after your attempt
Correct Answer
C. ( (5,3) )
Step 1
Concept
Since \(5\ge3\), \((5,3)\in R\). Put the first component on the left side of the inequality.
Step 2
Why this answer is correct
The correct answer is C. ( (5,3) ). Since \(5\ge3\), \((5,3)\in R\). Put the first component on the left side of the inequality.
Step 3
Exam Tip
क्योंकि \(5\ge3\), इसलिए \((5,3)\in R\) है। पहले घटक को inequality के बाएं भाग में रखें।
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यदि \(A=\{1,2,3,4\}\) और \(R={(a,b):a\) divides (b}) है, तो कौन-सा pair सही है?
If \(A=\{1,2,3,4\}\) and \(R={(a,b):a\) divides (b}), which pair is correct?
#relations
#divisibility
#ordered-pair
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A ( (3,2) )
B ( (4,2) )
C ( (2,4) )
D ( (4,3) )
Explanation opens after your attempt
Correct Answer
C. ( (2,4) )
Step 1
Concept
The number (2) divides (4). In a divisibility relation, ( (2,4) ) and ( (4,2) ) are not the same.
Step 2
Why this answer is correct
The correct answer is C. ( (2,4) ). The number (2) divides (4). In a divisibility relation, ( (2,4) ) and ( (4,2) ) are not the same.
Step 3
Exam Tip
(2) संख्या (4) को divide करती है। divisibility relation में ( (2,4) ) और ( (4,2) ) समान नहीं होते।
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यदि \(A=\{1,2,3\}\) है, तो (A) पर कुल कितने संबंध हो सकते हैं?
If \(A=\{1,2,3\}\), how many relations can be formed on (A)?
#relations
#number-of-relations
#counting
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A \(2^3\)
B \(3^2\)
C \(2^9\)
D \(9^2\)
Explanation opens after your attempt
Correct Answer
C. \(2^9\)
Step 1
Concept
There are \(3^2=9\) pairs in \(A\times A\), and they form \(2^9\) 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 \(A\times A\), and they form \(2^9\) subsets. The number of relations is \(2^{n(A)^2}\).
Step 3
Exam Tip
\(A\times A\) में \(3^2=9\) pairs होते हैं और उनके \(2^9\) subsets बनते हैं। संबंधों की संख्या \(2^{n(A)^2}\) होती है।
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यदि \(A=\{1,2\}\) और \(B=\{a,b,c,d\}\) हैं, तो (A) से (B) तक कुल कितने संबंध हो सकते हैं?
If \(A=\{1,2\}\) and \(B=\{a,b,c,d\}\), how many relations can be formed from (A) to (B)?
#relations
#from-A-to-B
#counting
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A \(2^4\)
B \(2^6\)
C \(2^8\)
D \(8^2\)
Explanation opens after your attempt
Correct Answer
C. \(2^8\)
Step 1
Concept
Here (n\(A\times B\)=2\cdot4=8), so the number of relations is \(2^8\). Find (n\(A\times B\)) first.
Step 2
Why this answer is correct
The correct answer is C. \(2^8\). Here (n\(A\times B\)=2\cdot4=8), so the number of relations is \(2^8\). Find (n\(A\times B\)) first.
Step 3
Exam Tip
(n\(A\times B\)=2\cdot4=8), इसलिए संबंधों की संख्या \(2^8\) है। पहले (n\(A\times B\)) निकालें।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(1,1),(2,2),(3,3)\}\) है, तो (R) स्वपरावर्ती क्यों नहीं है?
If \(A=\{1,2,3,4\}\) and \(R=\{(1,1),(2,2),(3,3)\}\), why is (R) not reflexive?
#relations
#reflexive
#missing-diagonal
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A क्योंकि ( (1,1) ) है / because ( (1,1) ) is present
B क्योंकि ( (4,4) ) नहीं है / because ( (4,4) ) is absent
C क्योंकि ( (1,2) ) नहीं है / because ( (1,2) ) is absent
D क्योंकि ( (2,3) ) नहीं है / because ( (2,3) ) is absent
Explanation opens after your attempt
Correct Answer
B. क्योंकि ( (4,4) ) नहीं है / because ( (4,4) ) is absent
Step 1
Concept
For reflexivity, \((a,a)\in R\) is needed for every \(a\in A\). Here ( (4,4) ) is missing.
Step 2
Why this answer is correct
The correct answer is B. क्योंकि ( (4,4) ) नहीं है / because ( (4,4) ) is absent. For reflexivity, \((a,a)\in R\) is needed for every \(a\in A\). Here ( (4,4) ) is missing.
