यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में कुल कितने तत्व होंगे?
If \(A=\{1,2,3\}\), how many elements will (\mathcal{P}(A)) have?
#sets
#power-set
#counting
#class-11
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A छह / 6
B आठ / 8
C नौ / 9
D बारह / 12
Explanation opens after your attempt
Step 1
Concept
A set with three elements has \(2^3=8\) subsets. In exams count (n(A)) first.
Step 2
Why this answer is correct
The correct answer is B. आठ / 8. A set with three elements has \(2^3=8\) subsets. In exams count (n(A)) first.
Step 3
Exam Tip
तीन तत्वों वाले समुच्चय के उपसमुच्चय \(2^3=8\) होते हैं। परीक्षा में पहले (n(A)) गिनें।
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यदि \(A=\{1,2,3,4\}\) है, तो (\mathcal{P}(A)) में कुल कितने तत्व होंगे?
If \(A=\{1,2,3,4\}\), how many elements will (\mathcal{P}(A)) have?
#sets
#power set
#cardinality
#class 11
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A (8)
B (12)
C (16)
D (4)
Explanation opens after your attempt
Step 1
Concept
If a set has (n) elements, its power set has \(2^n\) elements. Here \(2^4=16\), so remember this rule.
Step 2
Why this answer is correct
The correct answer is C. (16). If a set has (n) elements, its power set has \(2^n\) elements. Here \(2^4=16\), so remember this rule.
Step 3
Exam Tip
यदि समुच्चय में (n) तत्व हों, तो घात समुच्चय में \(2^n\) तत्व होते हैं। यहां \(2^4=16\), इसलिए यह नियम याद रखें।
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यदि सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5,6,7,8,9,10\}\) और \(A=\{2,4,6,8,10\}\) है, तो (A') क्या होगा?
If the universal set is \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{2,4,6,8,10\}\), what is (A')?
#sets
#universal set
#complement
#class 11
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A ({1,3,5,7,9})
B ({2,4,6,8,10})
C ({1,2,3,4,5})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7,9})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). In exams, always check the universal set before finding a complement.
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7,9}). (A') contains the elements of (U) that are not in (A). In exams, always check the universal set before finding a complement.
Step 3
Exam Tip
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। परीक्षा में पूरक निकालते समय पहले सार्वत्रिक समुच्चय देखें।
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यदि \(A=\{a,b\}\) है तो कौन सा तत्व (\mathcal{P}(A)) में नहीं होगा?
If \(A=\{a,b\}\), which element will not belong to (\mathcal{P}(A))?
#sets
#power-set
#membership
#class-11
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A \(\emptyset\)
B {(a)}
C {(b)}
D (a)
Explanation opens after your attempt
Step 1
Concept
Elements of (\mathcal{P}(A)) are subsets of (A). The symbol (a) is an element not a subset.
Step 2
Why this answer is correct
The correct answer is D. (a). Elements of (\mathcal{P}(A)) are subsets of (A). The symbol (a) is an element not a subset.
Step 3
Exam Tip
(\mathcal{P}(A)) के तत्व हमेशा (A) के उपसमुच्चय होते हैं। (a) स्वयं तत्व है उपसमुच्चय नहीं।
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यदि \(A=\{a,b,{c}\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{a,b,{c}\}\), which of the following is an element of (\mathcal{P}(A))?
#sets
#power set
#subset reasoning
#class 11
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A ({a,c})
B ({a,{c}})
C (c)
D ({a,b,c})
Explanation opens after your attempt
Correct Answer
B. ({a,{c}})
Step 1
Concept
Every element of a power set is a subset of the original set. Both elements of ({a,{c}}) are in (A), so it is correct.
Step 2
Why this answer is correct
The correct answer is B. ({a,{c}}). Every element of a power set is a subset of the original set. Both elements of ({a,{c}}) are in (A), so it is correct.
Step 3
Exam Tip
घात समुच्चय का हर तत्व मूल समुच्चय का उपसमुच्चय होता है। ({a,{c}}) के दोनों तत्व (A) में हैं, इसलिए यह सही है।
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सार्वत्रिक समुच्चय \(U=\{1,2,3,4,5\}\) और \(A=\{2,4\}\) हो तो (A') क्या है?
Let the universal set be \(U=\{1,2,3,4,5\}\) and \(A=\{2,4\}\). What is (A')?
#sets
#universal-set
#complement
#class-11
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A {(1,3,5)}
B {(2,4)}
C {(1,2,3)}
D {(4,5)}
Explanation opens after your attempt
Correct Answer
A. {(1,3,5)}
Step 1
Concept
The complement contains elements of (U) that are not in (A). If (U) changes the complement may change.
Step 2
Why this answer is correct
The correct answer is A. {(1,3,5)}. The complement contains elements of (U) that are not in (A). If (U) changes the complement may change.
Step 3
Exam Tip
पूरक में (U) के वे तत्व आते हैं जो (A) में नहीं हैं। (U) बदले तो पूरक भी बदल सकता है।
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यदि (n(\mathcal{P}(A))=32) है, तो (A) के उचित उपसमुच्चयों की संख्या कितनी होगी?
If (n(\mathcal{P}(A))=32), how many proper subsets does (A) have?
