यदि \(A={x\in\mathbb{R}:x\ne0}\) और \(B={x\in\mathbb{R}:x^2>0}\), तो \(A\triangle B\) क्या है?
If \(A={x\in\mathbb{R}:x\ne0}\) and \(B={x\in\mathbb{R}:x^2>0}\), what is \(A\triangle B\)?
#sets
#symmetric-difference
#equal-sets
#real-numbers
A \(\varnothing\)
B ({0})
C \(\mathbb{R}\)
D \(\mathbb{R}-{0}\)
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). For real numbers, \(x^2>0\) exactly when \(x\ne0\). Thus (A=B), and the symmetric difference is \(\varnothing\).
Step 3
Exam Tip
वास्तविक संख्याओं में \(x^2>0\) ठीक तब होता है जब \(x\ne0\)। इसलिए (A=B) और सममित अंतर \(\varnothing\) है।
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यदि \(A={x\in\mathbb{Z}:x^2-1=0}\) और \(B={x\in\mathbb{Z}:x^2=1}\), तो (A-B) क्या है?
If \(A={x\in\mathbb{Z}:x^2-1=0}\) and \(B={x\in\mathbb{Z}:x^2=1}\), what is (A-B)?
#sets
#equal-sets
#difference
#integers
A \(\varnothing\)
B ({-1,1})
C ({0})
D ({-1})
Explanation opens after your attempt
Correct Answer
A. \(\varnothing\)
Step 1
Concept
Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.
Step 2
Why this answer is correct
The correct answer is A. \(\varnothing\). Both conditions give the same set ({-1,1}). The difference of equal sets is the empty set.
Step 3
Exam Tip
दोनों शर्तों से वही समुच्चय ({-1,1}) मिलता है। समान समुच्चयों का अंतर खाली समुच्चय होता है।
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यदि \(A\setminus B=\emptyset\) और \(B\setminus A=\emptyset\) है, तो कौन सा निष्कर्ष सही है?
If \(A\setminus B=\emptyset\) and \(B\setminus A=\emptyset\), which conclusion is correct?
#sets
#reasoning
#equal-sets
A (A=B)
B \(A\cap B=\emptyset\)
C \(A\cup B=\emptyset\)
D \(A\subset B\) हमेशा / \(A\subset B\) always
Explanation opens after your attempt
Step 1
Concept
Both differences being empty means neither set has any extra element. Therefore (A=B).
Step 2
Why this answer is correct
The correct answer is A. (A=B). Both differences being empty means neither set has any extra element. Therefore (A=B).
Step 3
Exam Tip
दोनों अंतरों के रिक्त होने का अर्थ है कि दोनों समुच्चयों में कोई अतिरिक्त अवयव नहीं है। इसलिए (A=B) होगा।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,2,1\}\) हैं, तो \(A\cap B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{3,2,1\}\), what is \(A\cap B\)?
#sets
#intersection
#equal-sets
A ( {1,2,3} )
B \( \varnothing \)
C ( {3} )
D ( {1} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
Both sets are equal, so all elements are common. Hence \(A\cap B={1,2,3}\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). Both sets are equal, so all elements are common. Hence \(A\cap B={1,2,3}\).
Step 3
Exam Tip
दोनों समुच्चय समान हैं, इसलिए सभी अवयव सामान्य हैं। अतः \(A\cap B={1,2,3}\) है।
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यदि \(A=\{1,2,3\}\) और \(B=\{3,2,1\}\) हैं, तो \(A\cup B\) क्या है?
If \(A=\{1,2,3\}\) and \(B=\{3,2,1\}\), what is \(A\cup B\)?
#sets
#union
#equal-sets
A ( {1,2,3} )
B ( {1,2,3,3,2,1} )
C \( \varnothing \)
D ( {6} )
Explanation opens after your attempt
Correct Answer
A. ( {1,2,3} )
Step 1
Concept
Order and repetition do not matter in sets. Therefore (A=B) and \(A\cup B=A\).
Step 2
Why this answer is correct
The correct answer is A. ( {1,2,3} ). Order and repetition do not matter in sets. Therefore (A=B) and \(A\cup B=A\).