Step 3
Exam Tip
स्वपरावर्ती होने के लिए हर \(a\in A\) के लिए \((a,a)\in R\) चाहिए। यहाँ ( (4,4) ) missing है।
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यदि \(A=\{x,y\}\) और \(R=\{(x,x),(y,y),(x,y)\}\) है, तो (R) स्वपरावर्ती है या नहीं?
If \(A=\{x,y\}\) and \(R=\{(x,x),(y,y),(x,y)\}\), is (R) reflexive?
#relations
#reflexive
#extra-pair
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A हाँ / Yes
B नहीं / No
C केवल रिक्त / only empty
D केवल सार्वत्रिक / only universal
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Both ( (x,x) ) and ( (y,y) ) are present. The extra pair ( (x,y) ) does not stop reflexivity.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Both ( (x,x) ) and ( (y,y) ) are present. The extra pair ( (x,y) ) does not stop reflexivity.
Step 3
Exam Tip
( (x,x) ) और ( (y,y) ) दोनों मौजूद हैं। extra pair ( (x,y) ) reflexive property को नहीं रोकता।
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यदि \(R=\{(1,4),(4,1),(2,2)\}\) है, तो (R) सममित है या नहीं?
If \(R=\{(1,4),(4,1),(2,2)\}\), is (R) symmetric?
#relations
#symmetric
#reverse-pair
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A हाँ / Yes
B नहीं / No
C केवल स्वपरावर्ती / only reflexive
D निर्धारित नहीं / Cannot be decided
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
The pair ( (4,1) ) is present with ( (1,4) ), and ( (2,2) ) is its own reverse. Hence (R) is symmetric.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. The pair ( (4,1) ) is present with ( (1,4) ), and ( (2,2) ) is its own reverse. Hence (R) is symmetric.
Step 3
Exam Tip
( (1,4) ) के साथ ( (4,1) ) है और ( (2,2) ) अपना reverse खुद है। इसलिए (R) symmetric है।
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यदि \(R=\{(2,5),(5,2),(3,4)\}\) है, तो (R) सममित क्यों नहीं है?
If \(R=\{(2,5),(5,2),(3,4)\}\), why is (R) not symmetric?
#relations
#symmetric
#missing-reverse
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A ( (2,5) ) missing है / ( (2,5) ) is missing
B ( (5,2) ) missing है / ( (5,2) ) is missing
C ( (4,3) ) missing है / ( (4,3) ) is missing
D ( (3,3) ) missing है / ( (3,3) ) is missing
Explanation opens after your attempt
Correct Answer
C. ( (4,3) ) missing है / ( (4,3) ) is missing
Step 1
Concept
Here \((3,4)\in R\), but \((4,3)\notin R\). One missing reverse pair makes the relation non-symmetric.
Step 2
Why this answer is correct
The correct answer is C. ( (4,3) ) missing है / ( (4,3) ) is missing. Here \((3,4)\in R\), but \((4,3)\notin R\). One missing reverse pair makes the relation non-symmetric.
Step 3
Exam Tip
\((3,4)\in R\) है लेकिन \((4,3)\notin R\) है। एक reverse pair missing होने से relation symmetric नहीं होता।
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यदि \(R=\{(1,2),(2,4),(1,4)\}\) है, तो (R) के transitive check में कौन-सा pair जरूरी है?
If \(R=\{(1,2),(2,4),(1,4)\}\), which pair is required in the transitive check?
#relations
#transitive
#chain
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A ( (4,1) )
B ( (1,4) )
C ( (2,1) )
D ( (4,4) )
Explanation opens after your attempt
Correct Answer
B. ( (1,4) )
Step 1
Concept
From ( (1,2) ) and ( (2,4) ), ( (1,4) ) is required. This pair is present, so this chain is complete.
Step 2
Why this answer is correct
The correct answer is B. ( (1,4) ). From ( (1,2) ) and ( (2,4) ), ( (1,4) ) is required. This pair is present, so this chain is complete.
Step 3
Exam Tip
( (1,2) ) और ( (2,4) ) से ( (1,4) ) जरूरी है। यह pair मौजूद है इसलिए यह chain पूरी है।
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यदि \(R=\{(1,3),(3,5)\}\) है, तो (R) transitive क्यों नहीं है?
If \(R=\{(1,3),(3,5)\}\), why is (R) not transitive?
