यदि (A) में (7) तत्व हैं, तो (A) के ऐसे उपसमुच्चय कितने हैं जिनमें एक निश्चित तत्व अवश्य हो?
If (A) has (7) elements, how many subsets of (A) must contain one fixed element?
#sets
#power set
#subset counting
#class 11
A (32)
B (64)
C (96)
D (128)
Explanation opens after your attempt
Step 1
Concept
One element is fixed to be included and the remaining (6) elements are free. So the number of subsets is \(2^6=64\).
Step 2
Why this answer is correct
The correct answer is B. (64). One element is fixed to be included and the remaining (6) elements are free. So the number of subsets is \(2^6=64\).
Step 3
Exam Tip
एक तत्व को रखना तय है और बाकी (6) तत्व स्वतंत्र हैं। इसलिए उपसमुच्चयों की संख्या \(2^6=64\) होगी।
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यदि \(A=\{2,4,6,8,10\}\) है, तो (\mathcal{P}(A)) में ठीक (2) तत्व वाले समुच्चयों की संख्या कितनी है?
If \(A=\{2,4,6,8,10\}\), how many sets in (\mathcal{P}(A)) have exactly (2) elements?
#sets
#power set
#combination
#class 11
A (5)
B (10)
C (15)
D (20)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose exactly (2) elements is \(\binom{5}{2}=10\). Each choice becomes an element of the power set.
Step 2
Why this answer is correct
The correct answer is B. (10). The number of ways to choose exactly (2) elements is \(\binom{5}{2}=10\). Each choice becomes an element of the power set.
Step 3
Exam Tip
ठीक (2) तत्व चुनने की संख्या \(\binom{5}{2}=10\) है। हर चयन घात समुच्चय का एक तत्व बनता है।
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यदि (A) में (4) तत्व हैं, तो (A) के अरिक्त उचित उपसमुच्चयों की संख्या कितनी होगी?
If (A) has (4) elements, how many non-empty proper subsets does (A) have?
#sets
#proper subset
#non empty
#class 11
A (14)
B (15)
C (16)
D (12)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^4=16\). Removing \(\varnothing\) and (A) leaves (14) non-empty proper subsets.
Step 2
Why this answer is correct
The correct answer is A. (14). Total subsets are \(2^4=16\). Removing \(\varnothing\) and (A) leaves (14) non-empty proper subsets.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^4=16\) हैं। \(\varnothing\) और (A) को हटाने पर (14) अरिक्त उचित उपसमुच्चय बचते हैं।
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किसी समुच्चय (A) के लिए कौन सा कथन हमेशा सत्य है?
Which statement is always true for a set (A)?
#sets
#power set
#empty set
#class 11
A \(A\in A\)
B \(\varnothing\in A\)
C \(\varnothing\in \mathcal{P}(A)\)
D \(U\in \mathcal{P}(A)\)
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\in \mathcal{P}(A)\)
Step 1
Concept
\(\varnothing\) is a subset of every set. Therefore \(\varnothing\) is always an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is C. \(\varnothing\in \mathcal{P}(A)\). \(\varnothing\) is a subset of every set. Therefore \(\varnothing\) is always an element of (\mathcal{P}(A)).
Step 3
Exam Tip
\(\varnothing\) हर समुच्चय का उपसमुच्चय है। इसलिए \(\varnothing\) हमेशा (\mathcal{P}(A)) का तत्व होगा।
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यदि \(A={\varnothing,{\varnothing}}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A={\varnothing,{\varnothing}}\), which of the following is an element of (\mathcal{P}(A))?
#sets
#empty set
#power set
#class 11
A \({\varnothing}\)
B \({{\varnothing}}\)
C \(\varnothing\)
D उपरोक्त सभी / All of these
Explanation opens after your attempt
Correct Answer
D. उपरोक्त सभी / All of these
Step 1
Concept
All three given options are subsets of (A). Therefore all of them are elements of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is D. उपरोक्त सभी / All of these. All three given options are subsets of (A). Therefore all of them are elements of (\mathcal{P}(A)).
Step 3
Exam Tip
दिए गए तीनों विकल्प (A) के उपसमुच्चय हैं। इसलिए ये सभी (\mathcal{P}(A)) के तत्व हैं।
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यदि \({m,n}\in \mathcal{P}(A)\) है, तो कौन सा कथन निश्चित रूप से सही है?