Step 3
Exam Tip
समुच्चय में क्रम और दोहराव का महत्व नहीं होता। इसलिए (A=B) और \(A\cup B=A\) है।
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यदि (A=B), तो वेन आरेख में (A-B) किसके बराबर होगा?
If (A=B), then in a Venn diagram (A-B) will be equal to what?
#sets
#venn-diagrams
#equal-sets
A (A)
B (B)
C \(\varnothing\)
D (U)
Explanation opens after your attempt
Correct Answer
C. \(\varnothing\)
Step 1
Concept
When (A=B), no element remains in (A) that is not in (B). Therefore, \(A-B=\varnothing\).
Step 2
Why this answer is correct
The correct answer is C. \(\varnothing\). When (A=B), no element remains in (A) that is not in (B). Therefore, \(A-B=\varnothing\).
Step 3
Exam Tip
जब (A=B), तो (A) में ऐसा कोई अवयव नहीं बचता जो (B) में न हो। इसलिए \(A-B=\varnothing\)।
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यदि (A=B), तो वेन आरेख में \(A\cap B\) किसके बराबर होगा?
If (A=B), then in a Venn diagram, \(A\cap B\) will be equal to what?
#sets
#venn-diagrams
#equal-sets
A (A)
B \(\varnothing\)
C (U)
D (A')
Explanation opens after your attempt
Step 1
Concept
When (A=B), both circles are exactly the same. Therefore, \(A\cap B=A\).
Step 2
Why this answer is correct
The correct answer is A. (A). When (A=B), both circles are exactly the same. Therefore, \(A\cap B=A\).
Step 3
Exam Tip
जब (A=B), तब दोनों वृत्त पूरी तरह एक जैसे हैं। इसलिए \(A\cap B=A\) होता है।
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यदि (\mathcal{P}(A)=\mathcal{P}(B)), तो कौन सा निष्कर्ष हमेशा सही है?
If (\mathcal{P}(A)=\mathcal{P}(B)), which conclusion is always true?
#sets
#power-set
#equal-sets
#reasoning
A (A=B)
B \(A\subset B\)
C \(B\subset A\) पर \(A\ne B\) / \(B\subset A\) but \(A\ne B\)
D \(A\cap B=\varnothing\)
Explanation opens after your attempt
Step 1
Concept
If two sets have exactly the same subsets, the original sets must be equal. This is an important power set result for exams.
Step 2
Why this answer is correct
The correct answer is A. (A=B). If two sets have exactly the same subsets, the original sets must be equal. This is an important power set result for exams.
Step 3
Exam Tip
यदि दो समुच्चयों के सभी उपसमुच्चय समान हैं, तो मूल समुच्चय भी समान होंगे। यह घात समुच्चय की एक महत्वपूर्ण परीक्षा-युक्ति है।
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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 \(A={x:x\in\mathbb{N},x\) संख्या (18) का भाजक है(}) और \(B=\{1,2,3,6,9,18\}\) हैं, तो सही संबंध क्या है?
If \(A={x:x\in\mathbb{N},x\) is a divisor of (18)(}) and \(B=\{1,2,3,6,9,18\}\), what is the correct relation?
#sets
#equal-sets
#divisors
A (A=B)
B \(A\subset B\)
C \(B\subset A\)
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
The positive divisors of (18) are (1,2,3,6,9,18). Converting to roster form is the best way to compare elements.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The positive divisors of (18) are (1,2,3,6,9,18). Converting to roster form is the best way to compare elements.
Step 3
Exam Tip
(18) के धनात्मक भाजक (1,2,3,6,9,18) हैं। सूची रूप में बदलकर सदस्य मिलाना सबसे अच्छा तरीका है।
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कथन: यदि (n(A)=n(B)), तो (A=B)। कारण: समान सदस्य संख्या हमेशा समान सदस्य देती है। सही विकल्प चुनिए।
Assertion: If (n(A)=n(B)), then (A=B). Reason: Equal cardinality always gives identical elements. Choose the correct option.
