यदि \(A=\{1,4,7\}\) और \(B=\{0,2\}\) हैं, तो \(A\times B\) में कुल कितने क्रमित युग्म होंगे?
If \(A=\{1,4,7\}\) and \(B=\{0,2\}\), how many ordered pairs are there in \(A\times B\)?
#cartesian-product
#cardinality
#ordered-pairs
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A (5)
B (6)
C (3)
D (2)
Explanation opens after your attempt
Step 1
Concept
(n\(A\times B\)=n(A)n(B)=3\times2=6). Counting elements of both sets first is the safest method.
Step 2
Why this answer is correct
The correct answer is B. (6). (n\(A\times B\)=n(A)n(B)=3\times2=6). Counting elements of both sets first is the safest method.
Step 3
Exam Tip
(n\(A\times B\)=n(A)n(B)=3\times2=6) होता है। पहले दोनों समुच्चयों के अवयव गिनना सबसे सुरक्षित तरीका है।
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यदि \(A=\{p,q\}\) और \(B=\{3,6,9\}\) हैं, तो \(A\times B\) कौन सा है?
If \(A=\{p,q\}\) and \(B=\{3,6,9\}\), which one is \(A\times B\)?
#cartesian-product
#listing
#definition
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A ({(p,3),(p,6),(q,9)})
B ({(3,p),(6,p),(9,p),(3,q),(6,q),(9,q)})
C ({(p,3),(p,6),(p,9),(q,3),(q,6),(q,9)})
D ({(p,q),(3,6),(6,9)})
Explanation opens after your attempt
Correct Answer
C. ({(p,3),(p,6),(p,9),(q,3),(q,6),(q,9)})
Step 1
Concept
In \(A\times B\), the first component comes from (A) and the second from (B). Each element of (A) pairs with all elements of (B).
Step 2
Why this answer is correct
The correct answer is C. ({(p,3),(p,6),(p,9),(q,3),(q,6),(q,9)}). In \(A\times B\), the first component comes from (A) and the second from (B). Each element of (A) pairs with all elements of (B).
Step 3
Exam Tip
\(A\times B\) में पहला घटक (A) से और दूसरा (B) से आता है। हर (A) का अवयव (B) के सभी अवयवों से जुड़ता है।
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यदि \(A=\{2,5\}\) और \(B=\{1,3,5\}\) हैं, तो कौन सा युग्म \(B\times A\) में है?
If \(A=\{2,5\}\) and \(B=\{1,3,5\}\), which pair belongs to \(B\times A\)?
#cartesian-product
#membership
#order
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A ((2,3))
B ((3,2))
C ((5,1))
D ((1,3))
Explanation opens after your attempt
Correct Answer
B. ((3,2))
Step 1
Concept
In \(B\times A\), the first element must be from (B) and the second from (A). Hence ((3,2)) is correct.
Step 2
Why this answer is correct
The correct answer is B. ((3,2)). In \(B\times A\), the first element must be from (B) and the second from (A). Hence ((3,2)) is correct.
Step 3
Exam Tip
\(B\times A\) में पहला अवयव (B) से और दूसरा (A) से होना चाहिए। इसलिए ((3,2)) सही है।
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यदि \(A=\{0,3,6\}\) और \(B=\{2,4\}\) हैं, तो \((6,4)\in A\times B\) का सत्य मान क्या है?
If \(A=\{0,3,6\}\) and \(B=\{2,4\}\), what is the truth value of \((6,4)\in A\times B\)?
#cartesian-product
#membership
#truth-value
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A असत्य / false
B सत्य / true
C केवल जब (A=B) / only when (A=B)
D निर्धारित नहीं / not determined
Explanation opens after your attempt
Correct Answer
B. सत्य / true
Step 1
Concept
Since \(6\in A\) and \(4\in B\), \((6,4)\in A\times B\) is true. Check both positions separately for membership.
Step 2
Why this answer is correct
The correct answer is B. सत्य / true. Since \(6\in A\) and \(4\in B\), \((6,4)\in A\times B\) is true. Check both positions separately for membership.
Step 3
Exam Tip
क्योंकि \(6\in A\) और \(4\in B\), इसलिए \((6,4)\in A\times B\) सत्य है। सदस्यता में दोनों स्थान अलग-अलग जांचें।
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यदि \(A=\{1,3,5\}\) और \(B=\{2,4\}\) हैं, तो कौन सा युग्म \(A\times B\) में नहीं है?
If \(A=\{1,3,5\}\) and \(B=\{2,4\}\), which pair is not in \(A\times B\)?
#cartesian-product
#not-belonging
#common-error
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A ((3,4))
B ((5,2))
C ((2,5))
D ((1,2))
Explanation opens after your attempt
Correct Answer
C. ((2,5))
Step 1
Concept
In ((2,5)), the first element is not from (A) and the second is not from (B). Reversing order is a common Cartesian product mistake.
Step 2
Why this answer is correct
The correct answer is C. ((2,5)). In ((2,5)), the first element is not from (A) and the second is not from (B). Reversing order is a common Cartesian product mistake.
Step 3
Exam Tip
((2,5)) में पहला अवयव (A) से नहीं और दूसरा (B) से नहीं है। कार्तीय गुणन में क्रम बदलना सामान्य गलती है।
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यदि \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) और \(C=\{1,3,5\}\) हैं, तो (A\times\(B\cap C\)) में कितने अवयव होंगे?
If \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) and \(C=\{1,3,5\}\), how many elements are in (A\times\(B\cap C\))?
#cartesian-product
#intersection
#cardinality
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A (6)
B (9)
C (3)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(B\cap C={3}\), so (n(A\times\(B\cap C\))=3\times1=3). Find the intersection first and then multiply.
Step 2
Why this answer is correct
The correct answer is C. (3). \(B\cap C={3}\), so (n(A\times\(B\cap C\))=3\times1=3). Find the intersection first and then multiply.
Step 3
Exam Tip
\(B\cap C={3}\), इसलिए (n(A\times\(B\cap C\))=3\times1=3)। पहले प्रतिच्छेद निकालें फिर गुणन करें।
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यदि \(A=\{0,1\}\), \(B=\{2,4\}\) और \(C=\{4,6,8\}\) हैं, तो (A\times\(B\cup C\)) में कितने अवयव होंगे?
