Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
Difficulty select karke sirf is topic ke focused MCQs practice karein. Score, timer aur explanations student-friendly flow me milenge.
Showing 441-450 of 509 questions.
If \(A\cap B=A\), which conclusion is always correct?
A. \(A\subseteq B\)
साझा भाग (A) है, इसलिए (A) का हर सदस्य (B) में है। यह उपसमुच्चय की पहचान है। / The common part is (A), so every element of (A) is in (B). This is exactly subset relation.
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If \(A-B=\emptyset\), which conclusion is correct?
A. \(A\subseteq B\)
(A) में ऐसा कोई सदस्य नहीं जो (B) से बाहर हो। इसलिए \(A\subseteq B\) है। / There is no element in (A) outside (B). Hence \(A\subseteq B\).
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If \(A\triangle B=\emptyset\), which conclusion is correct?
A. (A=B)
सममित अंतर रिक्त है तो कोई सदस्य केवल एक ही सेट में नहीं है। इसलिए दोनों सेटों के सदस्य समान हैं। / If the symmetric difference is empty, no element belongs to exactly one set. Thus the sets have identical elements.
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If (A) is the set of prime divisors of (18) and \(B=\{2,3\}\), what is correct?
A. (A=B)
(18) के अभाज्य भाजक केवल (2) और (3) हैं। भाजक और अभाज्य भाजक में अंतर ध्यान रखें। / The prime divisors of (18) are only (2) and (3). Note the difference between divisors and prime divisors.
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If (A) is the set of even divisors of (24), which is a subset of (A)?
A. ({2,4,6,8})
\(A=\{2,4,6,8,12,24\}\) है। पहले पूरे सेट को लिखें, फिर हर विकल्प जांचें। / Here \(A=\{2,4,6,8,12,24\}\). Write the full set first, then test every option.
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If \(A=\{2,3,5,7\}\), how many subsets contain both (2) and (7)?
B. (4)
(2,7) निश्चित हैं और (3,5) वैकल्पिक हैं। इसलिए \(2^2=4\) उपसमुच्चय हैं। / Elements (2,7) are fixed, while (3,5) are optional. So there are \(2^2=4\) subsets.
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If \(A=\{1,2,3,4,5,6\}\), how many subsets can be formed using only odd elements?
C. (8)
विषम सदस्य (1,3,5) हैं। इनके उपसमुच्चय \(2^3=8\) होंगे। / The odd elements are (1,3,5). Their subsets are \(2^3=8\).
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If \(A=\{1,2,3,4\}\), how many subsets have at least one element?
B. (15)
कुल उपसमुच्चय (16) हैं और केवल रिक्त समुच्चय हटाना है। इसलिए (16-1=15) है। / Total subsets are (16), and only the empty set is excluded. Hence (16-1=15).
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If (A) has (3) elements, how many proper subsets does (\mathcal{P}(A)) have?
B. (255)
(\mathcal{P}(A)) में \(2^3=8\) सदस्य हैं। इसके उचित उपसमुच्चय \(2^8-1=255\) होंगे। / (\mathcal{P}(A)) has \(2^3=8\) elements. Its proper subsets are \(2^8-1=255\).
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C. (27)
हर सदस्य के लिए तीन स्थितियां हैं: दोनों में नहीं, केवल (Y) में, या दोनों में। इसलिए कुल \(3^3=27\) है। / Each element has three choices: in neither set, in (Y) only, or in both. Thus the total is \(3^3=27\).
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