यदि (f(x)=x+2) और (g(x)=3x), तो ((f+g)(x)) क्या होगा?
If (f(x)=x+2) and (g(x)=3x), what is ((f+g)(x))?
#algebra
#real functions
#function addition
#class 11
A (4x+2)
B (3x+2)
C (4x-2)
D (x+5)
Explanation opens after your attempt
Step 1
Concept
In addition, like (x) terms are added, so ((f+g)(x)=x+2+3x=4x+2). In exams, open brackets first.
Step 2
Why this answer is correct
The correct answer is A. (4x+2). In addition, like (x) terms are added, so ((f+g)(x)=x+2+3x=4x+2). In exams, open brackets first.
Step 3
Exam Tip
योग में समान (x) पद जोड़े जाते हैं, इसलिए ((f+g)(x)=x+2+3x=4x+2)। परीक्षा में पहले कोष्ठक खोलें।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\) और \(A=\{2,4,6,8\}\) है, तो (n(\mathcal{P}(A'))) कितना होगा?
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{2,4,6,8\}\), what is (n(\mathcal{P}(A')))?
#sets
#power set
#universal set
#complement
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
(A'={1,3,5,7}), so (n(A')=4). Hence (n(\mathcal{P}(A'))=24 =16).
Step 2
Why this answer is correct
The correct answer is C. (16). (A'={1,3,5,7}), so (n(A')=4). Hence (n(\mathcal{P}(A'))=24 =16).
Step 3
Exam Tip
(A'={1,3,5,7}) है, इसलिए (n(A')=4)। अतः (n(\mathcal{P}(A'))=24 =16) होगा।
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यदि \(A=\{1,2,3\}\) है, तो (\mathcal{P}(A)) के कितने तत्वों में कम से कम एक तत्व है?
If \(A=\{1,2,3\}\), how many elements of (\mathcal{P}(A)) have at least one element?
#sets
#power set
#non empty subsets
#class 11
A (6)
B (7)
C (8)
D (3)
Explanation opens after your attempt
Step 1
Concept
Subsets with at least one element are non-empty subsets. From total \(2^3=8\), removing \(\varnothing\) leaves (7).
Step 2
Why this answer is correct
The correct answer is B. (7). Subsets with at least one element are non-empty subsets. From total \(2^3=8\), removing \(\varnothing\) leaves (7).
Step 3
Exam Tip
कम से कम एक तत्व वाले उपसमुच्चय अरिक्त उपसमुच्चय होते हैं। कुल \(2^3=8\) में से \(\varnothing\) हटाने पर (7) बचते हैं।
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यदि \(U={x:x\in \mathbb{N}, x\leq 30}\) और \(A={x:x\) (30) का धनात्मक भाजक है(}) है, तो (n(A')) कितना होगा?
If \(U={x:x\in \mathbb{N}, x\leq 30}\) and \(A={x:x\) is a positive divisor of (30)(}), what is (n(A'))?
#sets
#universal set
#divisors complement
#class 11
A (8)
B (20)
C (22)
D (30)
Explanation opens after your attempt
Step 1
Concept
The divisors of (30) are (1,2,3,5,6,10,15,30), so (n(A)=8). Hence (n(A')=30-8=22).
Step 2
Why this answer is correct
The correct answer is C. (22). The divisors of (30) are (1,2,3,5,6,10,15,30), so (n(A)=8). Hence (n(A')=30-8=22).
Step 3
Exam Tip
(30) के भाजक (1,2,3,5,6,10,15,30) हैं इसलिए (n(A)=8)। अतः (n(A')=30-8=22)।
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यदि \(A=\{2,4,6\}\) और \(B=\{6,8,10\}\) हैं, तो (\mathcal{P}\(A\cup B\)) में कितने तत्व होंगे?
If \(A=\{2,4,6\}\) and \(B=\{6,8,10\}\), how many elements will (\mathcal{P}\(A\cup B\)) have?