If \(A=\{0,1\}\), \(B=\{2,4\}\) and \(C=\{4,6,8\}\), how many elements are in (A\times\(B\cup C\))?
#cartesian-product
#union
#counting
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A (8)
B (10)
C (6)
D (4)
Explanation opens after your attempt
Step 1
Concept
\(B\cup C={2,4,6,8}\), so (n(A\times\(B\cup C\))=2\times4=8). Do not count common elements twice in a union.
Step 2
Why this answer is correct
The correct answer is A. (8). \(B\cup C={2,4,6,8}\), so (n(A\times\(B\cup C\))=2\times4=8). Do not count common elements twice in a union.
Step 3
Exam Tip
\(B\cup C={2,4,6,8}\), इसलिए (n(A\times\(B\cup C\))=2\times4=8)। संघ में समान अवयव को दो बार न गिनें।
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यदि \(A=\{2,4,6,8\}\), \(B=\{4,8\}\) और \(C=\{1,3,5\}\) हैं, तो \((A-B)\times C\) में कितने अवयव होंगे?
If \(A=\{2,4,6,8\}\), \(B=\{4,8\}\) and \(C=\{1,3,5\}\), how many elements are in \((A-B)\times C\)?
#cartesian-product
#set-difference
#cardinality
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A (9)
B (6)
C (5)
D (12)
Explanation opens after your attempt
Step 1
Concept
(A-B={2,6}), so (n\((A-B)\times C\)=2\times3=6). It is necessary to find the set difference first.
Step 2
Why this answer is correct
The correct answer is B. (6). (A-B={2,6}), so (n\((A-B)\times C\)=2\times3=6). It is necessary to find the set difference first.
Step 3
Exam Tip
(A-B={2,6}), इसलिए (n\((A-B)\times C\)=2\times3=6)। पहले समुच्चय अंतर निकालना जरूरी है।
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यदि (n(A)=6) और (n\(A\times B\)=48) है, तो (n(B)) कितना होगा?
If (n(A)=6) and (n\(A\times B\)=48), what is (n(B))?
#cartesian-product
#cardinality
#numerical
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A (6)
B (42)
C (8)
D (54)
Explanation opens after your attempt
Step 1
Concept
(n\(A\times B\)=n(A)n(B)), so (48=6n(B)) and (n(B)=8). Use the formula in reverse in such questions.
Step 2
Why this answer is correct
The correct answer is C. (8). (n\(A\times B\)=n(A)n(B)), so (48=6n(B)) and (n(B)=8). Use the formula in reverse in such questions.
Step 3
Exam Tip
(n\(A\times B\)=n(A)n(B)), इसलिए (48=6n(B)) और (n(B)=8)। ऐसे प्रश्नों में सूत्र को उल्टा लगाएं।
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यदि (n(A)=4), (n(B)=5) और दोनों समुच्चय अरिक्त हैं, तो \(A\times B\) और \(B\times A\) की अवयव संख्या के बारे में सही कथन कौन सा है?
If (n(A)=4), (n(B)=5) and both sets are non-empty, which statement about the number of elements in \(A\times B\) and \(B\times A\) is correct?
#cartesian-product
#comparison
#noncommutative
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A दोनों में (9) अवयव होंगे / both have (9) elements
B दोनों में (20) अवयव होंगे / both have (20) elements
C दोनों हमेशा समान समुच्चय होंगे / both are always equal sets
D एक में (4) और दूसरे में (5) अवयव होंगे / one has (4) and the other has (5) elements
Explanation opens after your attempt
Correct Answer
B. दोनों में (20) अवयव होंगे / both have (20) elements
Step 1
Concept
Both have \(4\times5=20\) elements. The number can be the same but the order of pairs is generally different.
Step 2
Why this answer is correct
The correct answer is B. दोनों में (20) अवयव होंगे / both have (20) elements. Both have \(4\times5=20\) elements. The number can be the same but the order of pairs is generally different.
Step 3
Exam Tip
दोनों की अवयव संख्या \(4\times5=20\) होगी। संख्या समान हो सकती है पर युग्मों का क्रम सामान्यतः अलग होता है।
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यदि \(A={x:x\in\mathbb{N},2\le x\le5}\) और \(B={y:y\in\mathbb{N},y<4}\) हैं, तो (n\(A\times B\)) कितना है?
If \(A={x:x\in\mathbb{N},2\le x\le5}\) and \(B={y:y\in\mathbb{N},y<4}\), what is (n\(A\times B\))?
#cartesian-product
#set-builder
#natural-numbers
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A (7)
B (10)
C (12)
D (15)
Explanation opens after your attempt
Step 1
Concept
\(A=\{2,3,4,5\}\) and \(B=\{1,2,3\}\). Hence (n\(A\times B\)=4\times3=12).
Step 2
Why this answer is correct
The correct answer is C. (12). \(A=\{2,3,4,5\}\) and \(B=\{1,2,3\}\). Hence (n\(A\times B\)=4\times3=12).
Step 3
Exam Tip
\(A=\{2,3,4,5\}\) और \(B=\{1,2,3\}\) हैं। इसलिए (n\(A\times B\)=4\times3=12)।
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यदि \(A=\{5,10\}\) और \(B=\varnothing\) हैं, तो \(A\times B\) क्या होगा?
If \(A=\{5,10\}\) and \(B=\varnothing\), what is \(A\times B\)?
#cartesian-product
#empty-set
#concept
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A ({\(5,\varnothing\),\(10,\varnothing\)})
B ({5,10})
C \(\varnothing\)
D ({\(\varnothing,5\),\(\varnothing,10\)})
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\)
Step 1
Concept
The second component must come from (B), but \(B=\varnothing\). Hence no ordered pair is formed and the product is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \(\varnothing\). The second component must come from (B), but \(B=\varnothing\). Hence no ordered pair is formed and the product is \(\varnothing\).
Step 3
Exam Tip
दूसरा घटक (B) से लेना होता है पर \(B=\varnothing\) है। इसलिए कोई क्रमित युग्म नहीं बनेगा और गुणन \(\varnothing\) होगा।
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यदि \(A=\{m,n,o\}\) है, तो \(A\times A\) में कितने क्रमित युग्म होंगे?