#assertion-reason
#cardinality
#equal-sets
A कथन और कारण दोनों सही हैं / Both assertion and reason are true
B कथन सही है, कारण गलत है / Assertion is true, reason is false
C कथन गलत है, कारण सही है / Assertion is false, reason is true
D कथन और कारण दोनों गलत हैं / Both assertion and reason are false
Explanation opens after your attempt
Correct Answer
D. कथन और कारण दोनों गलत हैं / Both assertion and reason are false
Step 1
Concept
Equal cardinality does not force identical elements. For example, ({1,2}) and ({3,4}) are not equal.
Step 2
Why this answer is correct
The correct answer is D. कथन और कारण दोनों गलत हैं / Both assertion and reason are false. Equal cardinality does not force identical elements. For example, ({1,2}) and ({3,4}) are not equal.
Step 3
Exam Tip
सदस्य संख्या समान होने से सदस्य समान होना जरूरी नहीं है। जैसे ({1,2}) और ({3,4}) बराबर नहीं हैं।
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कथन: यदि (A=B), तो \(A\subseteq B\)। कारण: बराबर समुच्चयों में सभी सदस्य समान होते हैं। सही विकल्प चुनिए।
Assertion: If (A=B), then \(A\subseteq B\). Reason: Equal sets have all elements identical. Choose the correct option.
#assertion-reason
#equal-sets
#subsets
A कथन और कारण दोनों सही हैं, कारण सही व्याख्या है / Both assertion and reason are true, and the reason explains it
B कथन सही है, कारण गलत है / Assertion is true, reason is false
C कथन गलत है, कारण सही है / Assertion is false, reason is true
D कथन और कारण दोनों गलत हैं / Both assertion and reason are false
Explanation opens after your attempt
Correct Answer
A. कथन और कारण दोनों सही हैं, कारण सही व्याख्या है / Both assertion and reason are true, and the reason explains it
Step 1
Concept
When sets are equal, every element of (A) is in (B). So the subset relation follows directly.
Step 2
Why this answer is correct
The correct answer is A. कथन और कारण दोनों सही हैं, कारण सही व्याख्या है / Both assertion and reason are true, and the reason explains it. When sets are equal, every element of (A) is in (B). So the subset relation follows directly.
Step 3
Exam Tip
बराबर समुच्चय होने पर (A) का हर सदस्य (B) में होता है। इसलिए उपसमुच्चय संबंध तुरंत मिलता है।
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यदि \(A=\{2,4,6,8\}\) और \(B={x:x=2n,\ n\in{1,2,3,4}}\), तो कौन सा संबंध सही है?
If \(A=\{2,4,6,8\}\) and \(B={x:x=2n,\ n\in{1,2,3,4}}\), which relation is correct?
#equal-sets
#set-builder
#multiples
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
Putting (n=1,2,3,4) gives \(B=\{2,4,6,8\}\). Convert rule form into roster form.
Step 2
Why this answer is correct
The correct answer is A. (A=B). Putting (n=1,2,3,4) gives \(B=\{2,4,6,8\}\). Convert rule form into roster form.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर \(B=\{2,4,6,8\}\) मिलता है। नियम वाले सेट को सूची रूप में बदलें।
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यदि \(A\subseteq B\), (n(A)=4), (n(B)=4), और दोनों सीमित हैं, तो कौन सा कथन सही है?
If \(A\subseteq B\), (n(A)=4), (n(B)=4), and both are finite, which statement is correct?
#equal-sets
#finite-sets
#cardinality
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C (B-A) में (4) सदस्य हैं / (B-A) has (4) elements
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
For finite sets, a subset with equal cardinality leaves no extra element. Therefore the sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). For finite sets, a subset with equal cardinality leaves no extra element. Therefore the sets are equal.
Step 3
Exam Tip
सीमित सेट में उपसमुच्चय और बराबर सदस्य संख्या होने पर कोई अतिरिक्त सदस्य नहीं बचता। इसलिए सेट बराबर हैं।
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यदि \(A={x:x\in\mathbb{Z},x^2=16}\) और \(B=\{-4,4\}\), तो कौन सा सही है?
If \(A={x:x\in\mathbb{Z},x^2=16}\) and \(B=\{-4,4\}\), which is correct?
#equal-sets
#integers
#solution-set
A (A=B)
B \(A=\{4\}\)
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
The integer solutions are both (-4) and (4). Do not miss the negative solution in square equations.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The integer solutions are both (-4) and (4). Do not miss the negative solution in square equations.