If \({m,n}\in \mathcal{P}(A)\), which statement is definitely true?
#sets
#power set
#element subset
#class 11
A \(m\in A\) और \(n\in A\) / \(m\in A\) and \(n\in A\)
B \({m,n}\not\subseteq A\)
C \(A=\{m,n\}\)
D \(m\notin A\)
Explanation opens after your attempt
Correct Answer
A. \(m\in A\) और \(n\in A\) / \(m\in A\) and \(n\in A\)
Step 1
Concept
\({m,n}\in \mathcal{P}(A)\) means \({m,n}\subseteq A\). Therefore both (m) and (n) are elements of (A).
Step 2
Why this answer is correct
The correct answer is A. \(m\in A\) और \(n\in A\) / \(m\in A\) and \(n\in A\). \({m,n}\in \mathcal{P}(A)\) means \({m,n}\subseteq A\). Therefore both (m) and (n) are elements of (A).
Step 3
Exam Tip
\({m,n}\in \mathcal{P}(A)\) का अर्थ है \({m,n}\subseteq A\)। इसलिए (m) और (n) दोनों (A) के तत्व होंगे।
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यदि \(A=\{k\}\) है, तो (\mathcal{P}(A)) कौन सा है?
If \(A=\{k\}\), which is (\mathcal{P}(A))?
#sets
#singleton
#power set
#class 11
A ({k})
B \({\varnothing,k}\)
C \({\varnothing,{k}}\)
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
C. \({\varnothing,{k}}\)
Step 1
Concept
The subsets of a singleton set are \(\varnothing\) and the set itself. So the power set contains ({k}), not just (k).
Step 2
Why this answer is correct
The correct answer is C. \({\varnothing,{k}}\). The subsets of a singleton set are \(\varnothing\) and the set itself. So the power set contains ({k}), not just (k).
Step 3
Exam Tip
एकल समुच्चय के उपसमुच्चय \(\varnothing\) और वही समुच्चय होते हैं। इसलिए घात समुच्चय में ({k}) आएगा, केवल (k) नहीं।
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यदि \(A={x:x\) संख्या (24) का धनात्मक भाजक है(}), तो (n(\mathcal{P}(A))) क्या होगा?
If \(A={x:x\) is a positive divisor of (24)(}), what is (n(\mathcal{P}(A)))?
#sets
#power set
#divisors
#class 11
A (64)
B (128)
C (256)
D (24)
Explanation opens after your attempt
Step 1
Concept
The divisors of (24) are (1,2,3,4,6,8,12,24), so (n(A)=8). Hence (n(\mathcal{P}(A))=28 =256).
Step 2
Why this answer is correct
The correct answer is C. (256). The divisors of (24) are (1,2,3,4,6,8,12,24), so (n(A)=8). Hence (n(\mathcal{P}(A))=28 =256).
Step 3
Exam Tip
(24) के भाजक (1,2,3,4,6,8,12,24) हैं इसलिए (n(A)=8)। अतः (n(\mathcal{P}(A))=28 =256)।
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यदि (n(U)=80) और (n(A')=19) है, तो (n(A)) कितना होगा?
If (n(U)=80) and (n(A')=19), what is (n(A))?
#sets
#complement
#universal set
#class 11
A (19)
B (41)
C (61)
D (99)
Explanation opens after your attempt
Step 1
Concept
(A) and (A') together form the whole (U). So (n(A)=80-19=61).
Step 2
Why this answer is correct
The correct answer is C. (61). (A) and (A') together form the whole (U). So (n(A)=80-19=61).
Step 3
Exam Tip
(A) और (A') मिलकर पूरा (U) बनाते हैं। इसलिए (n(A)=80-19=61)।
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यदि \(A\subseteq U\) और \(A'= \varnothing\) है, तो कौन सा निष्कर्ष सही है?
If \(A\subseteq U\) and \(A'= \varnothing\), which conclusion is correct?
#sets
#universal set
#complement reasoning
#class 11
A \(A=\varnothing\)
B (A=U)
C \(U=\varnothing\)
D \(A\cap U=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
If the complement is empty, no element of (U) lies outside (A). Therefore (A=U).