If \(A=\{m,n,o\}\), how many ordered pairs are in \(A\times A\)?
#cartesian-product
#self-product
#cardinality
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A (6)
B (3)
C (12)
D (9)
Explanation opens after your attempt
Step 1
Concept
(n\(A\times A\)=n(A)2 =32 =9). Pairs with equal components are also included.
Step 2
Why this answer is correct
The correct answer is D. (9). (n\(A\times A\)=n(A)2 =32 =9). Pairs with equal components are also included.
Step 3
Exam Tip
(n\(A\times A\)=n(A)2 =32 =9) होता है। समान घटक वाले युग्म भी इसमें शामिल होते हैं।
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यदि \(A=\{2,3,4\}\) और \(B=\{3,4,5\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x=y)?
If \(A=\{2,3,4\}\) and \(B=\{3,4,5\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x=y)?
#cartesian-product
#equality-condition
#intersection
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A (3)
B (2)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((3,3)) and ((4,4)). Such pairs are formed from elements of \(A\cap B\).
Step 2
Why this answer is correct
The correct answer is B. (2). The valid pairs are ((3,3)) and ((4,4)). Such pairs are formed from elements of \(A\cap B\).
Step 3
Exam Tip
सही युग्म ((3,3)) और ((4,4)) हैं। ऐसे युग्म \(A\cap B\) के अवयवों से बनते हैं।
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यदि \(A=\{0,1,2,3\}\) और \(B=\{1,3,5\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x<y)?
If \(A=\{0,1,2,3\}\) and \(B=\{1,3,5\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x<y)?
#cartesian-product
#inequality
#counting
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A (8)
B (9)
C (10)
D (7)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((0,1),(0,3),(1,3),(2,3),(0,5),(1,5),(2,5),(3,5)), so the count is (8). Careful listing prevents overcounting.
Step 2
Why this answer is correct
The correct answer is B. (9). The valid pairs are ((0,1),(0,3),(1,3),(2,3),(0,5),(1,5),(2,5),(3,5)), so the count is (8). Careful listing prevents overcounting.
Step 3
Exam Tip
(y=1) के लिए (1) युग्म, (y=3) के लिए (3) युग्म और (y=5) के लिए (4) युग्म मिलते हैं। कुल (1+3+4=8) नहीं, ध्यान से सूची बनाने पर ((0,1),(0,3),(1,3),(2,3),(0,5),(1,5),(2,5),(3,5)) यानी (8) युग्म हैं।
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यदि \(A=\{0,1,2,4\}\) और \(B=\{1,2,3,4\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x+y=5)?
If \(A=\{0,1,2,4\}\) and \(B=\{1,2,3,4\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x+y=5)?
#cartesian-product
#sum-condition
#application
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A (2)
B (4)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((1,4),(2,3),(4,1)). Always check membership of both components in each pair.
Step 2
Why this answer is correct
The correct answer is C. (3). The valid pairs are ((1,4),(2,3),(4,1)). Always check membership of both components in each pair.
Step 3
Exam Tip
सही युग्म ((1,4),(2,3),(4,1)) हैं। हर युग्म में दोनों घटकों की सदस्यता जरूर जांचें।
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यदि \(A=\{1,3,5\}\) और \(B=\{2,6,10\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (y=2x)?
If \(A=\{1,3,5\}\) and \(B=\{2,6,10\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (y=2x)?
#cartesian-product
#equation-condition
#function-pattern
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A (3)
B (2)
C (6)
D (1)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((1,2),(3,6),(5,10)). Choosing (x) first and then finding (y) is a quick method.
Step 2
Why this answer is correct
The correct answer is A. (3). The valid pairs are ((1,2),(3,6),(5,10)). Choosing (x) first and then finding (y) is a quick method.
Step 3
Exam Tip
सही युग्म ((1,2),(3,6),(5,10)) हैं। पहले (x) चुनकर (y) निकालना तेज तरीका है।
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यदि \(A=\{4,6,8\}\) और \(B=\{1,2,4\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (y) संख्या (x) को विभाजित करती है?
If \(A=\{4,6,8\}\) and \(B=\{1,2,4\}\), how many pairs ((x,y)) in \(A\times B\) satisfy that (y) divides (x)?
#cartesian-product
#divisibility
#counting
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A (8)
B (7)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((4,1),(4,2),(4,4),(6,1),(6,2),(8,1),(8,2),(8,4)). In divisibility, note the positions of divisor and dividend carefully.
Step 2
Why this answer is correct
The correct answer is A. (8). The valid pairs are ((4,1),(4,2),(4,4),(6,1),(6,2),(8,1),(8,2),(8,4)). In divisibility, note the positions of divisor and dividend carefully.
Step 3
Exam Tip
सही युग्म ((4,1),(4,2),(4,4),(6,1),(6,2),(8,1),(8,2),(8,4)) हैं। विभाज्यता में भाजक और भाज्य की जगह ध्यान से देखें।
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यदि \(A=\{1,2,4\}\) और \(B=\{1,4,16\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि \(y=x^2\)?
If \(A=\{1,2,4\}\) and \(B=\{1,4,16\}\), how many pairs ((x,y)) in \(A\times B\) satisfy \(y=x^2\)?
#cartesian-product
#relation
#function-condition
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((1,1),(2,4),(4,16)). Applying a condition to a Cartesian product forms a relation.
Step 2
Why this answer is correct
The correct answer is B. (3). The valid pairs are ((1,1),(2,4),(4,16)). Applying a condition to a Cartesian product forms a relation.
Step 3
Exam Tip
सही युग्म ((1,1),(2,4),(4,16)) हैं। कार्तीय गुणन पर शर्त लगाने से संबंध बनता है।
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यदि \(A=\{0,2,4\}\) और \(B=\{1,3,5,7\}\) हैं, तो \(A\times B\) में पहले घटक (4) वाले कितने युग्म होंगे?
If \(A=\{0,2,4\}\) and \(B=\{1,3,5,7\}\), how many pairs in \(A\times B\) have first component (4)?