Step 3
Exam Tip
पूर्णांक हल (-4) और (4) दोनों हैं। वर्ग वाले प्रश्नों में ऋणात्मक हल न छोड़ें।
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यदि \(A={x:x\) (20) से छोटा (4) का धनात्मक गुणज है(}), तो कौन सा (A) के बराबर है?
If \(A={x:x\) is a positive multiple of (4) less than (20)(}), which is equal to (A)?
#equal-sets
#multiples
#set-builder
A ({4,8,12,16})
B ({0,4,8,12,16})
C ({4,8,12,16,20})
D ({8,12,16})
Explanation opens after your attempt
Correct Answer
A. ({4,8,12,16})
Step 1
Concept
The positive multiples less than (20) are (4,8,12,16). Check both the boundary and positivity condition.
Step 2
Why this answer is correct
The correct answer is A. ({4,8,12,16}). The positive multiples less than (20) are (4,8,12,16). Check both the boundary and positivity condition.
Step 3
Exam Tip
(20) से छोटे धनात्मक गुणज (4,8,12,16) हैं। सीमा और धनात्मक शर्त दोनों जांचें।
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यदि \(A\subseteq B\) और \(B-A=\emptyset\), तो कौन सा निष्कर्ष सही है?
If \(A\subseteq B\) and \(B-A=\emptyset\), which conclusion is correct?
#equal-sets
#difference
#logic
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A=\emptyset\) जरूरी / \(A=\emptyset\) necessarily
Explanation opens after your attempt
Step 1
Concept
We have \(A\subseteq B\), and (B) has no element outside (A). Therefore the two sets are equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). We have \(A\subseteq B\), and (B) has no element outside (A). Therefore the two sets are equal.
Step 3
Exam Tip
\(A\subseteq B\) है और (B) में (A) के बाहर कोई सदस्य नहीं है। इसलिए दोनों बराबर हैं।
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यदि \(A=\{1,2,3\}\) और \(B=\{2,3,4\}\), तो कौन सा समुच्चय \(A\cap B\) के बराबर है?
If \(A=\{1,2,3\}\) and \(B=\{2,3,4\}\), which set is equal to \(A\cap B\)?
#sets
#intersection
#equal-sets
A ({2,3})
B ({1,4})
C ({1,2,3,4})
D \(\emptyset\)
Explanation opens after your attempt
Correct Answer
A. ({2,3})
Step 1
Concept
Intersection contains only elements common to both sets. Here the common elements are (2) and (3).
Step 2
Why this answer is correct
The correct answer is A. ({2,3}). Intersection contains only elements common to both sets. Here the common elements are (2) and (3).
Step 3
Exam Tip
प्रतिच्छेद में केवल वे सदस्य आते हैं जो दोनों में हों। यहाँ साझा सदस्य (2) और (3) हैं।
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यदि \(A=\{1,1,2,2,3\}\) और \(B=\{3,2,1\}\), तो कौन सा कथन सत्य है?
If \(A=\{1,1,2,2,3\}\) and \(B=\{3,2,1\}\), which statement is true?
#sets
#duplicates
#equal-sets
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A\ne B\)
Explanation opens after your attempt
Step 1
Concept
Repeated elements are not counted separately in a set. Both sets contain only (1,2,3).
Step 2
Why this answer is correct
The correct answer is A. (A=B). Repeated elements are not counted separately in a set. Both sets contain only (1,2,3).
Step 3
Exam Tip
दोहराए गए सदस्य समुच्चय में अलग से नहीं गिने जाते। दोनों में केवल (1,2,3) सदस्य हैं।
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यदि ({2,a}={5,2}), तो (a) का मान क्या होगा?
If ({2,a}={5,2}), what is the value of (a)?
#equal-sets
#unordered-set
#parameter
A (2)
B (3)
C (5)
D (7)
Explanation opens after your attempt
Step 1
Concept
Both sets already share (2), so the other element must be (5). Order does not matter in sets.
Step 2
Why this answer is correct
The correct answer is C. (5). Both sets already share (2), so the other element must be (5). Order does not matter in sets.