#sets
#power set
#proper subset
#class 11
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A (5)
B (16)
C (31)
D (32)
Explanation opens after your attempt
Step 1
Concept
From \(2^n=32\), we get (n=5), so total subsets are (32). A proper subset excludes (A) itself, so the number is (31).
Step 2
Why this answer is correct
The correct answer is C. (31). From \(2^n=32\), we get (n=5), so total subsets are (32). A proper subset excludes (A) itself, so the number is (31).
Step 3
Exam Tip
\(2^n=32\) से (n=5), इसलिए कुल उपसमुच्चय (32) हैं। उचित उपसमुच्चय में स्वयं (A) नहीं आता, इसलिए संख्या (31) होगी।
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यदि (n(A)=4) है तो (A) के उचित उपसमुच्चयों की संख्या कितनी होगी?
If (n(A)=4), how many proper subsets does (A) have?
#sets
#power-set
#proper-subset
#class-11
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A (16)
B (15)
C (8)
D (4)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^4=16\) and a proper subset excludes (A) itself. Therefore the number is (15).
Step 2
Why this answer is correct
The correct answer is B. (15). Total subsets are \(2^4=16\) and a proper subset excludes (A) itself. Therefore the number is (15).
Step 3
Exam Tip
कुल उपसमुच्चय \(2^4=16\) हैं और उचित उपसमुच्चय में (A) स्वयं शामिल नहीं होता। इसलिए संख्या (15) है।
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एक सार्वत्रिक समुच्चय (U) में (50) विद्यार्थी हैं। यदि (n(A)=18), (n(B)=22) और (n\(A\cap B\)=7) है, तो \(A\cup B\) के बाहर कितने विद्यार्थी हैं?
A universal set (U) has (50) students. If (n(A)=18), (n(B)=22), and (n\(A\cap B\)=7), how many students are outside \(A\cup B\)?
#sets
#universal set
#venn diagram
#class 11
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A (13)
B (17)
C (27)
D (33)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=18+22-7=33). Students outside are (50-33=17).
Step 2
Why this answer is correct
The correct answer is B. (17). (n\(A\cup B\)=18+22-7=33). Students outside are (50-33=17).
Step 3
Exam Tip
(n\(A\cup B\)=18+22-7=33) होगा। बाहर के विद्यार्थी (50-33=17) हैं।
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यदि (\mathcal{P}(A)) में (32) तत्व हैं तो (A) में कितने तत्व होंगे?
If (\mathcal{P}(A)) has (32) elements, how many elements are in (A)?
#sets
#power-set
#inverse-counting
#class-11
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A (4)
B (5)
C (6)
D (16)
Explanation opens after your attempt
Step 1
Concept
If \(2^n=32\), then (n=5). Use the size of the power set to find the size of the original set.
Step 2
Why this answer is correct
The correct answer is B. (5). If \(2^n=32\), then (n=5). Use the size of the power set to find the size of the original set.
Step 3
Exam Tip
यदि \(2^n=32\) है तो (n=5) होगा। घात समुच्चय की संख्या देखकर मूल समुच्चय का आकार निकालें।
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रिक्त समुच्चय के घात समुच्चय के बारे में कौन सा कथन सही है?
Which statement is correct about the power set of the empty set?
#sets
#power set
#empty set
#class 11
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A (\mathcal{P}\(\varnothing\)=\varnothing)
B (\mathcal{P}\(\varnothing\)={\varnothing})
C (\mathcal{P}\(\varnothing\)={0})
D (\mathcal{P}\(\varnothing\)={1})
Explanation opens after your attempt
Correct Answer
B. (\mathcal{P}\(\varnothing\)={\varnothing})
Step 1
Concept
The empty set has only one subset, the empty set itself. Therefore (\mathcal{P}\(\varnothing\)) has one element.
Step 2
Why this answer is correct
The correct answer is B. (\mathcal{P}\(\varnothing\)={\varnothing}). The empty set has only one subset, the empty set itself. Therefore (\mathcal{P}\(\varnothing\)) has one element.
Step 3
Exam Tip
रिक्त समुच्चय का एक ही उपसमुच्चय होता है, वह स्वयं रिक्त समुच्चय है। इसलिए (\mathcal{P}\(\varnothing\)) में एक तत्व होता है।
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यदि \(A={\emptyset}\) है तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If \(A={\emptyset}\), how many elements will (\mathcal{P}(A)) have?
#sets
#power-set
#empty-set
#class-11
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(A) has one element which is \(\emptyset\). Hence it has \(2^1=2\) subsets.
Step 2
Why this answer is correct
The correct answer is B. (2). (A) has one element which is \(\emptyset\). Hence it has \(2^1=2\) subsets.
Step 3
Exam Tip
(A) में एक तत्व है जो \(\emptyset\) है। इसलिए उपसमुच्चय \(2^1=2\) होंगे।
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यदि \(A\subseteq U\) और \(A'= \varnothing\) है, तो सही निष्कर्ष क्या है?
If \(A\subseteq U\) and \(A'= \varnothing\), what is the correct conclusion?
#sets
#universal set
#complement reasoning
#class 11
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A \(A=\varnothing\)
B (A=U)
C \(U=\varnothing\)
D \(A\cap U=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
(A') being empty means there is no element of (U) outside (A). Hence (A) and (U) are equal.