#sets
#power set
#union
#class 11
A (16)
B (32)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
\(A\cup B={2,4,6,8,10}\), so it has (5) elements. Hence its power set has \(2^5=32\) elements.
Step 2
Why this answer is correct
The correct answer is B. (32). \(A\cup B={2,4,6,8,10}\), so it has (5) elements. Hence its power set has \(2^5=32\) elements.
Step 3
Exam Tip
\(A\cup B={2,4,6,8,10}\) है इसलिए इसमें (5) तत्व हैं। अतः घात समुच्चय में \(2^5=32\) तत्व होंगे।
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यदि \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7\}\) और \(B=\{2,3,6,7\}\) हैं, तो (\(A\cup B\)') क्या है?
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7\}\), and \(B=\{2,3,6,7\}\), what is (\(A\cup B\)')?
#sets
#universal set
#union complement
#class 11
A ({4,8,9,10})
B ({1,2,3,5,6,7})
C ({3,7})
D ({4,8,10})
Explanation opens after your attempt
Correct Answer
A. ({4,8,9,10})
Step 1
Concept
\(A\cup B={1,2,3,5,6,7}\). Removing it from (U) gives ({4,8,9,10}).
Step 2
Why this answer is correct
The correct answer is A. ({4,8,9,10}). \(A\cup B={1,2,3,5,6,7}\). Removing it from (U) gives ({4,8,9,10}).
Step 3
Exam Tip
\(A\cup B={1,2,3,5,6,7}\) है। (U) से इसे हटाने पर ({4,8,9,10}) मिलता है।
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यदि \(A=\{g,h,i,j\}\) है, तो (\mathcal{P}(A)) के कितने तत्व (A) के उचित उपसमुच्चय भी हैं?
If \(A=\{g,h,i,j\}\), how many elements of (\mathcal{P}(A)) are also proper subsets of (A)?
#sets
#power set
#proper subset
#class 11
A (14)
B (15)
C (16)
D (4)
Explanation opens after your attempt
Step 1
Concept
(\mathcal{P}(A)) has \(2^4=16\) elements. For proper subsets, remove only (A) itself, so (15) remain.
Step 2
Why this answer is correct
The correct answer is B. (15). (\mathcal{P}(A)) has \(2^4=16\) elements. For proper subsets, remove only (A) itself, so (15) remain.
Step 3
Exam Tip
(\mathcal{P}(A)) में कुल \(2^4=16\) तत्व हैं। उचित उपसमुच्चय के लिए केवल (A) को हटाते हैं, इसलिए (15) बचते हैं।
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यदि \(A=\{1,2,3,4,5,6\}\) है, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (1), (2) और (3) में से कोई भी न हो?
If \(A=\{1,2,3,4,5,6\}\), how many subsets of (A) contain none of (1), (2), and (3)?
#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 (1,2,3), the elements (4,5,6) remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding (1,2,3), the elements (4,5,6) remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
(1,2,3) हटाने पर (4,5,6) बचते हैं। इनके \(2^3=8\) उपसमुच्चय होंगे।
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यदि \(A=\{1,2,3,4,5,6,7\}\) है, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी है जिनमें (3) और (7) दोनों हों?
If \(A=\{1,2,3,4,5,6,7\}\), how many subsets of (A) contain both (3) and (7)?
#sets
#power set
#subset counting
#class 11
A (16)
B (32)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
Including (3) and (7) is fixed and the remaining (5) elements are free. So the number is \(2^5=32\).
Step 2
Why this answer is correct
The correct answer is B. (32). Including (3) and (7) is fixed and the remaining (5) elements are free. So the number is \(2^5=32\).
Step 3
Exam Tip
(3) और (7) को रखना तय है और बाकी (5) तत्व स्वतंत्र हैं। इसलिए संख्या \(2^5=32\) होगी।
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यदि \(A=\{p,q,r,s,t,u\}\) है, तो (A) के ऐसे कितने उपसमुच्चय हैं जिनमें कम से कम (5) तत्व हों?