Step 2
Why this answer is correct
The correct answer is B. (A=U). If the complement is empty, no element of (U) lies outside (A). Therefore (A=U).
Step 3
Exam Tip
पूरक खाली है तो (U) में (A) के बाहर कोई तत्व नहीं है। इसलिए (A=U) होगा।
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यदि (A) और (B), (U) के उपसमुच्चय हैं, तो (\(A\cap B\)') किसके बराबर होता है?
If (A) and (B) are subsets of (U), what is (\(A\cap B\)') equal to?
#sets
#de morgan law
#complement
#class 11
A \(A'\cap B'\)
B \(A'\cup B'\)
C \(A\cup B\)
D \(A\cap B\)
Explanation opens after your attempt
Correct Answer
B. \(A'\cup B'\)
Step 1
Concept
By De Morgan's law, (\(A\cap B\)'=A'\cup B'). The complement of an intersection includes elements outside at least one set.
Step 2
Why this answer is correct
The correct answer is B. \(A'\cup B'\). By De Morgan's law, (\(A\cap B\)'=A'\cup B'). The complement of an intersection includes elements outside at least one set.
Step 3
Exam Tip
डी मॉर्गन नियम के अनुसार (\(A\cap B\)'=A'\cup B')। प्रतिच्छेद के पूरक में कम से कम एक समुच्चय से बाहर वाले तत्व आते हैं।
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एक विद्यालय के (75) विद्यार्थियों में (32) संगीत में और (28) नाटक में भाग लेते हैं। यदि (10) विद्यार्थी दोनों में भाग लेते हैं, तो किसी भी गतिविधि में भाग न लेने वाले विद्यार्थी कितने हैं?
In a school of (75) students, (32) take part in music and (28) take part in drama. If (10) students take part in both, how many take part in neither activity?
#sets
#universal set
#venn diagram
#class 11
A (20)
B (25)
C (30)
D (35)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=32+28-10=50). Students in neither activity are (75-50=25).
Step 2
Why this answer is correct
The correct answer is B. (25). (n\(A\cup B\)=32+28-10=50). Students in neither activity are (75-50=25).
Step 3
Exam Tip
(n\(A\cup B\)=32+28-10=50) होगा। किसी में नहीं (75-50=25) विद्यार्थी हैं।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{1,4,9\}\) है, तो (A') में कितने तत्व होंगे?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{1,4,9\}\), how many elements will (A') have?
#sets
#complement
#cardinality
#class 11
A (3)
B (6)
C (7)
D (10)
Explanation opens after your attempt
Step 1
Concept
(U) has (10) elements and (A) has (3) elements. Hence (n(A')=10-3=7).
Step 2
Why this answer is correct
The correct answer is C. (7). (U) has (10) elements and (A) has (3) elements. Hence (n(A')=10-3=7).
Step 3
Exam Tip
(U) में (10) और (A) में (3) तत्व हैं। अतः (n(A')=10-3=7)।
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यदि \(U=\{a,b,c,d,e,f\}\) और \(A=\{a,c,f\}\) है, तो (A') क्या होगा?
If \(U=\{a,b,c,d,e,f\}\) and \(A=\{a,c,f\}\), what is (A')?
#sets
#universal set
#complement
#class 11
A ({b,d,e})
B ({a,c,f})
C ({a,b,c})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({b,d,e})
Step 1
Concept
(A') contains elements of (U) that are not in (A). Here those elements are (b,d,e).
Step 2
Why this answer is correct
The correct answer is A. ({b,d,e}). (A') contains elements of (U) that are not in (A). Here those elements are (b,d,e).
Step 3
Exam Tip
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। यहां वे तत्व (b,d,e) हैं।
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(\mathcal{P}(\mathcal{P}({a}))) में कितने तत्व होंगे?
How many elements are there in (\mathcal{P}(\mathcal{P}({a})))?
#sets
#iterated power set
#singleton
#class 11
A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(\mathcal{P}({a})) has (2) elements. Therefore its power set has \(2^2=4\) elements.
Step 2
Why this answer is correct
The correct answer is B. (4). (\mathcal{P}({a})) has (2) elements. Therefore its power set has \(2^2=4\) elements.
