यदि \(A\subseteq U\) है, तो ((A')') किसके बराबर होगा?
If \(A\subseteq U\), what will ((A')') be equal to?
#sets
#double complement
#universal set
#class 11
A (A)
B (A')
C (U)
D \(\varnothing\)
Explanation opens after your attempt
Step 1
Concept
The complement of the complement of a set is the set itself. This is called the double complement law.
Step 2
Why this answer is correct
The correct answer is A. (A). The complement of the complement of a set is the set itself. This is called the double complement law.
Step 3
Exam Tip
किसी समुच्चय के पूरक का पूरक वही समुच्चय होता है। इसे द्वि-पूरक नियम कहते हैं।
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यदि (A) और (B), (U) के उपसमुच्चय हैं, तो (\(A\cup B\)') किसके बराबर है?
If (A) and (B) are subsets of (U), what is (\(A\cup B\)') equal to?
#sets
#de morgan law
#complement
#class 11
A \(A'\cup B'\)
B \(A'\cap B'\)
C \(A\cap B\)
D \(A\cup B\)
Explanation opens after your attempt
Correct Answer
B. \(A'\cap B'\)
Step 1
Concept
By De Morgan's law, (\(A\cup B\)'=A'\cap B'). The complement of a union contains elements outside both sets.
Step 2
Why this answer is correct
The correct answer is B. \(A'\cap B'\). By De Morgan's law, (\(A\cup B\)'=A'\cap B'). The complement of a union contains elements outside both sets.
Step 3
Exam Tip
डी मॉर्गन नियम के अनुसार (\(A\cup B\)'=A'\cap B')। संघ के पूरक में केवल वे तत्व आते हैं जो दोनों से बाहर हों।
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एक कक्षा के (40) विद्यार्थियों में (18) गणित क्लब में और (15) विज्ञान क्लब में हैं। यदि (6) विद्यार्थी दोनों क्लब में हैं, तो किसी भी क्लब में नहीं होने वाले विद्यार्थी कितने हैं?
In a class of (40) students, (18) are in the maths club and (15) are in the science club. If (6) students are in both clubs, how many students are in neither club?
#sets
#universal set
#venn diagram
#class 11
A (7)
B (13)
C (19)
D (27)
Explanation opens after your attempt
Step 1
Concept
(n\(A\cup B\)=18+15-6=27), so students outside are (40-27=13). In such questions, the universal set is the total group.
Step 2
Why this answer is correct
The correct answer is B. (13). (n\(A\cup B\)=18+15-6=27), so students outside are (40-27=13). In such questions, the universal set is the total group.
Step 3
Exam Tip
(n\(A\cup B\)=18+15-6=27), इसलिए बाहर के विद्यार्थी (40-27=13) हैं। ऐसे प्रश्नों में सार्वत्रिक समुच्चय कुल विद्यार्थियों का होता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{1,3,5,7\}\) है, तो (A') में कितने तत्व हैं?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,3,5,7\}\), how many elements are in (A')?
#sets
#complement
#counting
#class 11
A (2)
B (3)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(A') contains (2,4,6,8), so it has (4) elements. A complement is always taken with respect to the given universal set.
Step 2
Why this answer is correct
The correct answer is C. (4). (A') contains (2,4,6,8), so it has (4) elements. A complement is always taken with respect to the given universal set.
Step 3
Exam Tip
(A') में (2,4,6,8) हैं, इसलिए इसमें (4) तत्व हैं। पूरक हमेशा दिए गए सार्वत्रिक समुच्चय के सापेक्ष होता है।
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यदि सार्वत्रिक समुच्चय \(U=\{a,b,c,d,e\}\) और \(A=\{b,d\}\) है, तो (A') क्या होगा?
If the universal set is \(U=\{a,b,c,d,e\}\) and \(A=\{b,d\}\), what is (A')?
#sets
#universal set
#complement
#class 11
A ({a,c,e})
B ({b,d})
C ({a,b,c,d,e})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({a,c,e})
Step 1
Concept
(A') contains the elements of (U) that are not in (A). Here those elements are (a,c,e).
Step 2
Why this answer is correct
The correct answer is A. ({a,c,e}). (A') contains the elements of (U) that are not in (A). Here those elements are (a,c,e).
Step 3
Exam Tip
(A') में (U) के वे तत्व आते हैं जो (A) में नहीं होते। यहां वे तत्व (a,c,e) हैं।
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(\mathcal{P}(\mathcal{P}\(\varnothing\))) में कितने तत्व होंगे?
How many elements will (\mathcal{P}(\mathcal{P}\(\varnothing\))) have?
#sets
#iterated power set
#empty set
#class 11
A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
(\mathcal{P}\(\varnothing\)={\varnothing}) has (1) element. Therefore its power set has \(2^1=2\) elements.
Step 2
Why this answer is correct
The correct answer is B. (2). (\mathcal{P}\(\varnothing\)={\varnothing}) has (1) element. Therefore its power set has \(2^1=2\) elements.
Step 3
Exam Tip
(\mathcal{P}\(\varnothing\)={\varnothing}) में (1) तत्व है। इसलिए उसके घात समुच्चय में \(2^1=2\) तत्व होंगे।
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रिक्त समुच्चय \(\varnothing\) के घात समुच्चय में कितने तत्व होते हैं?
How many elements are there in the power set of the empty set \(\varnothing\)?