Step 2
Why this answer is correct
The correct answer is B. (A=U). (A') being empty means there is no element of (U) outside (A). Hence (A) and (U) are equal.
Step 3
Exam Tip
(A') खाली होने का अर्थ है कि (U) में (A) के बाहर कोई तत्व नहीं है। इसलिए (A) और (U) समान हैं।
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कौन सा कथन सार्वत्रिक समुच्चय के बारे में सही है?
Which statement about a universal set is correct?
#sets
#universal-set
#definition
#class-11
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A यह हमेशा रिक्त होता है / It is always empty
B यह संदर्भ के सभी विचाराधीन तत्वों को रखता है / It contains all elements under consideration
C यह हमेशा अनंत होता है / It is always infinite
D यह केवल संख्याएं रखता है / It contains only numbers
Explanation opens after your attempt
Correct Answer
B. यह संदर्भ के सभी विचाराधीन तत्वों को रखता है / It contains all elements under consideration
Step 1
Concept
A universal set contains all elements under discussion in the given context. Always identify it from the question context.
Step 2
Why this answer is correct
The correct answer is B. यह संदर्भ के सभी विचाराधीन तत्वों को रखता है / It contains all elements under consideration. A universal set contains all elements under discussion in the given context. Always identify it from the question context.
Step 3
Exam Tip
सार्वत्रिक समुच्चय संदर्भ के अनुसार सभी विचाराधीन तत्वों का समुच्चय होता है। इसे हमेशा प्रश्न के संदर्भ से पहचानें।
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यदि \(U={x:x\) एक अंक है(}) और \(A=\{2,4,6,8\}\) है तो (A') कौन सा है?
If \(U={x:x\) is a digit(}) and \(A=\{2,4,6,8\}\), which is (A')?
#sets
#universal-set
#digits
#complement
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A {(0,1,3,5,7,9)}
B {(1,3,5,7,9)}
C {(2,4,6,8)}
D {(0,2,4,6,8)}
Explanation opens after your attempt
Correct Answer
A. {(0,1,3,5,7,9)}
Step 1
Concept
Digits are from (0) to (9). The digits outside (A) are (0,1,3,5,7,9).
Step 2
Why this answer is correct
The correct answer is A. {(0,1,3,5,7,9)}. Digits are from (0) to (9). The digits outside (A) are (0,1,3,5,7,9).
Step 3
Exam Tip
अंक (0) से (9) तक होते हैं। (A) के बाहर बचे अंक (0,1,3,5,7,9) हैं।
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यदि \(A=\{p,q,r\}\) है तो ({p,q}) और ({p,q,r}) का (\mathcal{P}(A)) से संबंध क्या है?
If \(A=\{p,q,r\}\), what is the relation of ({p,q}) and ({p,q,r}) with (\mathcal{P}(A))?
#sets
#power-set
#membership
#subsets
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A दोनों तत्व हैं / Both are elements
B केवल पहला तत्व है / Only the first is an element
C केवल दूसरा तत्व है / Only the second is an element
D दोनों तत्व नहीं हैं / Neither is an element
Explanation opens after your attempt
Correct Answer
A. दोनों तत्व हैं / Both are elements
Step 1
Concept
Both are subsets of (A), so both are elements of (\mathcal{P}(A)). The power set also contains (A) itself.
Step 2
Why this answer is correct
The correct answer is A. दोनों तत्व हैं / Both are elements. Both are subsets of (A), so both are elements of (\mathcal{P}(A)). The power set also contains (A) itself.
Step 3
Exam Tip
दोनों (A) के उपसमुच्चय हैं इसलिए दोनों (\mathcal{P}(A)) के तत्व हैं। घात समुच्चय में पूरा (A) भी शामिल होता है।
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यदि \(A=\{1,2\}\) है तो (\mathcal{P}(A)) के तत्वों में से कौन सा सही है?
If \(A=\{1,2\}\), which is a correct element of (\mathcal{P}(A))?
#sets
#power-set
#singleton
#class-11
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A (1)
B {(1)}
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
({1}) is a subset of (A), so it is an element of (\mathcal{P}(A)). Keep a single element and a singleton set distinct.
Step 2
Why this answer is correct
The correct answer is B. {(1)}. ({1}) is a subset of (A), so it is an element of (\mathcal{P}(A)). Keep a single element and a singleton set distinct.
Step 3
Exam Tip
({1}) समुच्चय (A) का उपसमुच्चय है इसलिए यह (\mathcal{P}(A)) का तत्व है। एकल तत्व और एकल समुच्चय में अंतर रखें।
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यदि \(A=\{क,ल,म\}\) है तो (n(\mathcal{P}(A))) कितना होगा?
If \(A=\{k,l,m\}\), what is (n(\mathcal{P}(A)))?
#sets
#power-set
#elements
#counting
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A (3)
B (6)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
The set (A) has three distinct elements, so (n(A)=3). The power set has \(2^3=8\) elements.
Step 2
Why this answer is correct
The correct answer is C. (8). The set (A) has three distinct elements, so (n(A)=3). The power set has \(2^3=8\) elements.