If \(A=\{p,q,r,s,t,u\}\), how many subsets of (A) contain at least (5) elements?
#sets
#power set
#at least subsets
#class 11
A (6)
B (7)
C (12)
D (22)
Explanation opens after your attempt
Step 1
Concept
At least (5) means (5) or (6) elements. The number is \(\binom{6}{5}+\binom{6}{6}=6+1=7\).
Step 2
Why this answer is correct
The correct answer is B. (7). At least (5) means (5) or (6) elements. The number is \(\binom{6}{5}+\binom{6}{6}=6+1=7\).
Step 3
Exam Tip
कम से कम (5) का अर्थ (5) या (6) तत्व है। संख्या \(\binom{6}{5}+\binom{6}{6}=6+1=7\) है।
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यदि \(A=\{1,2,3,4,5\}\) है, तो (\mathcal{P}(A)) में ऐसे कितने तत्व हैं जिनमें (2) हो लेकिन (5) न हो?
If \(A=\{1,2,3,4,5\}\), how many elements of (\mathcal{P}(A)) contain (2) but not (5)?
#sets
#power set
#conditional subsets
#class 11
A (4)
B (8)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
Including (2) and excluding (5) are fixed. For the remaining (1,3,4), there are \(2^3=8\) choices.
Step 2
Why this answer is correct
The correct answer is B. (8). Including (2) and excluding (5) are fixed. For the remaining (1,3,4), there are \(2^3=8\) choices.
Step 3
Exam Tip
(2) रखना और (5) हटाना निश्चित है। बचे (1,3,4) के लिए \(2^3=8\) विकल्प हैं।
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यदि \(U=\{2,4,6,8,10,12\}\) और (A'={4,10}) है, तो (A) क्या होगा?
If \(U=\{2,4,6,8,10,12\}\) and (A'={4,10}), what is (A)?
#sets
#universal set
#find set from complement
#class 11
A ({2,6,8,12})
B ({4,10})
C ({2,4,6,8})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({2,6,8,12})
Step 1
Concept
Elements of (A') are not in (A). Removing (4,10) from (U) gives \(A=\{2,6,8,12\}\).
Step 2
Why this answer is correct
The correct answer is A. ({2,6,8,12}). Elements of (A') are not in (A). Removing (4,10) from (U) gives \(A=\{2,6,8,12\}\).
Step 3
Exam Tip
(A') के तत्व (A) में नहीं होते। (U) से (4,10) हटाने पर \(A=\{2,6,8,12\}\) मिलता है।
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यदि \(A\subseteq B\subseteq U\) है, तो पूरकों के लिए कौन सा संबंध सही है?
If \(A\subseteq B\subseteq U\), which relation is correct for complements?
#sets
#complement
#subset relation
#class 11
A \(A'\subseteq B'\)
B \(B'\subseteq A'\)
C (A'=B')
D \(A'\cap B'=\varnothing\)
Explanation opens after your attempt
Correct Answer
B. \(B'\subseteq A'\)
Step 1
Concept
The complement of the smaller set is larger. If \(A\subseteq B\), then \(B'\subseteq A'\) is correct.
Step 2
Why this answer is correct
The correct answer is B. \(B'\subseteq A'\). The complement of the smaller set is larger. If \(A\subseteq B\), then \(B'\subseteq A'\) is correct.
Step 3
Exam Tip
छोटे समुच्चय का पूरक बड़ा होता है। \(A\subseteq B\) होने पर \(B'\subseteq A'\) सही है।
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यदि किसी समुच्चय (A) के कुल उपसमुच्चय (2048) हैं, तो (A) में कितने तत्व होंगे?
If a set (A) has (2048) total subsets, how many elements does (A) have?
#sets
#power set
#total subsets
#class 11
A (9)
B (10)
C (11)
D (12)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^n\), and \(2048=2^{11}\). Therefore (A) has (11) elements.