#relations
#transitive
#missing-pair
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A ( (1,5) ) missing है / ( (1,5) ) is missing
B ( (3,1) ) missing है / ( (3,1) ) is missing
C ( (5,3) ) missing है / ( (5,3) ) is missing
D ( (1,1) ) missing है / ( (1,1) ) is missing
Explanation opens after your attempt
Correct Answer
A. ( (1,5) ) missing है / ( (1,5) ) is missing
Step 1
Concept
When ( (1,3) ) and ( (3,5) ) are present, ( (1,5) ) is needed. Without it, transitivity is not satisfied.
Step 2
Why this answer is correct
The correct answer is A. ( (1,5) ) missing है / ( (1,5) ) is missing. When ( (1,3) ) and ( (3,5) ) are present, ( (1,5) ) is needed. Without it, transitivity is not satisfied.
Step 3
Exam Tip
( (1,3) ) और ( (3,5) ) होने पर ( (1,5) ) चाहिए। इसके बिना transitive property पूरी नहीं होती।
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यदि \(A=\{1,2,3\}\) और \(R=\varnothing\) है, तो (R) स्वपरावर्ती है या नहीं?
If \(A=\{1,2,3\}\) and \(R=\varnothing\), is (R) reflexive?
#relations
#empty-relation
#reflexive
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A हाँ / Yes
B नहीं / No
C हमेशा सार्वत्रिक / always universal
D निर्धारित नहीं / Cannot be decided
Explanation opens after your attempt
Correct Answer
B. नहीं / No
Step 1
Concept
For reflexivity, ( (1,1),(2,2),(3,3) ) are needed. These pairs are not present in the empty relation.
Step 2
Why this answer is correct
The correct answer is B. नहीं / No. For reflexivity, ( (1,1),(2,2),(3,3) ) are needed. These pairs are not present in the empty relation.
Step 3
Exam Tip
स्वपरावर्ती के लिए ( (1,1),(2,2),(3,3) ) चाहिए। empty relation में ये pairs नहीं हैं।
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यदि \(A=\{m,n\}\) और \(R=A\times A\) है, तो (R) किस प्रकार का संबंध है?
If \(A=\{m,n\}\) and \(R=A\times A\), what type of relation is (R)?
#relations
#universal-relation
#recognition
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A रिक्त संबंध / Empty relation
B पहचान संबंध / Identity relation
C सार्वत्रिक संबंध / Universal relation
D अवैध संबंध / Invalid relation
Explanation opens after your attempt
Correct Answer
C. सार्वत्रिक संबंध / Universal relation
Step 1
Concept
Taking all pairs of \(A\times A\) gives the universal relation. You can think of it as a complete relation.
Step 2
Why this answer is correct
The correct answer is C. सार्वत्रिक संबंध / Universal relation. Taking all pairs of \(A\times A\) gives the universal relation. You can think of it as a complete relation.
Step 3
Exam Tip
\(A\times A\) के सभी pairs लेने पर universal relation बनता है। इसे complete relation भी समझ सकते हैं।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a=b\}\) है, तो (R) में कौन-सा pair नहीं होगा?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a=b\}\), which pair will not be in (R)?
#relations
#equality-relation
#nonmembership
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A ( (1,1) )
B ( (2,2) )
C ( (3,3) )
D ( (1,3) )
Explanation opens after your attempt
Correct Answer
D. ( (1,3) )
Step 1
Concept
In ( (1,3) ), the two components are not equal. A relation (a=b) contains only diagonal pairs.
Step 2
Why this answer is correct
The correct answer is D. ( (1,3) ). In ( (1,3) ), the two components are not equal. A relation (a=b) contains only diagonal pairs.
Step 3
Exam Tip
( (1,3) ) में दोनों घटक बराबर नहीं हैं। (a=b) relation में केवल diagonal pairs आते हैं।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a\ne b\}\) है, तो (R) में कितने pairs होंगे?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a\ne b\}\), how many pairs will be in (R)?
#relations
#not-equal
#counting
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A (4)
B (8)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
There are (16) pairs in \(A\times A\), and (4) diagonal pairs are removed. So (16-4=12) pairs remain.
Step 2
Why this answer is correct
The correct answer is C. (12). There are (16) pairs in \(A\times A\), and (4) diagonal pairs are removed. So (16-4=12) pairs remain.
Step 3
Exam Tip
\(A\times A\) में (16) pairs हैं और (4) diagonal pairs हटेंगे। इसलिए (16-4=12) pairs बचेंगे।
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\(यदि (R={(x,y):x+y\) सम है}) है, तो कौन-सा pair (R) में है?
\(If (R={(x,y):x+y\) is even}), which pair is in (R)?