Step 3
Exam Tip
(\mathcal{P}({a})) में (2) तत्व होते हैं। इसलिए उसके घात समुच्चय में \(2^2=4\) तत्व होंगे।
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यदि \(A={\varnothing,{\varnothing}}\) है, तो (n(\mathcal{P}(A))) कितना होगा?
If \(A={\varnothing,{\varnothing}}\), what is (n(\mathcal{P}(A)))?
#sets
#empty set
#power set
#class 11
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Set (A) has two distinct elements so its power set has \(2^2=4\) elements. Treat \(\varnothing\) and \({\varnothing}\) as different.
Step 2
Why this answer is correct
The correct answer is C. (4). Set (A) has two distinct elements so its power set has \(2^2=4\) elements. Treat \(\varnothing\) and \({\varnothing}\) as different.
Step 3
Exam Tip
(A) में दो अलग-अलग तत्व हैं इसलिए उसके घात समुच्चय में \(2^2=4\) तत्व होंगे। \(\varnothing\) और \({\varnothing}\) को अलग समझें।
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यदि \(A=\{0,{1},2\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व नहीं है?
If \(A=\{0,{1},2\}\), which of the following is not an element of (\mathcal{P}(A))?
#sets
#power set
#nested set
#class 11
A ({0,2})
B ({{1}})
C ({0,{1}})
D ({0,1})
Explanation opens after your attempt
Correct Answer
D. ({0,1})
Step 1
Concept
(1) itself is not an element of (A); ({1}) is an element. So ({0,1}) is not a subset of (A).
Step 2
Why this answer is correct
The correct answer is D. ({0,1}). (1) itself is not an element of (A); ({1}) is an element. So ({0,1}) is not a subset of (A).
Step 3
Exam Tip
(1) स्वयं (A) का तत्व नहीं है बल्कि ({1}) तत्व है। इसलिए ({0,1}), (A) का उपसमुच्चय नहीं है।
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यदि \(A=\{r,s,t,u\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{r,s,t,u\}\), which of the following is an element of (\mathcal{P}(A))?
#sets
#power set
#subset
#class 11
A (r)
B ({r,t})
C ({r,v})
D ({s,t,v})
Explanation opens after your attempt
Correct Answer
B. ({r,t})
Step 1
Concept
Every element of a power set is a subset of the original set. ({r,t}) contains only elements of (A) so it is correct.
Step 2
Why this answer is correct
The correct answer is B. ({r,t}). Every element of a power set is a subset of the original set. ({r,t}) contains only elements of (A) so it is correct.
Step 3
Exam Tip
घात समुच्चय का प्रत्येक तत्व मूल समुच्चय का उपसमुच्चय होता है। ({r,t}) में केवल (A) के तत्व हैं इसलिए यह सही है।
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यदि किसी समुच्चय (B) के कुल उपसमुच्चय (1024) हैं, तो उसके उचित उपसमुच्चयों की संख्या कितनी होगी?
If a set (B) has (1024) total subsets, how many proper subsets does it have?
#sets
#proper subset
#power set
#class 11
A (1023)
B (1024)
C (512)
D (10)
Explanation opens after your attempt
Step 1
Concept
A proper subset does not include the whole set itself. Therefore the number is (1024-1=1023).
Step 2
Why this answer is correct
The correct answer is A. (1023). A proper subset does not include the whole set itself. Therefore the number is (1024-1=1023).
Step 3
Exam Tip
उचित उपसमुच्चय में पूरा समुच्चय स्वयं शामिल नहीं होता। इसलिए संख्या (1024-1=1023) है।
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यदि (n(\mathcal{P}(A))=512) है, तो (n(A)) का मान क्या होगा?
If (n(\mathcal{P}(A))=512), what is the value of (n(A))?
#sets
#power set
#elements
#class 11
A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
\(512=2^9\) so (n(A)=9). Always use the \(2^n\) rule for power set questions.
Step 2
Why this answer is correct
The correct answer is C. (9). \(512=2^9\) so (n(A)=9). Always use the \(2^n\) rule for power set questions.