Step 2
Why this answer is correct
The correct answer is C. (11). Total subsets are \(2^n\), and \(2048=2^{11}\). Therefore (A) has (11) elements.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^n\) होते हैं और \(2048=2^{11}\)। इसलिए (A) में (11) तत्व होंगे।
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यदि \(A=\{a,b,c,d,e,f,g\}\) है, तो (\mathcal{P}(A)) में ठीक (6) तत्व वाले उपसमुच्चयों की संख्या कितनी है?
If \(A=\{a,b,c,d,e,f,g\}\), how many subsets with exactly (6) elements are in (\mathcal{P}(A))?
#sets
#power set
#combination
#class 11
A (6)
B (7)
C (14)
D (21)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose (6) elements from (7) is \(\binom{7}{6}=7\). Each choice is a subset.
Step 2
Why this answer is correct
The correct answer is B. (7). The number of ways to choose (6) elements from (7) is \(\binom{7}{6}=7\). Each choice is a subset.
Step 3
Exam Tip
(7) में से (6) तत्व चुनने के तरीके \(\binom{7}{6}=7\) हैं। हर चयन एक उपसमुच्चय है।
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यदि \(A=\{4,4,5,6,6,7\}\) को समुच्चय माना जाए, तो (n(\mathcal{P}(A))) कितना होगा?
If \(A=\{4,4,5,6,6,7\}\) is considered as a set, what is (n(\mathcal{P}(A)))?
#sets
#power set
#repeated elements
#class 11
A (8)
B (16)
C (32)
D (64)
Explanation opens after your attempt
Step 1
Concept
Repeated elements are counted once in a set, so \(A=\{4,5,6,7\}\). Hence (n(\mathcal{P}(A))=24 =16).
Step 2
Why this answer is correct
The correct answer is B. (16). Repeated elements are counted once in a set, so \(A=\{4,5,6,7\}\). Hence (n(\mathcal{P}(A))=24 =16).
Step 3
Exam Tip
समुच्चय में दोहराए गए तत्व एक बार गिने जाते हैं इसलिए \(A=\{4,5,6,7\}\)। इसलिए (n(\mathcal{P}(A))=24 =16)।
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यदि \(A={x:x\) शब्द (MOON) के अलग-अलग अक्षर हैं(}), तो (\mathcal{P}(A)) में कितने तत्व होंगे?
If \(A={x:x\) is a distinct letter of the word (MOON)(}), how many elements will (\mathcal{P}(A)) have?
#sets
#power set
#distinct elements
#class 11
A (4)
B (8)
C (16)
D (32)
Explanation opens after your attempt
Step 1
Concept
The distinct letters of (MOON) are (M,O,N), so (n(A)=3). Therefore the power set has \(2^3=8\) elements.
Step 2
Why this answer is correct
The correct answer is B. (8). The distinct letters of (MOON) are (M,O,N), so (n(A)=3). Therefore the power set has \(2^3=8\) elements.
Step 3
Exam Tip
(MOON) के अलग-अलग अक्षर (M,O,N) हैं इसलिए (n(A)=3)। अतः घात समुच्चय में \(2^3=8\) तत्व होंगे।
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यदि \(A={x:x\in \mathbb{N}, 5<x<11}\) है, तो (n(\mathcal{P}(A))) क्या होगा?
If \(A={x:x\in \mathbb{N}, 5<x<11}\), what is (n(\mathcal{P}(A)))?
#sets
#power set
#set builder
#class 11
A (16)
B (32)
C (64)
D (128)
Explanation opens after your attempt
Step 1
Concept
\(A=\{6,7,8,9,10\}\), so (n(A)=5). Hence (n(\mathcal{P}(A))=25 =32).
Step 2
Why this answer is correct
The correct answer is B. (32). \(A=\{6,7,8,9,10\}\), so (n(A)=5). Hence (n(\mathcal{P}(A))=25 =32).