#cartesian-product
#components
#counting
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A (3)
B (4)
C (7)
D (12)
Explanation opens after your attempt
Step 1
Concept
When the first component (4) is fixed, the second component can be any of the (4) elements of (B). Hence (4) pairs are formed.
Step 2
Why this answer is correct
The correct answer is B. (4). When the first component (4) is fixed, the second component can be any of the (4) elements of (B). Hence (4) pairs are formed.
Step 3
Exam Tip
पहला घटक (4) तय होने पर दूसरा घटक (B) के (4) अवयवों में से कोई भी हो सकता है। इसलिए (4) युग्म बनते हैं।
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यदि \(A=\{a,b,c,d\}\) और \(B=\{10,20,30\}\) हैं, तो \(A\times B\) में दूसरा घटक (20) वाले कितने युग्म होंगे?
If \(A=\{a,b,c,d\}\) and \(B=\{10,20,30\}\), how many pairs in \(A\times B\) have second component (20)?
#cartesian-product
#components
#counting
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A (3)
B (4)
C (12)
D (1)
Explanation opens after your attempt
Step 1
Concept
When the second component (20) is fixed, the first component can be any of the (4) elements of (A). So there are (4) pairs.
Step 2
Why this answer is correct
The correct answer is B. (4). When the second component (20) is fixed, the first component can be any of the (4) elements of (A). So there are (4) pairs.
Step 3
Exam Tip
दूसरा घटक (20) तय होने पर पहला घटक (A) के (4) अवयवों में से कोई भी हो सकता है। इसलिए (4) युग्म होंगे।
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यदि \(A=\{1,2\}\) और \(B=\{5,6,7\}\) हैं, तो (A) से (B) तक कुल कितने संबंध संभव हैं?
If \(A=\{1,2\}\) and \(B=\{5,6,7\}\), how many relations are possible from (A) to (B)?
#cartesian-product
#relations
#subsets
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A (6)
B \(2^5\)
C \(2^6\)
D \(3^2\)
Explanation opens after your attempt
Correct Answer
C. \(2^6\)
Step 1
Concept
(n\(A\times B\)=2\times3=6), and every relation is a subset of \(A\times B\). Therefore the total number of relations is \(2^6\).
Step 2
Why this answer is correct
The correct answer is C. \(2^6\). (n\(A\times B\)=2\times3=6), and every relation is a subset of \(A\times B\). Therefore the total number of relations is \(2^6\).
Step 3
Exam Tip
(n\(A\times B\)=2\times3=6), और हर संबंध \(A\times B\) का उपसमुच्चय होता है। इसलिए कुल संबंध \(2^6\) हैं।
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यदि \(A=\{2,4,6\}\) और \(B=\{1,3\}\) हैं, तो कौन सा उपसमुच्चय (A) से (B) तक संबंध है?
If \(A=\{2,4,6\}\) and \(B=\{1,3\}\), which subset is a relation from (A) to (B)?
#cartesian-product
#relation
#subset
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A ({(2,1),(6,3)})
B ({(1,2),(3,6)})
C ({(4,5)})
D ({(0,1),(2,3)})
Explanation opens after your attempt
Correct Answer
A. ({(2,1),(6,3)})
Step 1
Concept
A relation is a subset of \(A\times B\). Only all pairs of ({(2,1),(6,3)}) belong to \(A\times B\).
Step 2
Why this answer is correct
The correct answer is A. ({(2,1),(6,3)}). A relation is a subset of \(A\times B\). Only all pairs of ({(2,1),(6,3)}) belong to \(A\times B\).
Step 3
Exam Tip
संबंध \(A\times B\) का उपसमुच्चय होता है। केवल ({(2,1),(6,3)}) के सभी युग्म \(A\times B\) में हैं।
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यदि \(A=\{1,3,5\}\) और \(B=\{0,2\}\) हैं, तो \(A\times B\) के कितने उपसमुच्चय होंगे?
If \(A=\{1,3,5\}\) and \(B=\{0,2\}\), how many subsets does \(A\times B\) have?
#cartesian-product
#subsets
#counting
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A \(2^6\)
B (6)
C \(2^5\)
D \(3^2\)
Explanation opens after your attempt
Correct Answer
A. \(2^6\)
Step 1
Concept
(n\(A\times B\)=3\times2=6), so the number of subsets is \(2^6\). Use \(2^n\) for counting subsets.
Step 2
Why this answer is correct
The correct answer is A. \(2^6\). (n\(A\times B\)=3\times2=6), so the number of subsets is \(2^6\). Use \(2^n\) for counting subsets.
Step 3
Exam Tip
(n\(A\times B\)=3\times2=6), इसलिए उपसमुच्चयों की संख्या \(2^6\) है। उपसमुच्चय गिनने में \(2^n\) लगाएं।
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यदि \(A=\{1,2,4\}\) और \(B=\{2,4,6\}\) हैं, तो \(A\times B\cap B\times A\) में कितने युग्म होंगे?
If \(A=\{1,2,4\}\) and \(B=\{2,4,6\}\), how many pairs are in \(A\times B\cap B\times A\)?
#cartesian-product
#intersection
#ordered-pairs
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A (2)
B (4)
C (6)
D (1)
Explanation opens after your attempt
Step 1
Concept
The common pairs are ((2,2),(2,4),(4,2),(4,4)). In intersection, the whole ordered pair must belong to both sets.
Step 2
Why this answer is correct
The correct answer is B. (4). The common pairs are ((2,2),(2,4),(4,2),(4,4)). In intersection, the whole ordered pair must belong to both sets.
Step 3
Exam Tip
साझा युग्म ((2,2),(2,4),(4,2),(4,4)) हैं। प्रतिच्छेद में पूरा क्रमित युग्म दोनों समुच्चयों में होना चाहिए।
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यदि \(A=\{1,2\}\) और \(B=\{3,4,5\}\) हैं, तो \(A\times B\) और \(B\times A\) के बारे में सही कथन कौन सा है?
If \(A=\{1,2\}\) and \(B=\{3,4,5\}\), which statement about \(A\times B\) and \(B\times A\) is correct?