Step 3
Exam Tip
समुच्चय (A) में तीन अलग तत्व हैं इसलिए (n(A)=3)। घात समुच्चय में \(2^3=8\) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,3,5\}\) है तो (A') में कितने तत्व हैं?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,3,5\}\), how many elements are in (A')?
#sets
#universal-set
#complement
#counting
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(A') contains (2,4,6), so it has three elements. While finding complement look only inside (U).
Step 2
Why this answer is correct
The correct answer is B. (3). (A') contains (2,4,6), so it has three elements. While finding complement look only inside (U).
Step 3
Exam Tip
(A') में (2,4,6) होंगे इसलिए तीन तत्व हैं। पूरक निकालते समय केवल (U) के अंदर देखें।
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यदि \(A=\{1,{2}\}\) है तो (A) के कितने उपसमुच्चय होंगे?
If \(A=\{1,{2}\}\), how many subsets will (A) have?
#sets
#power-set
#nested-set
#counting
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
(A) has two elements (1) and ({2}). Therefore it has \(2^2=4\) subsets.
Step 2
Why this answer is correct
The correct answer is C. (4). (A) has two elements (1) and ({2}). Therefore it has \(2^2=4\) subsets.
Step 3
Exam Tip
(A) में दो तत्व हैं (1) और ({2})। इसलिए उपसमुच्चय \(2^2=4\) होंगे।
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यदि \(U=\{a,b,c,d\}\) और \(A=\{a,d\}\) है तो (\mathcal{P}(A')) में कितने तत्व होंगे?
If \(U=\{a,b,c,d\}\) and \(A=\{a,d\}\), how many elements will (\mathcal{P}(A')) have?
#sets
#power-set
#universal-set
#complement
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A (2)
B (4)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
(A'={b,c}) has two elements. Hence (\mathcal{P}(A')) has \(2^2=4\) elements.
Step 2
Why this answer is correct
The correct answer is B. (4). (A'={b,c}) has two elements. Hence (\mathcal{P}(A')) has \(2^2=4\) elements.
Step 3
Exam Tip
(A'={b,c}) है जिसमें दो तत्व हैं। इसलिए (\mathcal{P}(A')) में \(2^2=4\) तत्व होंगे।
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यदि \(A=\{2,4,6\}\) है तो \(\emptyset\) का (\mathcal{P}(A)) से संबंध क्या है?
If \(A=\{2,4,6\}\), what is the relation of \(\emptyset\) with (\mathcal{P}(A))?
#sets
#power-set
#empty-set
#membership
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A \(\emptyset\in\mathcal{P}(A)\)
B \(\emptyset\notin\mathcal{P}(A)\)
C \(\emptyset=A\)
D \(\emptyset=U\)
Explanation opens after your attempt
Correct Answer
A. \(\emptyset\in\mathcal{P}(A)\)
Step 1
Concept
\(\emptyset\) is a subset of every set, so it is an element of its power set. This is a common exam confusion.
Step 2
Why this answer is correct
The correct answer is A. \(\emptyset\in\mathcal{P}(A)\). \(\emptyset\) is a subset of every set, so it is an element of its power set. This is a common exam confusion.
Step 3
Exam Tip
\(\emptyset\) हर समुच्चय का उपसमुच्चय है इसलिए यह उसके घात समुच्चय का तत्व है। यह बहुत सामान्य परीक्षा भ्रम है।
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यदि \(U=\{1,2,3,4\}\) और \(A=\emptyset\) है तो (A') क्या होगा?
If \(U=\{1,2,3,4\}\) and \(A=\emptyset\), what is (A')?
#sets
#universal-set
#empty-set
#complement
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A \(\emptyset\)
B (U)
C {(1)}
D {(4)}
Explanation opens after your attempt
Step 1
Concept
The empty set contains no element of (U), so its complement is the whole (U). Complement always depends on the context.
Step 2
Why this answer is correct
The correct answer is B. (U). The empty set contains no element of (U), so its complement is the whole (U). Complement always depends on the context.
Step 3
Exam Tip
रिक्त समुच्चय में (U) का कोई तत्व नहीं है इसलिए उसका पूरक पूरा (U) होता है। पूरक हमेशा संदर्भ पर निर्भर है।
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यदि (A) में (5) तत्व हैं तो (\mathcal{P}(A)) में एकल उपसमुच्चयों की संख्या कितनी होगी?
If (A) has (5) elements, how many singleton subsets are in (\mathcal{P}(A))?
#sets
#power-set
#singleton
#counting
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A (5)
B (10)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
Each singleton subset is formed from one element, so their number equals (n(A)). Here the number is (5).
Step 2
Why this answer is correct
The correct answer is A. (5). Each singleton subset is formed from one element, so their number equals (n(A)). Here the number is (5).
Step 3
Exam Tip
एकल उपसमुच्चय प्रत्येक एक तत्व से बनता है इसलिए उनकी संख्या (n(A)) के बराबर होती है। यहां संख्या (5) है।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में दो तत्वों वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{1,2,3,4\}\), how many two-element subsets are in (\mathcal{P}(A))?
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#power-set
#combination
#counting
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A (4)
B (6)
C (8)
D (16)
Explanation opens after your attempt
Step 1
Concept
The number of two-element subsets is \({}^4C_2=6\). Use combinations for subsets of fixed size.