Step 3
Exam Tip
दोनों समुच्चयों में (2) पहले से समान है, इसलिए दूसरा सदस्य (5) होना चाहिए। समुच्चय में क्रम का महत्व नहीं होता।
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यदि ({a+2}={9}), तो (a) का मान क्या है?
If ({a+2}={9}), what is the value of (a)?
#equal-sets
#singleton
#parameter
A (5)
B (6)
C (7)
D (11)
Explanation opens after your attempt
Step 1
Concept
Singleton sets are equal, so (a+2=9). Hence (a=7).
Step 2
Why this answer is correct
The correct answer is C. (7). Singleton sets are equal, so (a+2=9). Hence (a=7).
Step 3
Exam Tip
एक-सदस्यीय समुच्चय बराबर हैं, इसलिए (a+2=9)। इससे (a=7) मिलता है।
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यदि \(A={x:x\in\mathbb{Z},-3<x\le2}\), तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\in\mathbb{Z},-3<x\le2}\), which set is equal to (A)?
#sets
#integers
#equal-sets
A ({-2,-1,0,1,2})
B ({-3,-2,-1,0,1,2})
C ({-2,-1,0,1})
D ({-3,-2,-1,0,1})
Explanation opens after your attempt
Correct Answer
A. ({-2,-1,0,1,2})
Step 1
Concept
The condition excludes (-3) and includes (2). Read open and closed endpoints carefully.
Step 2
Why this answer is correct
The correct answer is A. ({-2,-1,0,1,2}). The condition excludes (-3) and includes (2). Read open and closed endpoints carefully.
Step 3
Exam Tip
शर्त में (-3) शामिल नहीं है और (2) शामिल है। अंतराल में खुले और बंद चिह्न ध्यान से पढ़ें।
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यदि \(A={x:x^2-7x+12=0}\) और \(B=\{3,4\}\) हैं, तो सही संबंध कौन सा है?
If \(A={x:x^2-7x+12=0}\) and \(B=\{3,4\}\), which relation is correct?
#sets
#equal-sets
#quadratic
A (A=B)
B \(A\subset B\)
C \(B\subset A\)
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
The roots are (3) and (4), so both sets have the same elements. First solve, then compare the sets.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The roots are (3) and (4), so both sets have the same elements. First solve, then compare the sets.
Step 3
Exam Tip
समीकरण के मूल (3) और (4) हैं, इसलिए दोनों समुच्चयों के सदस्य समान हैं। पहले हल निकालकर फिर समुच्चय मिलाएं।
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यदि \(A={x:x\in\mathbb{Z},-2\le x<2}\) है, तो कौन सा समुच्चय (A) के बराबर है?
If \(A={x:x\in\mathbb{Z},-2\le x<2}\), which set is equal to (A)?
#equal-sets
#integers
#interval-condition
A ({-2,-1,0,1})
B ({-1,0,1,2})
C ({-2,-1,0,1,2})
D ({-2,0,2})
Explanation opens after your attempt
Correct Answer
A. ({-2,-1,0,1})
Step 1
Concept
The condition includes (-2) but excludes (2). The integer list is (-2,-1,0,1).
Step 2
Why this answer is correct
The correct answer is A. ({-2,-1,0,1}). The condition includes (-2) but excludes (2). The integer list is (-2,-1,0,1).
Step 3
Exam Tip
शर्त में (-2) शामिल है और (2) शामिल नहीं है। पूर्णांकों की सूची (-2,-1,0,1) है।
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यदि ({a,4}={2,b}) और \(a\ne4\), तो सही युग्म कौन सा है?
If ({a,4}={2,b}) and \(a\ne4\), which pair is correct?
#equal-sets
#parameter
#two-element-set
A (a=2,\ b=4)
B (a=4,\ b=2)
C (a=2,\ b=2)
D (a=4,\ b=4)
Explanation opens after your attempt
Correct Answer
A. (a=2,\ b=4)
Step 1
Concept
Equal sets must contain both (2) and (4). Since \(a\ne4\), (a=2) and then (b=4).
Step 2
Why this answer is correct
The correct answer is A. (a=2,\ b=4). Equal sets must contain both (2) and (4). Since \(a\ne4\), (a=2) and then (b=4).