#cartesian-product
#noncommutative
#comparison
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A दोनों में (6) अवयव हैं पर समुच्चय सामान्यतः अलग हैं / both have (6) elements but the sets are generally different
B दोनों में (5) अवयव हैं / both have (5) elements
C दोनों हमेशा समान हैं / both are always equal
D \(A\times B\) रिक्त है / \(A\times B\) is empty
Explanation opens after your attempt
Correct Answer
A. दोनों में (6) अवयव हैं पर समुच्चय सामान्यतः अलग हैं / both have (6) elements but the sets are generally different
Step 1
Concept
Both have \(2\times3=6\) elements, but changing the order changes pairs. Cartesian product is generally not commutative.
Step 2
Why this answer is correct
The correct answer is A. दोनों में (6) अवयव हैं पर समुच्चय सामान्यतः अलग हैं / both have (6) elements but the sets are generally different. Both have \(2\times3=6\) elements, but changing the order changes pairs. Cartesian product is generally not commutative.
Step 3
Exam Tip
दोनों की अवयव संख्या \(2\times3=6\) है, पर क्रम बदलने से युग्म बदल जाते हैं। कार्तीय गुणन सामान्यतः क्रमविनिमेय नहीं होता।
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यदि (A=[2,5]) और \(B=\{3\}\) हैं, तो \(A\times B\) का ज्यामितीय रूप क्या है?
If (A=[2,5]) and \(B=\{3\}\), what is the geometric form of \(A\times B\)?
#cartesian-product
#interval
#geometry
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A रेखा (x=3) पर \(2\le y\le5\) वाला रेखाखंड / line segment on (x=3) with \(2\le y\le5\)
B रेखा (y=3) पर \(2\le x\le5\) वाला रेखाखंड / line segment on (y=3) with \(2\le x\le5\)
C पूरा तल \(\mathbb{R}^2\) / whole plane \(\mathbb{R}^2\)
D केवल बिंदु ((3,2)) / only point ((3,2))
Explanation opens after your attempt
Correct Answer
B. रेखा (y=3) पर \(2\le x\le5\) वाला रेखाखंड / line segment on (y=3) with \(2\le x\le5\)
Step 1
Concept
\(A\times B={(x,3):2\le x\le5}\). Hence it is a horizontal line segment on (y=3).
Step 2
Why this answer is correct
The correct answer is B. रेखा (y=3) पर \(2\le x\le5\) वाला रेखाखंड / line segment on (y=3) with \(2\le x\le5\). \(A\times B={(x,3):2\le x\le5}\). Hence it is a horizontal line segment on (y=3).
Step 3
Exam Tip
\(A\times B={(x,3):2\le x\le5}\) है। इसलिए यह (y=3) पर क्षैतिज रेखाखंड है।
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यदि \(A=\{2\}\) और (B=[-1,4]) हैं, तो \(A\times B\) कौन सा है?
If \(A=\{2\}\) and (B=[-1,4]), which one is \(A\times B\)?
#cartesian-product
#interval
#set-builder
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A ({(x,2):-1\le x\le4})
B ({(2,y):-1\le y\le4})
C ({(-1,2),(4,2)})
D ({(2,-1)})
Explanation opens after your attempt
Correct Answer
B. ({(2,y):-1\le y\le4})
Step 1
Concept
The first component is always (2), and the second varies in ([-1,4]). This is a vertical line segment on (x=2).
Step 2
Why this answer is correct
The correct answer is B. ({(2,y):-1\le y\le4}). The first component is always (2), and the second varies in ([-1,4]). This is a vertical line segment on (x=2).
Step 3
Exam Tip
पहला घटक हमेशा (2) है और दूसरा ([-1,4]) में बदलता है। यह (x=2) पर ऊर्ध्वाधर रेखाखंड है।
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यदि \(A=\{1,2,3\}\), \(B=\{4,5\}\) और \(C=\{6\}\) हैं, तो (\(A\times B\)\times C) में कितने अवयव होंगे?
If \(A=\{1,2,3\}\), \(B=\{4,5\}\) and \(C=\{6\}\), how many elements are in (\(A\times B\)\times C)?
#cartesian-product
#nested-product
#cardinality
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A (5)
B (6)
C (12)
D (3)
Explanation opens after your attempt
Step 1
Concept
(n\(A\times B\)=3\times2=6) and (n(C)=1). Therefore (n(\(A\times B\)\times C)=6\times1=6).
Step 2
Why this answer is correct
The correct answer is B. (6). (n\(A\times B\)=3\times2=6) and (n(C)=1). Therefore (n(\(A\times B\)\times C)=6\times1=6).
Step 3
Exam Tip
(n\(A\times B\)=3\times2=6) और (n(C)=1) है। इसलिए (n(\(A\times B\)\times C)=6\times1=6)।
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यदि \(A=\{2,4,6,8\}\) और \(B=\{1,3\}\) हैं, तो \(A\times B\) में पहले घटकों का समुच्चय क्या है?
If \(A=\{2,4,6,8\}\) and \(B=\{1,3\}\), what is the set of first components in \(A\times B\)?
#cartesian-product
#projection
#components
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A ({1,3})
B ({2,4,6,8})
C ({1,2,3,4,6,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
B. ({2,4,6,8})
Step 1
Concept
Since (B) is non-empty, every element of (A) appears as a first component. Therefore the set of first components is (A).
Step 2
Why this answer is correct
The correct answer is B. ({2,4,6,8}). Since (B) is non-empty, every element of (A) appears as a first component. Therefore the set of first components is (A).
Step 3
Exam Tip
क्योंकि (B) अरिक्त है, (A) का हर अवयव पहले घटक के रूप में आएगा। इसलिए पहले घटकों का समुच्चय (A) है।
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यदि \(A=\{u,v,w\}\) और \(B=\{0,1\}\) हैं, तो \(A\times B\) में दूसरे घटकों का समुच्चय क्या है?
If \(A=\{u,v,w\}\) and \(B=\{0,1\}\), what is the set of second components in \(A\times B\)?
#cartesian-product
#projection
#components
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A ({u,v,w})
B ({0,1})
C ({u,v,w,0,1})
D ({(u,0),(w,1)})
Explanation opens after your attempt
Correct Answer
B. ({0,1})
Step 1
Concept
Second components always come from (B). Since (A) is non-empty, every element of (B) appears as a second component.