Step 2
Why this answer is correct
The correct answer is B. (6). The number of two-element subsets is \({}^4C_2=6\). Use combinations for subsets of fixed size.
Step 3
Exam Tip
दो तत्वों वाले उपसमुच्चय चुनने की संख्या \({}^4C_2=6\) है। निश्चित आकार के उपसमुच्चयों में संयोजन का प्रयोग करें।
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यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में तीन तत्वों वाले कितने उपसमुच्चय होंगे?
If \(A=\{1,2,3\}\), how many three-element subsets will be in (\mathcal{P}(A))?
#sets
#power-set
#fixed-size-subsets
#class-11
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A (0)
B (1)
C (3)
D (8)
Explanation opens after your attempt
Step 1
Concept
There is only one three-element subset which is (A) itself. The whole set is also an element of the power set.
Step 2
Why this answer is correct
The correct answer is B. (1). There is only one three-element subset which is (A) itself. The whole set is also an element of the power set.
Step 3
Exam Tip
तीन तत्वों वाला एक ही उपसमुच्चय (A) स्वयं है। पूरा समुच्चय भी घात समुच्चय का तत्व होता है।
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यदि (\mathcal{P}(A)={\emptyset,{x}}) है तो (A) क्या होगा?
If (\mathcal{P}(A)={\emptyset,{x}}), what is (A)?
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#power-set
#reverse-thinking
#class-11
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A \(\emptyset\)
B {(x)}
C {\(\emptyset\)}
D {\(\emptyset,x\)}
Explanation opens after your attempt
Step 1
Concept
The power set contains (A) itself as an element. Hence here \(A=\{x\}\).
Step 2
Why this answer is correct
The correct answer is B. {(x)}. The power set contains (A) itself as an element. Hence here \(A=\{x\}\).
Step 3
Exam Tip
घात समुच्चय में (A) स्वयं भी एक तत्व होता है। इसलिए यहां \(A=\{x\}\) है।
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यदि \(A=\{1,2\}\) और (B=\mathcal{P}(A)) है तो (n(B)) कितना होगा?
If \(A=\{1,2\}\) and (B=\mathcal{P}(A)), what is (n(B))?
#sets
#power-set
#counting
#class-11
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A) has two elements, so (\mathcal{P}(A)) has \(2^2=4\) elements. (B) is that power set.
Step 2
Why this answer is correct
The correct answer is C. (4). (A) has two elements, so (\mathcal{P}(A)) has \(2^2=4\) elements. (B) is that power set.
Step 3
Exam Tip
(A) में दो तत्व हैं इसलिए (\mathcal{P}(A)) में \(2^2=4\) तत्व हैं। (B) वही घात समुच्चय है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{2,4,6,8\}\) है तो (A') में कौन सा तत्व है?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{2,4,6,8\}\), which element is in (A')?
#sets
#universal-set
#complement
#element
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A (2)
B (4)
C (5)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A') contains elements of (U) that are not in (A). The element (5) is included.
Step 2
Why this answer is correct
The correct answer is C. (5). (A') contains elements of (U) that are not in (A). The element (5) is included.
Step 3
Exam Tip
(A') में (U) के वे तत्व होंगे जो (A) में नहीं हैं। उनमें (5) शामिल है।
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कौन सा समुच्चय (\mathcal{P}({m,n})) के बराबर है?
Which set is equal to (\mathcal{P}({m,n}))?
#sets
#power-set
#listing
#class-11
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A {\(\emptyset,m,n\)}
B {\(\emptyset,{m},{n},{m,n}\)}
C {(m,n,{m,n})}
D {({m},{n})}
Explanation opens after your attempt
Correct Answer
B. {\(\emptyset,{m},{n},{m,n}\)}
Step 1
Concept
The power set of a two-element set has four subsets. The elements must be written as subsets.
Step 2
Why this answer is correct
The correct answer is B. {\(\emptyset,{m},{n},{m,n}\)}. The power set of a two-element set has four subsets. The elements must be written as subsets.
Step 3
Exam Tip
दो तत्वों वाले समुच्चय का घात समुच्चय चार उपसमुच्चयों से बनता है। तत्वों को उपसमुच्चय की तरह लिखना जरूरी है।
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यदि \(A=\{0,1,2\}\) है तो ({0,2}) के लिए सही कथन कौन सा है?
If \(A=\{0,1,2\}\), which statement is correct for ({0,2})?
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#power-set
#subset-membership
#class-11
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A \({0,2}\in\mathcal{P}(A)\)
B \({0,2}\not\subseteq A\)
C ({0,2}=A)
D \({0,2}\in A\)
Explanation opens after your attempt
Correct Answer
A. \({0,2}\in\mathcal{P}(A)\)
Step 1
Concept
All elements of ({0,2}) are in (A), so it is a subset of (A). Hence it is an element of (\mathcal{P}(A)).
Step 2
Why this answer is correct
The correct answer is A. \({0,2}\in\mathcal{P}(A)\). All elements of ({0,2}) are in (A), so it is a subset of (A). Hence it is an element of (\mathcal{P}(A)).