Step 3
Exam Tip
बराबर समुच्चयों में (2) और (4) दोनों सदस्य होने चाहिए। \(a\ne4\) से (a=2) और फिर (b=4) होगा।
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यदि ({2a+1}={7}), तो (a) का मान क्या है?
If ({2a+1}={7}), what is the value of (a)?
#equal-sets
#singleton
#parameter
A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
The singleton sets are equal, so (2a+1=7). This gives (a=3).
Step 2
Why this answer is correct
The correct answer is B. (3). The singleton sets are equal, so (2a+1=7). This gives (a=3).
Step 3
Exam Tip
एक-सदस्यीय समुच्चय बराबर हैं, इसलिए (2a+1=7)। इससे (a=3) मिलता है।
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यदि (A) संख्या (18) के अभाज्य भाजकों का समुच्चय है और \(B=\{2,3\}\), तो सही कथन क्या है?
If (A) is the set of prime divisors of (18) and \(B=\{2,3\}\), what is correct?
#equal-sets
#prime-divisors
#set-builder
A (A=B)
B \(A=\{2,3,9\}\)
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
The prime divisors of (18) are only (2) and (3). Note the difference between divisors and prime divisors.
Step 2
Why this answer is correct
The correct answer is A. (A=B). The prime divisors of (18) are only (2) and (3). Note the difference between divisors and prime divisors.
Step 3
Exam Tip
(18) के अभाज्य भाजक केवल (2) और (3) हैं। भाजक और अभाज्य भाजक में अंतर ध्यान रखें।
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यदि \(A\triangle B=\emptyset\), तो कौन सा निष्कर्ष सही है?
If \(A\triangle B=\emptyset\), which conclusion is correct?
#equal-sets
#symmetric-difference
#logic
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C \(B\subset A\) उचित / \(B\subset A\) proper
D दोनों असंबद्ध / Both disjoint
Explanation opens after your attempt
Step 1
Concept
If the symmetric difference is empty, no element belongs to exactly one set. Thus the sets have identical elements.
Step 2
Why this answer is correct
The correct answer is A. (A=B). If the symmetric difference is empty, no element belongs to exactly one set. Thus the sets have identical elements.
Step 3
Exam Tip
सममित अंतर रिक्त है तो कोई सदस्य केवल एक ही सेट में नहीं है। इसलिए दोनों सेटों के सदस्य समान हैं।
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यदि (\mathcal{P}(A)=\mathcal{P}(B)) है, तो कौन सा निष्कर्ष सही है?
If (\mathcal{P}(A)=\mathcal{P}(B)), which conclusion is correct?
#power-set
#equal-sets
#reasoning
A (A=B)
B \(A\subset B\) उचित / \(A\subset B\) proper
C \(B\subset A\) उचित / \(B\subset A\) proper
D \(A\cap B=\emptyset\)
Explanation opens after your attempt
Step 1
Concept
A set itself appears in its power set. Equal power sets force the original sets to be equal.
Step 2
Why this answer is correct
The correct answer is A. (A=B). A set itself appears in its power set. Equal power sets force the original sets to be equal.
Step 3
Exam Tip
किसी समुच्चय का पूरा समुच्चय स्वयं उसके घात समुच्चय में आता है। बराबर घात समुच्चय मूल समुच्चय भी बराबर बनाते हैं।
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यदि (A=B) है, तो (\mathcal{P}(A)) और (\mathcal{P}(B)) के बारे में क्या सत्य है?
If (A=B), what is true about (\mathcal{P}(A)) and (\mathcal{P}(B))?
#equal-sets
#power-set
#theory
A (\mathcal{P}(A)=\mathcal{P}(B))
B (\mathcal{P}(A)\subset \mathcal{P}(B)) उचित / (\mathcal{P}(A)\subset \mathcal{P}(B)) proper
C वे असंबंधित हैं / They are unrelated
D दोनों रिक्त हैं / Both are empty
Explanation opens after your attempt
Correct Answer
A. (\mathcal{P}(A)=\mathcal{P}(B))
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}(B)). Equal sets have exactly the same subsets. Therefore their power sets are equal.
Step 3
Exam Tip
बराबर समुच्चयों के सभी उपसमुच्चय भी समान होते हैं। इसलिए उनके घात समुच्चय बराबर होते हैं।
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