#relations
#even-sum
#membership
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A ( (1,2) )
B ( (2,5) )
C ( (3,7) )
D ( (4,7) )
Explanation opens after your attempt
Correct Answer
C. ( (3,7) )
Step 1
Concept
Since (3+7=10) is even, \((3,7)\in R\). Always check the parity of the sum.
Step 2
Why this answer is correct
The correct answer is C. ( (3,7) ). Since (3+7=10) is even, \((3,7)\in R\). Always check the parity of the sum.
Step 3
Exam Tip
(3+7=10) सम है, इसलिए \((3,7)\in R\) है। sum की parity जरूर जांचें।
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\(यदि (R={(x,y):x+y\) विषम है}) है, तो कौन-सा pair (R) में नहीं है?
\(If (R={(x,y):x+y\) is odd}), which pair is not in (R)?
#relations
#odd-sum
#nonmembership
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A ( (1,4) )
B ( (2,5) )
C ( (3,6) )
D ( (4,8) )
Explanation opens after your attempt
Correct Answer
D. ( (4,8) )
Step 1
Concept
Since (4+8=12) is even, it will not belong to the odd-sum relation. For an odd sum, one number should be even and the other odd.
Step 2
Why this answer is correct
The correct answer is D. ( (4,8) ). Since (4+8=12) is even, it will not belong to the odd-sum relation. For an odd sum, one number should be even and the other odd.
Step 3
Exam Tip
(4+8=12) सम है, इसलिए यह odd-sum relation में नहीं आएगा। विषम योग के लिए एक संख्या सम और दूसरी विषम होनी चाहिए।
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यदि \(A=\{1,2,3,4,5\}\) और \(R=\{(a,b):b=a+2\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,4,5\}\) and \(R=\{(a,b):b=a+2\}\), which pair is in (R)?
#relations
#successor-rule
#membership
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A ( (1,2) )
B ( (2,4) )
C ( (4,2) )
D ( (5,3) )
Explanation opens after your attempt
Correct Answer
B. ( (2,4) )
Step 1
Concept
Since (4=2+2), ( (2,4) ) belongs to the relation. Changing the order of an ordered pair can change the answer.
Step 2
Why this answer is correct
The correct answer is B. ( (2,4) ). Since (4=2+2), ( (2,4) ) belongs to the relation. Changing the order of an ordered pair can change the answer.
Step 3
Exam Tip
(4=2+2), इसलिए ( (2,4) ) relation में है। ordered pair का क्रम बदलने से उत्तर बदल सकता है।
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यदि \(A=\{1,2,3,4,5\}\) और \(R={(a,b):a\) is two more than (b}) है, तो कौन-सा pair सही है?
If \(A=\{1,2,3,4,5\}\) and \(R={(a,b):a\) is two more than (b}), which pair is correct?
#relations
#word-condition
#ordered-pair
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A ( (1,3) )
B ( (2,4) )
C ( (5,3) )
D ( (3,5) )
Explanation opens after your attempt
Correct Answer
C. ( (5,3) )
Step 1
Concept
The number (5) is (2) more than (3), so ( (5,3) ) is correct. Convert the word condition into an equation.
Step 2
Why this answer is correct
The correct answer is C. ( (5,3) ). The number (5) is (2) more than (3), so ( (5,3) ) is correct. Convert the word condition into an equation.
Step 3
Exam Tip
(5), (3) से (2) अधिक है, इसलिए ( (5,3) ) सही है। शब्दों वाली condition को equation में बदलें।
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यदि \(A=\{1,2,4,8\}\) और \(R=\{(a,b):b=2a\}\) है, तो (R) में कौन-सा pair होगा?
If \(A=\{1,2,4,8\}\) and \(R=\{(a,b):b=2a\}\), which pair will be in (R)?
#relations
#double-rule
#membership
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A ( (4,2) )
B ( (8,4) )
C ( (2,4) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
C. ( (2,4) )
Step 1
Concept
Since \(4=2\cdot2\), \((2,4)\in R\). In multiplication rules, check the second component carefully.
Step 2
Why this answer is correct
The correct answer is C. ( (2,4) ). Since \(4=2\cdot2\), \((2,4)\in R\). In multiplication rules, check the second component carefully.
Step 3
Exam Tip
\(4=2\cdot2\), इसलिए \((2,4)\in R\) है। गुणा वाले rule में second component ध्यान से देखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):ab=6\}\) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):ab=6\}\), which pair is in (R)?