Step 2
Why this answer is correct
The correct answer is B. ({0,1}). Second components always come from (B). Since (A) is non-empty, every element of (B) appears as a second component.
Step 3
Exam Tip
दूसरे घटक हमेशा (B) से आते हैं। क्योंकि (A) अरिक्त है, (B) का हर अवयव दूसरे घटक के रूप में आता है।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{1,2,3\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x+y) सम है?
If \(A=\{1,2,3,4\}\) and \(B=\{1,2,3\}\), how many pairs ((x,y)) in \(A\times B\) have (x+y) even?
#cartesian-product
#parity
#counting
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A (6)
B (5)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
The sum is even when both components have the same parity. Here such pairs are \(2\times2+2\times1=6\).
Step 2
Why this answer is correct
The correct answer is A. (6). The sum is even when both components have the same parity. Here such pairs are \(2\times2+2\times1=6\).
Step 3
Exam Tip
योग सम तब होगा जब दोनों घटक समान सम-विषम प्रकृति के हों। यहां ऐसे \(2\times2+2\times1=6\) युग्म हैं।
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यदि \(A=\{0,2,4,6\}\) और \(B=\{1,3,5\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x+y=7)?
If \(A=\{0,2,4,6\}\) and \(B=\{1,3,5\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x+y=7)?
#cartesian-product
#sum-condition
#membership
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A (2)
B (3)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((2,5),(4,3),(6,1)). Count pairs only after applying the condition.
Step 2
Why this answer is correct
The correct answer is B. (3). The valid pairs are ((2,5),(4,3),(6,1)). Count pairs only after applying the condition.
Step 3
Exam Tip
सही युग्म ((2,5),(4,3),(6,1)) हैं। शर्त लगाने के बाद ही युग्मों की गिनती करें।
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यदि \(A=\{2,5,8\}\) और \(B=\{1,4,7\}\) हैं, तो \(A\times B\) में सबसे बड़े घटक-योग वाला युग्म कौन सा है?
If \(A=\{2,5,8\}\) and \(B=\{1,4,7\}\), which pair in \(A\times B\) has the greatest sum of components?
#cartesian-product
#maximum
#application
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A ((7,8))
B ((8,4))
C ((8,7))
D ((5,7))
Explanation opens after your attempt
Correct Answer
C. ((8,7))
Step 1
Concept
The greatest first component is (8) and the greatest second component is (7). Therefore ((8,7)) has the greatest sum.
Step 2
Why this answer is correct
The correct answer is C. ((8,7)). The greatest first component is (8) and the greatest second component is (7). Therefore ((8,7)) has the greatest sum.
Step 3
Exam Tip
सबसे बड़ा पहला घटक (8) और सबसे बड़ा दूसरा घटक (7) है। इसलिए ((8,7)) का योग सबसे बड़ा होगा।
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यदि \(A=\{2,3,4,5\}\) और \(B=\{1,2,3\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x-y=2)?
If \(A=\{2,3,4,5\}\) and \(B=\{1,2,3\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x-y=2)?
#cartesian-product
#difference-condition
#application
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A (2)
B (3)
C (4)
D (1)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((3,1),(4,2),(5,3)). Choosing (y) and finding (x=y+2) is easy.
Step 2
Why this answer is correct
The correct answer is B. (3). The valid pairs are ((3,1),(4,2),(5,3)). Choosing (y) and finding (x=y+2) is easy.
Step 3
Exam Tip
सही युग्म ((3,1),(4,2),(5,3)) हैं। (y) चुनकर (x=y+2) निकालना आसान है।
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यदि \(A=\{1,2,3,6\}\) और \(B=\{1,2,3,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (xy=6)?
If \(A=\{1,2,3,6\}\) and \(B=\{1,2,3,6\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (xy=6)?
#cartesian-product
#product-condition
#ordered-pairs
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((1,6),(2,3),(3,2),(6,1)). In ordered pairs, ((2,3)) and ((3,2)) are different.
Step 2
Why this answer is correct
The correct answer is C. (4). The valid pairs are ((1,6),(2,3),(3,2),(6,1)). In ordered pairs, ((2,3)) and ((3,2)) are different.
Step 3
Exam Tip
सही युग्म ((1,6),(2,3),(3,2),(6,1)) हैं। क्रमित युग्मों में ((2,3)) और ((3,2)) अलग हैं।
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यदि \(A=\{1,2,3\}\), \(B=\{3,6,9\}\) और \(C=\{6\}\) हैं, तो \(A\times(B-C)\) क्या होगा?
If \(A=\{1,2,3\}\), \(B=\{3,6,9\}\) and \(C=\{6\}\), what is \(A\times(B-C)\)?
#cartesian-product
#set-difference
#listing
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A ({(1,3),(1,9),(2,3),(2,9),(3,3),(3,9)})
B ({(3,1),(9,1),(3,2),(9,2),(3,3),(9,3)})
C ({(1,6),(2,6),(3,6)})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({(1,3),(1,9),(2,3),(2,9),(3,3),(3,9)})
Step 1
Concept
(B-C={3,9}), so each element of (A) pairs with (3) and (9). Find the difference first and then write the pairs.
Step 2
Why this answer is correct
The correct answer is A. ({(1,3),(1,9),(2,3),(2,9),(3,3),(3,9)}). (B-C={3,9}), so each element of (A) pairs with (3) and (9). Find the difference first and then write the pairs.
Step 3
Exam Tip
(B-C={3,9}), इसलिए (A) के हर अवयव के साथ (3) और (9) जुड़ेंगे। पहले अंतर निकालें फिर युग्म लिखें।
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यदि \(A=\{4,5\}\) और \(B=\{6,7,8\}\) हैं, तो \(A\times B\) का सही सेट-बिल्डर रूप कौन सा है?
If \(A=\{4,5\}\) and \(B=\{6,7,8\}\), which is the correct set-builder form of \(A\times B\)?