Step 3
Exam Tip
\(A=\{6,7,8,9,10\}\) है इसलिए (n(A)=5)। अतः (n(\mathcal{P}(A))=25 =32)।
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यदि (n(A)=6) और (n(B)=4) है, तो (n(\mathcal{P}(A)) : n(\mathcal{P}(B))) क्या होगा?
If (n(A)=6) and (n(B)=4), what is (n(\mathcal{P}(A)) : n(\mathcal{P}(B)))?
#sets
#power set
#ratio
#class 11
A (3:2)
B (4:1)
C (6:4)
D (16:1)
Explanation opens after your attempt
Step 1
Concept
(n(\mathcal{P}(A))=64) and (n(\mathcal{P}(B))=16). The ratio is (64:16=4:1).
Step 2
Why this answer is correct
The correct answer is B. (4:1). (n(\mathcal{P}(A))=64) and (n(\mathcal{P}(B))=16). The ratio is (64:16=4:1).
Step 3
Exam Tip
(n(\mathcal{P}(A))=64) और (n(\mathcal{P}(B))=16) हैं। अनुपात (64:16=4:1) होगा।
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यदि \(U=\{p,q,r,s,t\}\), \(A=\{p,q,r\}\) और \(B=\{r,s\}\) हैं, तो (\(A\cap B\)') क्या होगा?
If \(U=\{p,q,r,s,t\}\), \(A=\{p,q,r\}\), and \(B=\{r,s\}\), what is (\(A\cap B\)')?
#sets
#universal set
#complement of intersection
#class 11
A ({r})
B ({p,q,s,t})
C ({p,q,r,s})
D ({t})
Explanation opens after your attempt
Correct Answer
B. ({p,q,s,t})
Step 1
Concept
\(A\cap B={r}\). Removing (r) from (U) gives ({p,q,s,t}).
Step 2
Why this answer is correct
The correct answer is B. ({p,q,s,t}). \(A\cap B={r}\). Removing (r) from (U) gives ({p,q,s,t}).
Step 3
Exam Tip
\(A\cap B={r}\) है। (U) से (r) हटाने पर ({p,q,s,t}) मिलता है।
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यदि \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{2,4,6\}\) और \(B=\{4,6,8\}\) हैं, तो \(A'\cap B'\) क्या है?
If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{2,4,6\}\), and \(B=\{4,6,8\}\), what is \(A'\cap B'\)?
#sets
#complement
#intersection
#class 11
A ({1,3,5,7})
B ({4,6})
C ({1,2,3,5,7})
D \(\varnothing\)
Explanation opens after your attempt
Correct Answer
A. ({1,3,5,7})
Step 1
Concept
(A'={1,3,5,7,8}) and (B'={1,2,3,5,7}). Their intersection is ({1,3,5,7}).
Step 2
Why this answer is correct
The correct answer is A. ({1,3,5,7}). (A'={1,3,5,7,8}) and (B'={1,2,3,5,7}). Their intersection is ({1,3,5,7}).
Step 3
Exam Tip
(A'={1,3,5,7,8}) और (B'={1,2,3,5,7}) हैं। इनका प्रतिच्छेद ({1,3,5,7}) है।
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यदि \(A=\{2,3\}\) है, तो (\mathcal{P}(A)) का सही रूप कौन सा है?
If \(A=\{2,3\}\), which is the correct form of (\mathcal{P}(A))?
#sets
#power set
#representation
#class 11
A \({\varnothing,{2},{3},{2,3}}\)
B ({2,3,{2,3}})
C ({{2},{3}})
D \({\varnothing,2,3}\)
Explanation opens after your attempt
Correct Answer
A. \({\varnothing,{2},{3},{2,3}}\)
Step 1
Concept
A two-element set has four subsets. In the power set, (2) and (3) appear as ({2}) and ({3}), not alone.