#relations
#product-condition
#membership
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A ( (1,3) )
B ( (2,3) )
C ( (3,3) )
D ( (1,2) )
Explanation opens after your attempt
Correct Answer
B. ( (2,3) )
Step 1
Concept
Since \(2\cdot3=6\), ( (2,3) ) belongs to the relation. In a product condition, check the product of both components.
Step 2
Why this answer is correct
The correct answer is B. ( (2,3) ). Since \(2\cdot3=6\), ( (2,3) ) belongs to the relation. In a product condition, check the product of both components.
Step 3
Exam Tip
\(2\cdot3=6\), इसलिए ( (2,3) ) relation में है। product condition में दोनों घटकों का गुणनफल देखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):ab=6\}\) है, तो (R) में कितने ordered pairs हैं?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):ab=6\}\), how many ordered pairs are in (R)?
#relations
#product-condition
#counting
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
This condition gives ( (2,3) ) and ( (3,2) ). In ordered pairs, these two are considered different.
Step 2
Why this answer is correct
The correct answer is B. (2). This condition gives ( (2,3) ) and ( (3,2) ). In ordered pairs, these two are considered different.
Step 3
Exam Tip
इस condition से ( (2,3) ) और ( (3,2) ) मिलते हैं। ordered pairs में दोनों अलग माने जाते हैं।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a+b<5\}\) है, तो कौन-सा pair (R) में नहीं है?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a+b<5\}\), which pair is not in (R)?
#relations
#inequality-sum
#nonmembership
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A ( (1,2) )
B ( (2,2) )
C ( (3,1) )
D ( (4,2) )
Explanation opens after your attempt
Correct Answer
D. ( (4,2) )
Step 1
Concept
Here (4+2=6), and (6<5) is false. Therefore, ( (4,2) ) is not in the relation.
Step 2
Why this answer is correct
The correct answer is D. ( (4,2) ). Here (4+2=6), and (6<5) is false. Therefore, ( (4,2) ) is not in the relation.
Step 3
Exam Tip
(4+2=6) है और (6<5) असत्य है। इसलिए ( (4,2) ) relation में नहीं है।
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यदि \(R=\{(a,b):a-b=2\}\) है, तो कौन-सा pair (R) में आएगा?
If \(R=\{(a,b):a-b=2\}\), which pair will belong to (R)?
#relations
#difference-condition
#membership
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A ( (5,3) )
B ( (3,5) )
C ( (4,4) )
D ( (2,5) )
Explanation opens after your attempt
Correct Answer
A. ( (5,3) )
Step 1
Concept
Since (5-3=2), \((5,3)\in R\). In a subtraction relation, changing the order changes the value.
Step 2
Why this answer is correct
The correct answer is A. ( (5,3) ). Since (5-3=2), \((5,3)\in R\). In a subtraction relation, changing the order changes the value.
Step 3
Exam Tip
(5-3=2), इसलिए \((5,3)\in R\) है। subtraction relation में order बदलने से value बदल जाती है।
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यदि \(R=\{(a,b):|a-b|=1\}\) है, तो कौन-सा pair (R) में है?
If \(R=\{(a,b):|a-b|=1\}\), which pair is in (R)?
#relations
#absolute-difference
#membership
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A ( (2,4) )
B ( (5,4) )
C ( (3,3) )
D ( (1,4) )
Explanation opens after your attempt
Correct Answer
B. ( (5,4) )
Step 1
Concept
Since (|5-4|=1), ( (5,4) ) belongs to the relation. In absolute value, the sign of the difference does not matter.
Step 2
Why this answer is correct
The correct answer is B. ( (5,4) ). Since (|5-4|=1), ( (5,4) ) belongs to the relation. In absolute value, the sign of the difference does not matter.
Step 3
Exam Tip
(|5-4|=1), इसलिए ( (5,4) ) relation में है। absolute value में difference का sign मायने नहीं रखता।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\) है, तो (R) transitive क्यों नहीं है?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,3)\}\), why is (R) not transitive?
#relations
#transitive
#diagnosis
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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) ) present है / ( (1,1) ) is present
Explanation opens after your attempt
Correct Answer
A. ( (1,3) ) missing है / ( (1,3) ) is missing
Step 1
Concept
When ( (1,2) ) and ( (2,3) ) are present, ( (1,3) ) is required. This pair is missing.
Step 2
Why this answer is correct
The correct answer is A. ( (1,3) ) missing है / ( (1,3) ) is missing. When ( (1,2) ) and ( (2,3) ) are present, ( (1,3) ) is required. This pair is missing.