#cartesian-product
#set-builder
#definition
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A \({(x,y):x\in B,,y\in A}\)
B \({x+y:x\in A,,y\in B}\)
C \({(x,y):x\in A,,y\in B}\)
D \({xy:x\in A,,y\in B}\)
Explanation opens after your attempt
Correct Answer
C. \({(x,y):x\in A,,y\in B}\)
Step 1
Concept
Cartesian product is a set of ordered pairs. In the correct form, the first component is from (A) and the second is from (B).
Step 2
Why this answer is correct
The correct answer is C. \({(x,y):x\in A,,y\in B}\). Cartesian product is a set of ordered pairs. In the correct form, the first component is from (A) and the second is from (B).
Step 3
Exam Tip
कार्तीय गुणन क्रमित युग्मों का समुच्चय है। सही रूप में पहला घटक (A) से और दूसरा (B) से होना चाहिए।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{2,3,4\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि \(x\le y\)?
If \(A=\{1,2,3,4\}\) and \(B=\{2,3,4\}\), how many pairs ((x,y)) in \(A\times B\) satisfy \(x\le y\)?
#cartesian-product
#inequality
#equality-included
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A (7)
B (8)
C (9)
D (6)
Explanation opens after your attempt
Step 1
Concept
For (y=2), there are (2) pairs; for (y=3), (3) pairs; and for (y=4), (4) pairs. Total pairs are (2+3+4=9).
Step 2
Why this answer is correct
The correct answer is C. (9). For (y=2), there are (2) pairs; for (y=3), (3) pairs; and for (y=4), (4) pairs. Total pairs are (2+3+4=9).
Step 3
Exam Tip
(y=2) के लिए (2) युग्म, (y=3) के लिए (3) युग्म और (y=4) के लिए (4) युग्म हैं। कुल (2+3+4=9) युग्म मिलते हैं।
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यदि \(A=\{3,6,9\}\) और \(B=\{1,2,3\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x=3y)?
If \(A=\{3,6,9\}\) and \(B=\{1,2,3\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x=3y)?
#cartesian-product
#equation-condition
#counting
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A (2)
B (6)
C (1)
D (3)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((3,1),(6,2),(9,3)). While applying the condition, remember the limits of both sets.
Step 2
Why this answer is correct
The correct answer is D. (3). The valid pairs are ((3,1),(6,2),(9,3)). While applying the condition, remember the limits of both sets.
Step 3
Exam Tip
सही युग्म ((3,1),(6,2),(9,3)) हैं। शर्त लगाते समय दोनों समुच्चयों की सीमा याद रखें।
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यदि \(A=\{1,2,5\}\) और \(B=\{2,4,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x+y>7)?
If \(A=\{1,2,5\}\) and \(B=\{2,4,6\}\), how many pairs ((x,y)) in \(A\times B\) satisfy (x+y>7)?
#cartesian-product
#inequality
#sum-condition
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The valid pairs are ((2,6),(5,4),(5,6)). Pairs with (x+y=7) are not included.
Step 2
Why this answer is correct
The correct answer is B. (3). The valid pairs are ((2,6),(5,4),(5,6)). Pairs with (x+y=7) are not included.
Step 3
Exam Tip
सही युग्म ((2,6),(5,4),(5,6)) हैं। (x+y=7) वाले युग्म शामिल नहीं होंगे।
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कथन: यदि \(A=\varnothing\) और \(B\ne\varnothing\), तो \(A\times B=\varnothing\)। यह कथन कैसा है?
Statement: If \(A=\varnothing\) and \(B\ne\varnothing\), then \(A\times B=\varnothing\). What is this statement?
#cartesian-product
#assertion
#empty-set
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A असत्य / false
B सत्य / true
C केवल जब (B=A) / only when (B=A)
D निर्धारित नहीं / not determined
Explanation opens after your attempt
Correct Answer
B. सत्य / true
Step 1
Concept
The first component must come from (A), but \(A=\varnothing\). Therefore no ordered pair is formed.
Step 2
Why this answer is correct
The correct answer is B. सत्य / true. The first component must come from (A), but \(A=\varnothing\). Therefore no ordered pair is formed.
Step 3
Exam Tip
पहला घटक (A) से आना चाहिए पर \(A=\varnothing\) है। इसलिए कोई क्रमित युग्म नहीं बनेगा।
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कथन: यदि (A=B), तो \(A\times B=B\times A\)। सही विकल्प चुनिए।
Statement: If (A=B), then \(A\times B=B\times A\). Choose the correct option.
#cartesian-product
#assertion
#equality
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A कथन असत्य है / the statement is false
B कथन सत्य है / the statement is true
C कथन केवल रिक्त समुच्चय के लिए सत्य है / the statement is true only for the empty set
D कथन संख्या पर निर्भर है / the statement depends on number only
Explanation opens after your attempt
Correct Answer
B. कथन सत्य है / the statement is true
Step 1
Concept
If (A=B), then both sides are actually \(A\times A\). Therefore both Cartesian products are equal.
Step 2
Why this answer is correct
The correct answer is B. कथन सत्य है / the statement is true. If (A=B), then both sides are actually \(A\times A\). Therefore both Cartesian products are equal.
Step 3
Exam Tip
यदि (A=B), तो दोनों तरफ वास्तव में \(A\times A\) ही है। इसलिए दोनों कार्तीय गुणन समान होंगे।
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\(यदि (A={1,2,3,4}), (B={a,b}) और (R={(x,y):x\in A,,y\in B,,x\) सम है}) है, तो कौन सा युग्म (R) में होगा?
\(If (A={1,2,3,4}), (B={a,b}) and (R={(x,y):x\in A,,y\in B,,x\) is even}), which pair belongs to (R)?
#cartesian-product
#relation
#condition
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A ((1,a))
B ((a,2))
C ((4,b))
D ((3,b))
Explanation opens after your attempt
Correct Answer
C. ((4,b))
Step 1
Concept
\(4\in A\) is even and \(b\in B\), so \((4,b)\in R\). Apply the relation condition to every option.
Step 2
Why this answer is correct
The correct answer is C. ((4,b)). \(4\in A\) is even and \(b\in B\), so \((4,b)\in R\). Apply the relation condition to every option.