Step 3
Exam Tip
\(512=2^9\) इसलिए (n(A)=9) होगा। घात समुच्चय में हमेशा \(2^n\) नियम लगाएं।
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यदि \(A=\{0,2,4,6\}\) है, तो (\mathcal{P}(A)) में कुल कितने तत्व होंगे?
If \(A=\{0,2,4,6\}\), how many elements will (\mathcal{P}(A)) have?
#sets
#power set
#cardinality
#class 11
A (8)
B (12)
C (16)
D (24)
Explanation opens after your attempt
Step 1
Concept
Set (A) has (4) elements so (\mathcal{P}(A)) has \(2^4=16\) elements. In exams first count the distinct elements of the original set.
Step 2
Why this answer is correct
The correct answer is C. (16). Set (A) has (4) elements so (\mathcal{P}(A)) has \(2^4=16\) elements. In exams first count the distinct elements of the original set.
Step 3
Exam Tip
(A) में (4) तत्व हैं इसलिए (\mathcal{P}(A)) में \(2^4=16\) तत्व होंगे। परीक्षा में पहले मूल समुच्चय के अलग-अलग तत्व गिनें।
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यदि \(U={x:x\in \mathbb{N}, x\leq 15}\) और \(A={x:x\) (5) का गुणज है(}), तो (n(A')) कितना होगा?
If \(U={x:x\in \mathbb{N}, x\leq 15}\) and \(A={x:x\) is a multiple of (5)(}), what is (n(A'))?
#sets
#universal set
#cardinality
#class 11
A (3)
B (5)
C (10)
D (12)
Explanation opens after your attempt
Step 1
Concept
\(A=\{5,10,15\}\), so (n(A)=3). Since (U) has (15) elements, (n(A')=15-3=12).
Step 2
Why this answer is correct
The correct answer is D. (12). \(A=\{5,10,15\}\), so (n(A)=3). Since (U) has (15) elements, (n(A')=15-3=12).
Step 3
Exam Tip
\(A=\{5,10,15\}\) है, इसलिए (n(A)=3)। (U) में (15) तत्व हैं, अतः (n(A')=15-3=12)।
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यदि \(A=\{a,{b},c\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व नहीं है?
If \(A=\{a,{b},c\}\), which of the following is not an element of (\mathcal{P}(A))?
#sets
#power set
#element subset
#class 11
A ({a,c})
B ({{b}})
C ({a,{b}})
D ({a,b})
Explanation opens after your attempt
Correct Answer
D. ({a,b})
Step 1
Concept
(b) itself is not an element of (A); ({b}) is an element. So ({a,b}) is not a subset of (A).
Step 2
Why this answer is correct
The correct answer is D. ({a,b}). (b) itself is not an element of (A); ({b}) is an element. So ({a,b}) is not a subset of (A).
Step 3
Exam Tip
(b) स्वयं (A) का तत्व नहीं है, बल्कि ({b}) तत्व है। इसलिए ({a,b}), (A) का उपसमुच्चय नहीं है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{2,3,5,7\}\) है, तो (A') क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{2,3,5,7\}\), what is (A')?
#sets
#universal set
#complement
#class 11
A ({1,4,6,8})
B ({2,3,5,7})
C ({1,2,4,6})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,4,6,8})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). Therefore (1,4,6,8) form the correct complement.
Step 2
Why this answer is correct
The correct answer is A. ({1,4,6,8}). (A') contains the elements of (U) that are not in (A). Therefore (1,4,6,8) form the correct complement.
Step 3
Exam Tip
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। इसलिए (1,4,6,8) सही पूरक हैं।
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यदि \(A=\{1,3,5\}\) है, तो (\mathcal{P}(A)) में ऐसे कितने उपसमुच्चय होंगे जिनमें (3) अवश्य हो?
If \(A=\{1,3,5\}\), how many subsets in (\mathcal{P}(A)) must contain (3)?
#sets
#power set
#subset counting
#class 11
A (2)
B (4)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
Keeping (3) is fixed and the remaining (1,5) may be chosen or not chosen. So the number is \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is B. (4). Keeping (3) is fixed and the remaining (1,5) may be chosen or not chosen. So the number is \(2^2=4\).