Step 3
Exam Tip
( (1,2) ) और ( (2,3) ) होने पर ( (1,3) ) चाहिए। यह pair missing है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\) है, तो (R) किस property को अवश्य पूरा करता है?
If \(A=\{1,2,3\}\) and \(R=\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\), which property does (R) definitely satisfy?
#relations
#reflexive
#property
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A स्वपरावर्ती / Reflexive
B रिक्त / Empty
C केवल सार्वत्रिक / Only universal
D कोई relation नहीं / Not a relation
Explanation opens after your attempt
Correct Answer
A. स्वपरावर्ती / Reflexive
Step 1
Concept
It contains all diagonal pairs of (A). Therefore, (R) is definitely reflexive.
Step 2
Why this answer is correct
The correct answer is A. स्वपरावर्ती / Reflexive. It contains all diagonal pairs of (A). Therefore, (R) is definitely reflexive.
Step 3
Exam Tip
इसमें (A) के सभी diagonal pairs मौजूद हैं। इसलिए (R) reflexive जरूर है।
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यदि \(A=\{1,2,3\}\) पर \(R=\{(1,1),(2,2),(3,3)\}\) है, तो (R) कौन-सी properties रखता है?
If \(R=\{(1,1),(2,2),(3,3)\}\) on \(A=\{1,2,3\}\), which properties does (R) have?
#relations
#identity
#properties
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A केवल सममित / only symmetric
B स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive
C केवल संक्रामक / only transitive
D कोई property नहीं / no property
Explanation opens after your attempt
Correct Answer
B. स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive
Step 1
Concept
The identity relation contains all diagonal pairs, and each reverse is the same pair. It is also transitive.
Step 2
Why this answer is correct
The correct answer is B. स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive. The identity relation contains all diagonal pairs, and each reverse is the same pair. It is also transitive.
Step 3
Exam Tip
identity relation सभी diagonal pairs रखता है और reverse भी वही pair होता है। यह transitive भी होता है।
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यदि \(A=\{1,2\}\) पर \(R=A\times A\) है, तो (R) कौन-सी properties रखता है?
If \(R=A\times A\) on \(A=\{1,2\}\), which properties does (R) have?
#relations
#universal-relation
#properties
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A स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive
B केवल रिक्त / only empty
C केवल सममित नहीं / not symmetric only
D केवल पहचान / only identity
Explanation opens after your attempt
Correct Answer
A. स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive
Step 1
Concept
A universal relation contains all possible pairs. Hence reflexive, symmetric, and transitive conditions are all satisfied.
Step 2
Why this answer is correct
The correct answer is A. स्वपरावर्ती, सममित और संक्रामक / reflexive, symmetric and transitive. A universal relation contains all possible pairs. Hence reflexive, symmetric, and transitive conditions are all satisfied.
Step 3
Exam Tip
universal relation में सभी possible pairs होते हैं। इसलिए reflexive, symmetric और transitive तीनों conditions पूरी होती हैं।
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यदि \(R=\{(1,2),(2,1)\}\) है और आधार set \(A=\{1,2\}\) है, तो (R) स्वपरावर्ती क्यों नहीं है?
If \(R=\{(1,2),(2,1)\}\) and the base set is \(A=\{1,2\}\), why is (R) not reflexive?
#relations
#reflexive
#common-mistake
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A ( (1,2) ) present है / ( (1,2) ) is present
B ( (2,1) ) present है / ( (2,1) ) is present
C ( (1,1) ) और ( (2,2) ) missing हैं / ( (1,1) ) and ( (2,2) ) are missing
D (A) में दो तत्व हैं / (A) has two elements
Explanation opens after your attempt
Correct Answer
C. ( (1,1) ) और ( (2,2) ) missing हैं / ( (1,1) ) and ( (2,2) ) are missing
Step 1
Concept
A reflexive relation needs all diagonal pairs. Here ( (1,1) ) and ( (2,2) ) are absent.
Step 2
Why this answer is correct
The correct answer is C. ( (1,1) ) और ( (2,2) ) missing हैं / ( (1,1) ) and ( (2,2) ) are missing. A reflexive relation needs all diagonal pairs. Here ( (1,1) ) and ( (2,2) ) are absent.
Step 3
Exam Tip
Reflexive relation में सभी diagonal pairs चाहिए। यहाँ ( (1,1) ) और ( (2,2) ) नहीं हैं।
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यदि \(R=\{(1,1),(1,2),(2,1),(2,2)\}\) है, तो (R) किस set पर universal relation है?
If \(R=\{(1,1),(1,2),(2,1),(2,2)\}\), on which set is (R) the universal relation?