Step 3
Exam Tip
({0,2}) के सभी तत्व (A) में हैं इसलिए यह (A) का उपसमुच्चय है। अतः यह (\mathcal{P}(A)) का तत्व है।
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यदि \(A=\{1,2,3,4,5\}\) है तो (\mathcal{P}(A)) में तीन तत्वों वाले उपसमुच्चयों की संख्या कितनी होगी?
If \(A=\{1,2,3,4,5\}\), how many three-element subsets are in (\mathcal{P}(A))?
#sets
#power-set
#combination
#medium
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A (5)
B (10)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
The number of three-element subsets is \({}^5C_3=10\). Order is not considered in fixed-size subset counting.
Step 2
Why this answer is correct
The correct answer is B. (10). The number of three-element subsets is \({}^5C_3=10\). Order is not considered in fixed-size subset counting.
Step 3
Exam Tip
तीन तत्वों वाले उपसमुच्चयों की संख्या \({}^5C_3=10\) है। निश्चित आकार की गिनती में क्रम नहीं माना जाता।
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यदि \(U={x:x\in \mathbb{N}, x\leq 10}\) और \(A={x:x\) अभाज्य संख्या है(}) है तो (A') क्या है?
If \(U={x:x\in \mathbb{N}, x\leq 10}\) and \(A={x:x\) is prime(}), what is (A')?
#sets
#universal-set
#prime
#complement
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A {(1,4,6,8,9,10)}
B {(2,3,5,7)}
C {(1,2,3,5,7)}
D {(4,6,8,10)}
Explanation opens after your attempt
Correct Answer
A. {(1,4,6,8,9,10)}
Step 1
Concept
The primes up to (10) are (2,3,5,7). Outside these in (U), the elements are (1,4,6,8,9,10).
Step 2
Why this answer is correct
The correct answer is A. {(1,4,6,8,9,10)}. The primes up to (10) are (2,3,5,7). Outside these in (U), the elements are (1,4,6,8,9,10).
Step 3
Exam Tip
(10) तक अभाज्य संख्याएं (2,3,5,7) हैं। (U) में इनके बाहर (1,4,6,8,9,10) बचते हैं।
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यदि \(A=\{a,b,c,d\}\) है तो (\mathcal{P}(A)) में चार तत्वों वाला उपसमुच्चय कौन सा है?
If \(A=\{a,b,c,d\}\), which is the four-element subset in (\mathcal{P}(A))?
#sets
#power-set
#full-set
#subset
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A \(\emptyset\)
B {(a,b)}
C {(a,b,c)}
D {(a,b,c,d)}
Explanation opens after your attempt
Correct Answer
D. {(a,b,c,d)}
Step 1
Concept
The only four-element subset is (A) itself. A set is an element of its own power set.
Step 2
Why this answer is correct
The correct answer is D. {(a,b,c,d)}. The only four-element subset is (A) itself. A set is an element of its own power set.
Step 3
Exam Tip
चार तत्वों वाला एकमात्र उपसमुच्चय (A) स्वयं है। पूरा समुच्चय अपने घात समुच्चय का तत्व होता है।
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यदि \(U=\{0,1,2,3,4,5\}\), \(A=\{0,2,4\}\) और \(B=\{1,3,5\}\) है तो (A') किसके बराबर है?
If \(U=\{0,1,2,3,4,5\}\), \(A=\{0,2,4\}\), and \(B=\{1,3,5\}\), what is (A') equal to?
#sets
#universal-set
#complement
#equality
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A (A)
B (B)
C (U)
D \(\emptyset\)
Explanation opens after your attempt
Step 1
Concept
(A) has even elements and the remaining elements in (U) are (1,3,5). These are equal to (B).
Step 2
Why this answer is correct
The correct answer is B. (B). (A) has even elements and the remaining elements in (U) are (1,3,5). These are equal to (B).
Step 3
Exam Tip
(A) में सम तत्व हैं और (U) में बचे तत्व (1,3,5) हैं। ये (B) के बराबर हैं।
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किस स्थिति में (\mathcal{P}(A)) में ठीक (16) तत्व होंगे?
In which case will (\mathcal{P}(A)) have exactly (16) elements?
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#power-set
#counting
#formula
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A (n(A)=2)
B (n(A)=3)
C (n(A)=4)
D (n(A)=8)
Explanation opens after your attempt
Correct Answer
C. (n(A)=4)
Step 1
Concept
\(2^4=16\), so (A) must have four elements. Remember the power set formula \(2^n\).
Step 2
Why this answer is correct
The correct answer is C. (n(A)=4). \(2^4=16\), so (A) must have four elements. Remember the power set formula \(2^n\).
Step 3
Exam Tip
\(2^4=16\) इसलिए (A) में चार तत्व होने चाहिए। घात समुच्चय का सूत्र \(2^n\) याद रखें।
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यदि (A) में (6) तत्व हैं तो (\mathcal{P}(A)) में कुल कितने तत्व होंगे?
If (A) has (6) elements, how many total elements will (\mathcal{P}(A)) have?
#sets
#power-set
#counting
#medium
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A (12)
B (32)
C (36)
D (64)
Explanation opens after your attempt
Step 1
Concept
A six-element set has \(2^6=64\) subsets. Each element has two choices included or not included.
Step 2
Why this answer is correct
The correct answer is D. (64). A six-element set has \(2^6=64\) subsets. Each element has two choices included or not included.