Step 2
Why this answer is correct
The correct answer is A. \({\varnothing,{2},{3},{2,3}}\). A two-element set has four subsets. In the power set, (2) and (3) appear as ({2}) and ({3}), not alone.
Step 3
Exam Tip
दो तत्वों वाले समुच्चय के चार उपसमुच्चय होते हैं। घात समुच्चय में (2) और (3) अकेले नहीं बल्कि ({2}) और ({3}) आते हैं।
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यदि \(A=\{1,2,3,4,5,6\}\) है, तो (\mathcal{P}(A)) में ठीक (4) तत्व वाले समुच्चयों की संख्या कितनी है?
If \(A=\{1,2,3,4,5,6\}\), how many sets in (\mathcal{P}(A)) have exactly (4) elements?
#sets
#power set
#combination
#class 11
A (12)
B (15)
C (20)
D (24)
Explanation opens after your attempt
Step 1
Concept
The number of ways to choose exactly (4) elements is \(\binom{6}{4}=15\). Every such subset is counted in the power set.
Step 2
Why this answer is correct
The correct answer is B. (15). The number of ways to choose exactly (4) elements is \(\binom{6}{4}=15\). Every such subset is counted in the power set.
Step 3
Exam Tip
ठीक (4) तत्व चुनने की संख्या \(\binom{6}{4}=15\) है। ऐसे हर उपसमुच्चय को घात समुच्चय में गिना जाता है।
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यदि \(A=\{a,e,i,o,u\}\) है, तो (\mathcal{P}(A)) में कितने एक-तत्वीय समुच्चय होंगे?
If \(A=\{a,e,i,o,u\}\), how many singleton sets are in (\mathcal{P}(A))?
#sets
#power set
#singleton subsets
#class 11
A (4)
B (5)
C (10)
D (32)
Explanation opens after your attempt
Step 1
Concept
Each original element forms one singleton subset. From (5) elements, there are (5) singleton subsets.
Step 2
Why this answer is correct
The correct answer is B. (5). Each original element forms one singleton subset. From (5) elements, there are (5) singleton subsets.
Step 3
Exam Tip
हर मूल तत्व से एक एक-तत्वीय उपसमुच्चय बनता है। (5) तत्वों से (5) singleton subsets बनेंगे।
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यदि \(A=\{3,6,9,12\}\) है, तो (\mathcal{P}(A)) में कितने अरिक्त तत्व होंगे?
If \(A=\{3,6,9,12\}\), how many non-empty elements are there in (\mathcal{P}(A))?
#sets
#power set
#non empty subsets
#class 11
A (14)
B (15)
C (16)
D (4)
Explanation opens after your attempt
Step 1
Concept
Total subsets are \(2^4=16\). Only \(\varnothing\) is empty so there are (15) non-empty subsets.
Step 2
Why this answer is correct
The correct answer is B. (15). Total subsets are \(2^4=16\). Only \(\varnothing\) is empty so there are (15) non-empty subsets.
Step 3
Exam Tip
कुल उपसमुच्चय \(2^4=16\) हैं। केवल \(\varnothing\) रिक्त है इसलिए अरिक्त उपसमुच्चय (15) होंगे।
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यदि \(A=\varnothing\) और सार्वत्रिक समुच्चय \(U=\{2,4,6\}\) है, तो (A') क्या होगा?
If \(A=\varnothing\) and the universal set is \(U=\{2,4,6\}\), what is (A')?
#sets
#empty set
#complement
#class 11
A \(\varnothing\)
B ({2,4,6})
C ({0})
D (\mathcal{P}(U))
Explanation opens after your attempt
Correct Answer
B. ({2,4,6})
Step 1
Concept
The empty set has no elements. Therefore its complement is the whole (U).
Step 2
Why this answer is correct
The correct answer is B. ({2,4,6}). The empty set has no elements. Therefore its complement is the whole (U).