#sets
#empty set
#power set
#class 11
A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
The empty set has (0) elements, so (\mathcal{P}\(\varnothing\)) has \(2^0=1\) element. Remember that \(\varnothing\) is also a subset.
Step 2
Why this answer is correct
The correct answer is B. (1). The empty set has (0) elements, so (\mathcal{P}\(\varnothing\)) has \(2^0=1\) element. Remember that \(\varnothing\) is also a subset.
Step 3
Exam Tip
रिक्त समुच्चय में (0) तत्व हैं, इसलिए (\mathcal{P}\(\varnothing\)) में \(2^0=1\) तत्व होता है। याद रखें कि \(\varnothing\) भी एक उपसमुच्चय है।
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यदि \(A=\{1,2,{3}\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व नहीं है?
If \(A=\{1,2,{3}\}\), which of the following is not an element of (\mathcal{P}(A))?
#sets
#power set
#common mistake
#class 11
A ({1,2})
B ({{3}})
C ({1,{3}})
D ({1,3})
Explanation opens after your attempt
Correct Answer
D. ({1,3})
Step 1
Concept
(3) itself is not an element of (A); ({3}) is an element. So ({1,3}) is not a subset of (A).
Step 2
Why this answer is correct
The correct answer is D. ({1,3}). (3) itself is not an element of (A); ({3}) is an element. So ({1,3}) is not a subset of (A).
Step 3
Exam Tip
(3) स्वयं (A) का तत्व नहीं है, बल्कि ({3}) तत्व है। इसलिए ({1,3}) (A) का उपसमुच्चय नहीं है।
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यदि \(A=\{p,q,r\}\) है, तो निम्न में से कौन सा (\mathcal{P}(A)) का तत्व है?
If \(A=\{p,q,r\}\), which of the following is an element of (\mathcal{P}(A))?
#sets
#power set
#subset
#class 11
A (p)
B ({p,q})
C ({p,s})
D ({q,r,s})
Explanation opens after your attempt
Correct Answer
B. ({p,q})
Step 1
Concept
An element of a power set is always a subset of the original set. ({p,q}) contains only elements of (A), so it is correct.
Step 2
Why this answer is correct
The correct answer is B. ({p,q}). An element of a power set is always a subset of the original set. ({p,q}) contains only elements of (A), so it is correct.
Step 3
Exam Tip
घात समुच्चय का तत्व हमेशा मूल समुच्चय का उपसमुच्चय होता है। ({p,q}) में केवल (A) के तत्व हैं, इसलिए यह सही है।
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यदि (n(\mathcal{P}(B))=128) है, तो (B) के उचित उपसमुच्चयों की संख्या कितनी होगी?
If (n(\mathcal{P}(B))=128), how many proper subsets does (B) have?
#sets
#power set
#proper subsets
#class 11
A (7)
B (64)
C (127)
D (128)
Explanation opens after your attempt
Step 1
Concept
There are (128) total subsets, and a proper subset does not include the whole set itself. So the number is (128-1=127).
Step 2
Why this answer is correct
The correct answer is C. (127). There are (128) total subsets, and a proper subset does not include the whole set itself. So the number is (128-1=127).
Step 3
Exam Tip
कुल उपसमुच्चय (128) हैं और उचित उपसमुच्चय में पूरा समुच्चय नहीं गिना जाता। इसलिए संख्या (128-1=127) होगी।
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यदि \(A=\{2,4,6,8,10\}\) है, तो (\mathcal{P}(A)) में कुल कितने तत्व होंगे?
If \(A=\{2,4,6,8,10\}\), how many elements will (\mathcal{P}(A)) have?
#sets
#power set
#cardinality
#class 11
A (16)
B (25)
C (32)
D (10)
Explanation opens after your attempt
Step 1
Concept
Set (A) has (5) elements, so its power set has \(2^5=32\) elements. In exams, first count the elements of the original set.
Step 2
Why this answer is correct
The correct answer is C. (32). Set (A) has (5) elements, so its power set has \(2^5=32\) elements. In exams, first count the elements of the original set.
Step 3
Exam Tip
(A) में (5) तत्व हैं, इसलिए घात समुच्चय में \(2^5=32\) तत्व होंगे। परीक्षा में पहले मूल समुच्चय के तत्व गिनें।
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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
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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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
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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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
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 (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
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 \(A=\{a,b,{c}\}\) 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
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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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
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 \(A=\{1,2,3,4\}\) 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
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 \(A=\{a,b,c\}\) 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)?
#sets
#power-set
#conditional-counting
#class-11
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 \(A=\{x,y,z\}\) 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)?
#sets
#power-set
#counting-with-condition
#class-11
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 \(A=\{0,1,2\}\) है तो ({0,2}) के लिए सही कथन कौन सा है?
If \(A=\{0,1,2\}\), which statement is correct for ({0,2})?
#sets
#power-set
#subset-membership
#class-11
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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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
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 \(A=\{1,2\}\) 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
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 (\mathcal{P}(A)={\emptyset,{x}}) है तो (A) क्या होगा?
If (\mathcal{P}(A)={\emptyset,{x}}), what is (A)?
#sets
#power-set
#reverse-thinking
#class-11
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 \(A=\{1,2,3\}\) 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
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 \(A=\{1,2\}\) 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
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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कौन सा कथन सार्वत्रिक समुच्चय के बारे में सही है?
Which statement about a universal set is correct?
#sets
#universal-set
#definition
#class-11
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 \(A={\emptyset}\) 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
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 (\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
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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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
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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