Step 3
Exam Tip
\(4\in A\) सम है और \(b\in B\), इसलिए \((4,b)\in R\)। संबंध की शर्त को हर विकल्प पर लगाएं।
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यदि \(A=\{0,1,2\}\), \(B=\{3,4\}\) और \(R=\{(0,3),(2,4)\}\) है, तो (R) किसका उपसमुच्चय है?
If \(A=\{0,1,2\}\), \(B=\{3,4\}\) and \(R=\{(0,3),(2,4)\}\), then (R) is a subset of which set?
#cartesian-product
#subset
#relation
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A \(B\times A\)
B \(A\cap B\)
C \(A\times B\)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
C. \(A\times B\)
Step 1
Concept
In every pair of (R), the first component is from (A) and the second is from (B). Therefore \(R\subseteq A\times B\).
Step 2
Why this answer is correct
The correct answer is C. \(A\times B\). In every pair of (R), the first component is from (A) and the second is from (B). Therefore \(R\subseteq A\times B\).
Step 3
Exam Tip
(R) के हर युग्म में पहला घटक (A) से और दूसरा (B) से है। इसलिए \(R\subseteq A\times B\)।
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यदि \(A=\{1,2\}\) और \(B=\{2,5\}\) हैं, तो \(A\times B\) में सभी युग्मों के घटक-योगों का समुच्चय क्या है?
If \(A=\{1,2\}\) and \(B=\{2,5\}\), what is the set of sums of components of all pairs in \(A\times B\)?
#cartesian-product
#sum-set
#application
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A ({3,4,6,7})
B ({2,5})
C ({1,2,5})
D ({3,7})
Explanation opens after your attempt
Correct Answer
A. ({3,4,6,7})
Step 1
Concept
The sums are (1+2=3), (1+5=6), (2+2=4) and (2+5=7). Write each result once in a set.
Step 2
Why this answer is correct
The correct answer is A. ({3,4,6,7}). The sums are (1+2=3), (1+5=6), (2+2=4) and (2+5=7). Write each result once in a set.
Step 3
Exam Tip
योग (1+2=3), (1+5=6), (2+2=4) और (2+5=7) मिलते हैं। समुच्चय में परिणामों को एक बार लिखें।
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यदि \(A=\{1,2,3,4\}\) और \(B=\{2,4,6\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (y) सम है?
If \(A=\{1,2,3,4\}\) and \(B=\{2,4,6\}\), how many pairs ((x,y)) in \(A\times B\) have (y) even?
#cartesian-product
#parity
#components
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A (7)
B (12)
C (6)
D (4)
Explanation opens after your attempt
Step 1
Concept
All (3) elements of (B) are even and pair with (4) elements of (A). Hence \(4\times3=12\) pairs are formed.
Step 2
Why this answer is correct
The correct answer is B. (12). All (3) elements of (B) are even and pair with (4) elements of (A). Hence \(4\times3=12\) pairs are formed.
Step 3
Exam Tip
(B) के सभी (3) अवयव सम हैं और (A) के (4) अवयवों से जुड़ते हैं। इसलिए \(4\times3=12\) युग्म बनेंगे।
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यदि \(A=\{1,2,3,4,5\}\) और \(B=\{0,1\}\) हैं, तो \(A\times B\) में कितने युग्म ((x,y)) ऐसे हैं कि (x) अभाज्य है?
If \(A=\{1,2,3,4,5\}\) and \(B=\{0,1\}\), how many pairs ((x,y)) in \(A\times B\) have (x) prime?
#cartesian-product
#prime-numbers
#counting
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A (4)
B (5)
C (6)
D (3)
Explanation opens after your attempt
Step 1
Concept
The prime elements in (A) are (2,3,5), and each pairs with (2) elements of (B). Therefore \(3\times2=6\) pairs are formed.
Step 2
Why this answer is correct
The correct answer is C. (6). The prime elements in (A) are (2,3,5), and each pairs with (2) elements of (B). Therefore \(3\times2=6\) pairs are formed.
Step 3
Exam Tip
(A) में अभाज्य अवयव (2,3,5) हैं और हर एक (B) के (2) अवयवों से जुड़ता है। इसलिए \(3\times2=6\) युग्म होंगे।
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यदि \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) और \(C=\{0,3\}\) हैं, तो (\(A\cap B\)\times C) में कौन सा युग्म होगा?
If \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) and \(C=\{0,3\}\), which pair belongs to (\(A\cap B\)\times C)?
#cartesian-product
#intersection
#membership
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A ((1,0))
B ((4,3))
C ((3,0))
D ((0,3))
Explanation opens after your attempt
Correct Answer
C. ((3,0))
Step 1
Concept
\(A\cap B={2,3}\), so the first component must be (2) or (3) and the second must be from (C). ((3,0)) satisfies this condition.
Step 2
Why this answer is correct
The correct answer is C. ((3,0)). \(A\cap B={2,3}\), so the first component must be (2) or (3) and the second must be from (C). ((3,0)) satisfies this condition.
Step 3
Exam Tip
\(A\cap B={2,3}\), इसलिए पहला घटक (2) या (3) और दूसरा (C) से होना चाहिए। ((3,0)) यह शर्त पूरी करता है।
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यदि \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) और \(C=\{3,4,5\}\) हैं, तो (A\times(\(B\cup C\)-A)) में कितने अवयव होंगे?
If \(A=\{1,2,3\}\), \(B=\{2,3,4\}\) and \(C=\{3,4,5\}\), how many elements are in (A\times(\(B\cup C\)-A))?
#cartesian-product
#union
#set-difference
#cardinality
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A (3)
B (4)
C (6)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(B\cup C={2,3,4,5}\) and (\(B\cup C\)-A={4,5}). Therefore (n(A\times(\(B\cup C\)-A))=3\times2=6).
Step 2
Why this answer is correct
The correct answer is C. (6). \(B\cup C={2,3,4,5}\) and (\(B\cup C\)-A={4,5}). Therefore (n(A\times(\(B\cup C\)-A))=3\times2=6).
Step 3
Exam Tip
\(B\cup C={2,3,4,5}\) और (\(B\cup C\)-A={4,5}) है। इसलिए (n(A\times(\(B\cup C\)-A))=3\times2=6)।
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