#relations
#universal-relation
#base-set
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A \(A=\{1\}\)
B \(A=\{2\}\)
C \(A=\{1,2\}\)
D \(A=\{1,2,3\}\)
Explanation opens after your attempt
Correct Answer
C. \(A=\{1,2\}\)
Step 1
Concept
These are exactly all pairs of \({1,2}\times{1,2}\). So the base set is \(A=\{1,2\}\).
Step 2
Why this answer is correct
The correct answer is C. \(A=\{1,2\}\). These are exactly all pairs of \({1,2}\times{1,2}\). So the base set is \(A=\{1,2\}\).
Step 3
Exam Tip
ये exactly \({1,2}\times{1,2}\) के सभी pairs हैं। इसलिए base set \(A=\{1,2\}\) है।
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यदि \(A=\{1,2,3,4\}\) और \(R={(a,b):a\) and (b) have same parity(}) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,4\}\) and \(R={(a,b):a\) and (b) have same parity(}), which pair is in (R)?
#relations
#parity
#membership
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A ( (1,2) )
B ( (2,3) )
C ( (1,3) )
D ( (3,4) )
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Correct Answer
C. ( (1,3) )
Step 1
Concept
Both (1) and (3) 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. ( (1,3) ). Both (1) and (3) are odd, so they have the same parity. In a parity relation, even-even or odd-odd pairs are correct.
Step 3
Exam Tip
(1) और (3) दोनों विषम हैं, इसलिए same parity है। parity relation में सम-सम या विषम-विषम pair सही होता है।
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यदि \(A=\{2,3,5,6\}\) और \(R={(a,b):a\) is a factor of (b}) है, तो कौन-सा pair (R) में नहीं है?
If \(A=\{2,3,5,6\}\) and \(R={(a,b):a\) is a factor of (b}), which pair is not in (R)?
#relations
#factor-relation
#nonmembership
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A ( (2,6) )
B ( (3,6) )
C ( (5,5) )
D ( (5,6) )
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Correct Answer
D. ( (5,6) )
Step 1
Concept
The number (5) is not a factor of (6). In a factor relation, the first component should divide the second.
Step 2
Why this answer is correct
The correct answer is D. ( (5,6) ). The number (5) is not a factor of (6). In a factor relation, the first component should divide the second.
Step 3
Exam Tip
(5), (6) का factor नहीं है। factor relation में पहला घटक दूसरे को divide करना चाहिए।
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यदि \(A=\{1,2,3,6\}\) और \(R={(a,b):a\) is a multiple of (b}) है, तो कौन-सा pair (R) में है?
If \(A=\{1,2,3,6\}\) and \(R={(a,b):a\) is a multiple of (b}), which pair is in (R)?
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#multiple-relation
#membership
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A ( (2,6) )
B ( (6,3) )
C ( (3,6) )
D ( (1,6) )
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Correct Answer
B. ( (6,3) )
Step 1
Concept
The number (6) is a multiple of (3), so \((6,3)\in R\). Remember the order in multiple and factor relations.
Step 2
Why this answer is correct
The correct answer is B. ( (6,3) ). The number (6) is a multiple of (3), so \((6,3)\in R\). Remember the order in multiple and factor relations.
Step 3
Exam Tip
(6), (3) का multiple है, इसलिए \((6,3)\in R\) है। multiple और factor relations में order याद रखें।
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यदि \(A=\{0,1,2\}\) और \(R=\{(a,b):a+b=2\}\) है, तो (R) क्या होगा?
If \(A=\{0,1,2\}\) and \(R=\{(a,b):a+b=2\}\), what is (R)?
#relations
#list-relation
#sum
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A \(R=\{(0,2),(1,1),(2,0)\}\)
B \(R=\{(0,1),(1,0)\}\)
C \(R=\{(2,2)\}\)
D \(R=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(R=\{(0,2),(1,1),(2,0)\}\)
Step 1
Concept
The pairs giving sum (2) are ( (0,2),(1,1),(2,0) ). Check all possible orders in ordered pairs.
Step 2
Why this answer is correct
The correct answer is A. \(R=\{(0,2),(1,1),(2,0)\}\). The pairs giving sum (2) are ( (0,2),(1,1),(2,0) ). Check all possible orders in ordered pairs.
Step 3
Exam Tip
योग (2) देने वाले pairs ( (0,2),(1,1),(2,0) ) हैं। ordered pairs में सभी संभव क्रम देखें।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a+b>5\}\) है, तो (R) क्या होगा?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a+b>5\}\), what is (R)?