Step 3
Exam Tip
छह तत्वों वाले समुच्चय के उपसमुच्चय \(2^6=64\) होते हैं। हर तत्व के लिए शामिल या न शामिल दो विकल्प होते हैं।
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यदि \(U=\{1,2,3,4,5\}\) है तो (U') क्या होगा?
If \(U=\{1,2,3,4,5\}\), what is (U')?
#sets
#universal-set
#complement
#identity
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A (U)
B {(1)}
C \(\emptyset\)
D {(5)}
Explanation opens after your attempt
Correct Answer
C. \(\emptyset\)
Step 1
Concept
The complement of the universal set is empty in that context. No considered element lies outside (U).
Step 2
Why this answer is correct
The correct answer is C. \(\emptyset\). The complement of the universal set is empty in that context. No considered element lies outside (U).
Step 3
Exam Tip
सार्वत्रिक समुच्चय का पूरक उसी संदर्भ में रिक्त होता है। (U) के बाहर कोई विचाराधीन तत्व नहीं माना जाता।
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कौन सा विकल्प (\mathcal{P}\(\emptyset\)) का सही सदस्य है?
Which option is a correct member of (\mathcal{P}\(\emptyset\))?
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#power-set
#empty-set
#membership
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A (0)
B \(\emptyset\)
C {(0)}
D {\(\emptyset\)}
Explanation opens after your attempt
Correct Answer
B. \(\emptyset\)
Step 1
Concept
(\mathcal{P}\(\emptyset\)={\emptyset}), so its member is \(\emptyset\). \({\emptyset}\) is the whole power set not its member.
Step 2
Why this answer is correct
The correct answer is B. \(\emptyset\). (\mathcal{P}\(\emptyset\)={\emptyset}), so its member is \(\emptyset\). \({\emptyset}\) is the whole power set not its member.
Step 3
Exam Tip
(\mathcal{P}\(\emptyset\)={\emptyset}) होता है इसलिए उसका सदस्य \(\emptyset\) है। \({\emptyset}\) पूरा घात समुच्चय है सदस्य नहीं।
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यदि \(U=\{a,b,c,e\}\) और \(A=\{a,b,c,d\}\) है तो पूरक (A') निकालने से पहले कौन सी समस्या है?
If \(U=\{a,b,c,e\}\) and \(A=\{a,b,c,d\}\), what problem occurs before finding (A')?
#sets
#universal-set
#subset-condition
#complement
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A \(A\subseteq U\) नहीं है / \(A\subseteq U\) is not true
B \(U\subseteq A\) है / \(U\subseteq A\) is true
C (A=U) है / (A=U)
D (A) रिक्त है / (A) is empty
Explanation opens after your attempt
Correct Answer
A. \(A\subseteq U\) नहीं है / \(A\subseteq U\) is not true
Step 1
Concept
Complement is normally taken when \(A\subseteq U\). Here (d) is not in (U), so there is a problem.
Step 2
Why this answer is correct
The correct answer is A. \(A\subseteq U\) नहीं है / \(A\subseteq U\) is not true. Complement is normally taken when \(A\subseteq U\). Here (d) is not in (U), so there is a problem.
Step 3
Exam Tip
पूरक सामान्यतः तब लिया जाता है जब \(A\subseteq U\) हो। यहां (d), (U) में नहीं है इसलिए समस्या है।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में विषम संख्या वाले एकल उपसमुच्चय कितने हैं?
If \(A=\{1,2,3,4\}\), how many singleton subsets containing odd numbers are in (\mathcal{P}(A))?
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#power-set
#singleton
#odd-numbers
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
The odd elements are (1) and (3), so the singleton subsets are ({1},{3}). The number is (2).
Step 2
Why this answer is correct
The correct answer is B. (2). The odd elements are (1) and (3), so the singleton subsets are ({1},{3}). The number is (2).
Step 3
Exam Tip
विषम तत्व (1) और (3) हैं इसलिए एकल उपसमुच्चय ({1},{3}) होंगे। संख्या (2) है।
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यदि \(A=\{x,y,z\}\) है तो (\mathcal{P}(A)) में (x) को रखने वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{x,y,z\}\), how many subsets in (\mathcal{P}(A)) contain (x)?
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A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
Fix (x) and each of (y,z) has two choices. Therefore the number is \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is C. (4). Fix (x) and each of (y,z) has two choices. Therefore the number is \(2^2=4\).
Step 3
Exam Tip
(x) को स्थिर रखें और (y,z) के लिए दो दो विकल्प होंगे। इसलिए संख्या \(2^2=4\) है।
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यदि \(U=\{1,2,3,4,5,6\}\) और \(A=\{1,2\}\) है तो (n(A')) कितना होगा?
If \(U=\{1,2,3,4,5,6\}\) and \(A=\{1,2\}\), what is (n(A'))?
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
(U) has (6) elements and (A) has (2) elements. The remaining (4) elements will be in (A').
Step 2
Why this answer is correct
The correct answer is C. (4). (U) has (6) elements and (A) has (2) elements. The remaining (4) elements will be in (A').
Step 3
Exam Tip
(U) में (6) और (A) में (2) तत्व हैं। बचे हुए (4) तत्व (A') में होंगे।
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यदि \(A=\{1,2,3\}\) है तो (\mathcal{P}(A)) में खाली नहीं होने वाले उपसमुच्चयों की संख्या कितनी होगी?