Step 3
Exam Tip
(3) को रखना निश्चित है और बाकी (1,5) चुने या छोड़े जा सकते हैं। इसलिए संख्या \(2^2=4\) होगी।
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यदि \(U={x:x\in \mathbb{N}, x\leq 20}\) और \(A={x:x\) (20) का धनात्मक भाजक है(}) है, तो (n(A')) कितना होगा?
If \(U={x:x\in \mathbb{N}, x\leq 20}\) and \(A={x:x\) is a positive divisor of (20)(}), what is (n(A'))?
#sets
#universal set
#divisors complement
#class 11
A (4)
B (6)
C (14)
D (20)
Explanation opens after your attempt
Step 1
Concept
The positive divisors of (20) are (1,2,4,5,10,20), so (n(A)=6). Thus (n(A')=20-6=14).
Step 2
Why this answer is correct
The correct answer is C. (14). The positive divisors of (20) are (1,2,4,5,10,20), so (n(A)=6). Thus (n(A')=20-6=14).
Step 3
Exam Tip
(20) के धनात्मक भाजक (1,2,4,5,10,20) हैं, इसलिए (n(A)=6)। (n(A')=20-6=14) होगा।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,4\}\) हैं, तो (\mathcal{P}\(A\cup B\)) में कितने तत्व होंगे?
If \(A=\{1,2,3\}\) and \(B=\{3,4\}\), how many elements will (\mathcal{P}\(A\cup B\)) have?
#sets
#power set
#union
#class 11
A (8)
B (16)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={1,2,3,4}\), so it has (4) elements. Therefore its power set has \(2^4=16\) elements.
Step 2
Why this answer is correct
The correct answer is B. (16). \(A\cup B={1,2,3,4}\), so it has (4) elements. Therefore its power set has \(2^4=16\) elements.
Step 3
Exam Tip
\(A\cup B={1,2,3,4}\), इसलिए इसमें (4) तत्व हैं। अतः उसके घात समुच्चय में \(2^4=16\) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,4,7\}\) और \(B=\{2,4,8\}\) हैं, तो (\(A\cup B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,4,7\}\), and \(B=\{2,4,8\}\), what is (\(A\cup B\)')?
#sets
#universal set
#union complement
#class 11
A ({3,5,6,9})
B ({1,2,4,7,8})
C ({4})
D ({3,5,6})
Explanation opens after your attempt
Correct Answer
A. ({3,5,6,9})
Step 1
Concept
\(A\cup B={1,2,4,7,8}\). Removing these from (U) gives ({3,5,6,9}).
Step 2
Why this answer is correct
The correct answer is A. ({3,5,6,9}). \(A\cup B={1,2,4,7,8}\). Removing these from (U) gives ({3,5,6,9}).
Step 3
Exam Tip
\(A\cup B={1,2,4,7,8}\) है। (U) से इन्हें हटाने पर ({3,5,6,9}) मिलता है।
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यदि \(A=\{x,y,z\}\) है, तो (\mathcal{P}(A)) में ऐसे कितने तत्व हैं जो (A) के उचित उपसमुच्चय भी हैं?
If \(A=\{x,y,z\}\), how many elements of (\mathcal{P}(A)) are also proper subsets of (A)?
#sets
#power set
#proper subset
#class 11
A (3)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
(\mathcal{P}(A)) has (8) total subsets. For proper subsets, only (A) itself is removed, so (7) remain.
Step 2
Why this answer is correct
The correct answer is C. (7). (\mathcal{P}(A)) has (8) total subsets. For proper subsets, only (A) itself is removed, so (7) remain.
Step 3
Exam Tip
(\mathcal{P}(A)) में कुल (8) उपसमुच्चय हैं। उचित उपसमुच्चय के लिए केवल (A) को हटाते हैं, इसलिए (7) बचते हैं।
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यदि \(A=\{1,2,3,4,5\}\) है, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1) या (2) में से कोई भी न हो?
If \(A=\{1,2,3,4,5\}\), how many subsets of (A) contain neither (1) nor (2)?
#sets
#power set
#restricted subsets
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
After excluding (1) and (2), the elements (3,4,5) remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding (1) and (2), the elements (3,4,5) remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
(1) और (2) को हटाने के बाद (3,4,5) बचते हैं। इनके \(2^3=8\) उपसमुच्चय होंगे।
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