#relations
#inequality-sum
#list-form
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A \(R=\{(3,3)\}\)
B \(R=\{(2,3),(3,2),(3,3)\}\)
C \(R=\{(1,3),(3,1)\}\)
D \(R=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. \(R=\{(3,3)\}\)
Step 1
Concept
Only (3+3=6) is greater than (5). Therefore, \(R=\{(3,3)\}\).
Step 2
Why this answer is correct
The correct answer is A. \(R=\{(3,3)\}\). Only (3+3=6) is greater than (5). Therefore, \(R=\{(3,3)\}\).
Step 3
Exam Tip
केवल (3+3=6) है जो (5) से बड़ा है। इसलिए \(R=\{(3,3)\}\) है।
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यदि \(A=\{1,2,3\}\) और \(R=\{(a,b):a+b<3\}\) है, तो (R) क्या होगा?
If \(A=\{1,2,3\}\) and \(R=\{(a,b):a+b<3\}\), what is (R)?
#relations
#less-than-sum
#list-form
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A \(R=\{(1,1)\}\)
B \(R=\{(1,2),(2,1)\}\)
C \(R=\{(2,2)\}\)
D \(R=A\times A\)
Explanation opens after your attempt
Correct Answer
A. \(R=\{(1,1)\}\)
Step 1
Concept
Only (1+1=2) is less than (3). Hence only ( (1,1) ) will be in (R).
Step 2
Why this answer is correct
The correct answer is A. \(R=\{(1,1)\}\). Only (1+1=2) is less than (3). Hence only ( (1,1) ) will be in (R).
Step 3
Exam Tip
केवल (1+1=2) है जो (3) से छोटा है। इसलिए (R) में सिर्फ ( (1,1) ) आएगा।
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यदि \(A=\{1,2,3,4\}\) और \(R=\{(a,b):a=1\}\) है, तो (R) में कितने pairs होंगे?
If \(A=\{1,2,3,4\}\) and \(R=\{(a,b):a=1\}\), how many pairs will be in (R)?
#relations
#fixed-first-component
#counting
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A (1)
B (2)
C (4)
D (8)
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Step 1
Concept
The first component is fixed as (1), and the second component can take (4) values from (A). Hence there will be (4) pairs.
Step 2
Why this answer is correct
The correct answer is C. (4). The first component is fixed as (1), and the second component can take (4) values from (A). Hence there will be (4) pairs.
Step 3
Exam Tip
पहला घटक (1) fixed है और दूसरा घटक (A) के (4) मान ले सकता है। इसलिए (4) pairs होंगे।
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यदि \(A=\{1,2,3,4,5\}\) और \(R=\{(a,b):b=5\}\) है, तो (R) में कितने pairs होंगे?
If \(A=\{1,2,3,4,5\}\) and \(R=\{(a,b):b=5\}\), how many pairs will be in (R)?
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#fixed-second-component
#counting
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A (1)
B (5)
C (10)
D (25)
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Step 1
Concept
The second component is fixed as (5), and the first component can take (5) values from (A). Hence there will be (5) pairs.
Step 2
Why this answer is correct
The correct answer is B. (5). The second component is fixed as (5), and the first component can take (5) values from (A). Hence there will be (5) pairs.
Step 3
Exam Tip
दूसरा घटक (5) fixed है और पहला घटक (A) के (5) मान ले सकता है। इसलिए (5) pairs होंगे।
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यदि \(R=\{(1,2),(2,3),(3,4),(1,3)\}\) है, तो transitive property के लिए ( (2,3) ) और ( (3,4) ) से कौन-सा pair चाहिए?
If \(R=\{(1,2),(2,3),(3,4),(1,3)\}\), which pair is needed from ( (2,3) ) and ( (3,4) ) for transitive property?
#relations
#transitive
#required-pair
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A ( (2,4) )
B ( (4,2) )
C ( (3,2) )
D ( (1,4) )
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Correct Answer
A. ( (2,4) )
Step 1
Concept
In the transitive rule, ( (a,b) ) and ( (b,c) ) require ( (a,c) ). Here the needed pair is ( (2,4) ).
Step 2
Why this answer is correct
The correct answer is A. ( (2,4) ). In the transitive rule, ( (a,b) ) and ( (b,c) ) require ( (a,c) ). Here the needed pair is ( (2,4) ).
Step 3
Exam Tip
Transitive rule में ( (a,b) ) और ( (b,c) ) से ( (a,c) ) चाहिए। यहाँ जरूरी pair ( (2,4) ) है।
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