If \(A=\{1,2,3\}\), how many non-empty subsets are in (\mathcal{P}(A))?
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A (6)
B (7)
C (8)
D (9)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^3=8\) and one subset is empty. Therefore non-empty subsets are (7).
Step 2
Why this answer is correct
The correct answer is B. (7). Total subsets are \(2^3=8\) and one subset is empty. Therefore non-empty subsets are (7).
Step 3
Exam Tip
कुल उपसमुच्चय \(2^3=8\) हैं और खाली उपसमुच्चय एक है। इसलिए खाली नहीं उपसमुच्चय (7) हैं।
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यदि \(A=\{a,b,c\}\) है तो (\mathcal{P}(A)) में (a) को न रखने वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{a,b,c\}\), how many subsets in (\mathcal{P}(A)) do not contain (a)?
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A (2)
B (3)
C (4)
D (6)
Explanation opens after your attempt
Step 1
Concept
Keep (a) out and (b,c) each have two choices included or not. The number is \(2^2=4\).
Step 2
Why this answer is correct
The correct answer is C. (4). Keep (a) out and (b,c) each have two choices included or not. The number is \(2^2=4\).
Step 3
Exam Tip
(a) को बाहर रखें और (b,c) के लिए शामिल या न शामिल दो विकल्प होंगे। संख्या \(2^2=4\) है।
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यदि \(U=\{1,2,3,4,5,6,7\}\) और \(A=\{3,5,7\}\) है तो (A') में सबसे छोटी संख्या कौन सी है?
If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{3,5,7\}\), what is the smallest number in (A')?
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A (1)
B (2)
C (3)
D (5)
Explanation opens after your attempt
Step 1
Concept
(A') contains (1,2,4,6). The smallest among these is (1).
Step 2
Why this answer is correct
The correct answer is A. (1). (A') contains (1,2,4,6). The smallest among these is (1).
Step 3
Exam Tip
(A') में (1,2,4,6) होंगे। इनमें सबसे छोटी संख्या (1) है।
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यदि \(A=\{1,2,3,4\}\) है तो (\mathcal{P}(A)) में कम से कम तीन तत्वों वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{1,2,3,4\}\), how many subsets in (\mathcal{P}(A)) have at least three elements?
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A (4)
B (5)
C (6)
D (8)
Explanation opens after your attempt
Step 1
Concept
There are \({}^4C_3=4\) three-element subsets and (1) four-element subset. The total is (5).
Step 2
Why this answer is correct
The correct answer is B. (5). There are \({}^4C_3=4\) three-element subsets and (1) four-element subset. The total is (5).
Step 3
Exam Tip
तीन तत्वों वाले \({}^4C_3=4\) और चार तत्वों वाला (1) उपसमुच्चय है। कुल (5) हैं।
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यदि (\mathcal{P}(A)) में (8) तत्व हैं तो (A) के खाली नहीं उपसमुच्चयों की संख्या कितनी होगी?
If (\mathcal{P}(A)) has (8) elements, how many non-empty subsets does (A) have?
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A (3)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
From \(2^n=8\), (n=3), and total subsets are (8). Removing the empty subset leaves (7).
Step 2
Why this answer is correct
The correct answer is C. (7). From \(2^n=8\), (n=3), and total subsets are (8). Removing the empty subset leaves (7).
Step 3
Exam Tip
\(2^n=8\) से (n=3) है और कुल उपसमुच्चय (8) हैं। खाली उपसमुच्चय हटाने पर (7) बचते हैं।
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यदि (U) सप्ताह के सभी दिनों का समुच्चय है और (A) में सोमवार, बुधवार, शुक्रवार हैं तो (A') में कितने दिन होंगे?
If (U) is the set of all days of the week and (A) contains Monday, Wednesday, and Friday, how many days are in (A')?
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A (3)
B (4)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
A week has seven days and (A) has three days. Therefore the complement has four days.
Step 2
Why this answer is correct
The correct answer is B. (4). A week has seven days and (A) has three days. Therefore the complement has four days.
Step 3
Exam Tip
सप्ताह में सात दिन होते हैं और (A) में तीन दिन हैं। इसलिए पूरक में चार दिन होंगे।
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यदि \(A=\{1,2\}\) और \(U=\{1,2,3\}\) है तो (\mathcal{P}(A')) क्या होगा?
If \(A=\{1,2\}\) and \(U=\{1,2,3\}\), what is (\mathcal{P}(A'))?
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A {\(\emptyset,{3}\)}
B {\(\emptyset,3\)}
C {({1},{2})}
D {(1,2,3)}
Explanation opens after your attempt
Correct Answer
A. {\(\emptyset,{3}\)}
Step 1
Concept
First (A'={3}). Then (\mathcal{P}(A')={\emptyset,{3}}).
Step 2
Why this answer is correct
The correct answer is A. {\(\emptyset,{3}\)}. First (A'={3}). Then (\mathcal{P}(A')={\emptyset,{3}}).
Step 3
Exam Tip
पहले (A'={3}) मिलेगा। फिर (\mathcal{P}(A')={\emptyset,{3}}) होगा।
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