Step 3
Exam Tip
रिक्त समुच्चय में कोई तत्व नहीं होता। इसलिए उसका पूरक पूरा (U) होगा।
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यदि (A=U) है, तो (\mathcal{P}(A)) और (\mathcal{P}(U)) के बारे में कौन सा कथन सही है?
If (A=U), which statement about (\mathcal{P}(A)) and (\mathcal{P}(U)) is correct?
#sets
#power set
#equal sets
#class 11
A (\mathcal{P}(A)=\mathcal{P}(U))
B (\mathcal{P}(A)=\varnothing)
C (\mathcal{P}\((U)\subset A\))
D \(\mathcal{P}(A)\cap \mathcal{P}(U)=\varnothing\)
Explanation opens after your attempt
Correct Answer
A. (\mathcal{P}(A)=\mathcal{P}(U))
Step 1
Concept
Equal sets have exactly the same subsets. Therefore their power sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (\mathcal{P}(A)=\mathcal{P}(U)). Equal sets have exactly the same subsets. Therefore their power sets are equal.
Step 3
Exam Tip
समान समुच्चयों के सभी उपसमुच्चय भी समान होते हैं। इसलिए उनके घात समुच्चय बराबर होंगे।
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यदि \(A=\varnothing\) है, तो (\mathcal{P}(A)) के बारे में कौन सा कथन सही है?
If \(A=\varnothing\), which statement about (\mathcal{P}(A)) is correct?
#sets
#empty set
#power set
#class 11
A (\mathcal{P}(A)=\varnothing)
B (\mathcal{P}(A)={\varnothing})
C (\mathcal{P}(A)={0})
D (\mathcal{P}(A)={A,{A}})
Explanation opens after your attempt
Correct Answer
B. (\mathcal{P}(A)={\varnothing})
Step 1
Concept
The only subset of the empty set is the empty set itself. Therefore (\mathcal{P}\(\varnothing\)={\varnothing}).
Step 2
Why this answer is correct
The correct answer is B. (\mathcal{P}(A)={\varnothing}). The only subset of the empty set is the empty set itself. Therefore (\mathcal{P}\(\varnothing\)={\varnothing}).
Step 3
Exam Tip
रिक्त समुच्चय का एकमात्र उपसमुच्चय वही रिक्त समुच्चय है। इसलिए (\mathcal{P}\(\varnothing\)={\varnothing})।
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यदि \(U={x:x\in \mathbb{N}, x\leq 18}\) और \(A={x:x\) (4) का गुणज है(}), तो (A') में कितने तत्व होंगे?
If \(U={x:x\in \mathbb{N}, x\leq 18}\) and \(A={x:x\) is a multiple of (4)(}), how many elements are in (A')?
#sets
#universal set
#multiples
#class 11
A (4)
B (12)
C (14)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(A=\{4,8,12,16\}\), so (n(A)=4). Since (U) has (18) elements, (n(A')=18-4=14).
Step 2
Why this answer is correct
The correct answer is C. (14). \(A=\{4,8,12,16\}\), so (n(A)=4). Since (U) has (18) elements, (n(A')=18-4=14).
Step 3
Exam Tip
\(A=\{4,8,12,16\}\) है इसलिए (n(A)=4)। (U) में (18) तत्व हैं अतः (n(A')=18-4=14)।
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यदि (A) में (5) तत्व हैं, तो (A) के ऐसे उपसमुच्चयों की संख्या कितनी होगी जिनमें दो निश्चित तत्व न हों?
If (A) has (5) elements, how many subsets of (A) do not contain two fixed elements?
#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 two fixed elements, (3) elements remain. Their subsets are \(2^3=8\).
Step 2
Why this answer is correct
The correct answer is B. (8). After excluding two fixed elements, (3) elements remain. Their subsets are \(2^3=8\).
Step 3
Exam Tip
दो निश्चित तत्व हटाने पर (3) तत्व बचते हैं। इनके उपसमुच्चय \(2^3=8\) होंगे।
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