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.
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If \(A=\{9\}\), which is (\mathcal{P}(A))?
C. \({\emptyset,{9}}\)
एक तत्व वाले समुच्चय के उपसमुच्चय \(\emptyset\) और ({9}) होते हैं। इसलिए घात समुच्चय \({\emptyset,{9}}\) है। / A one element set has subsets \(\emptyset\) and ({9}). Hence the power set is \({\emptyset,{9}}\).
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If \(A={\emptyset,5,10}\), what is (n(\mathcal{P}(A)))?
C. (8)
यहां \(\emptyset\) भी एक तत्व है इसलिए (A) में कुल (3) तत्व हैं। अतः \(2^3=8\) उपसमुच्चय होंगे। / Here \(\emptyset\) is also one element so (A) has (3) elements. Thus there are \(2^3=8\) subsets.
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B. पुस्तकालय की हिंदी न होने वाली पुस्तकेंlibrary books that are not Hindi books
पूरक उसी (U) के अंदर दिए गए समुच्चय से बाहर के तत्व दिखाता है। यहां (H') हिंदी न होने वाली पुस्तकें हैं। / A complement shows elements inside the same (U) but outside the given set. Here (H') means books that are not Hindi books.
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If \(A=\{l,m,n,o,p\}\), how many one element subsets are in (\mathcal{P}(A))?
B. (5)
हर तत्व से एक एकल उपसमुच्चय बनता है। पांच तत्व होने पर पांच एक तत्व वाले उपसमुच्चय होंगे। / Each element forms one singleton subset. With five elements there are five one element subsets.
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If \(A=\{11,22\}\), which is (\mathcal{P}(A))?
A. \({\emptyset,{11},{22},{11,22}}\)
दो तत्वों वाले समुच्चय के चार उपसमुच्चय होते हैं। घात समुच्चय में \(\emptyset\) और पूरा समुच्चय भी शामिल करें। / A two element set has four subsets. Include \(\emptyset\) and the whole set in the power set.
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If \(A=\{2,3,4,5,6\}\), how many four element subsets are in (\mathcal{P}(A))?
B. (5)
पांच तत्वों में से चार चुनने के (5) तरीके हैं। हर उपसमुच्चय में एक अलग तत्व छूटता है। / There are (5) ways to choose four elements from five. In each subset one different element is left out.
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If \(U=\{1,2,3,4,5,6,7\}\) and \(A=\{2,4,7\}\), how many elements will be in (\mathcal{P}(A'))?
C. (16)
पहले (A'={1,3,5,6}) है जिसमें (4) तत्व हैं। इसलिए (\mathcal{P}(A')) में \(2^4=16\) तत्व होंगे। / First (A'={1,3,5,6}), which has (4) elements. So (\mathcal{P}(A')) has \(2^4=16\) elements.
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If \(A=\{a,b,c,d\}\), why will ({a,d}) be in (\mathcal{P}(A))?
A. क्योंकि यह (A) का उपसमुच्चय हैbecause it is a subset of (A)
({क,घ}) के सभी तत्व (A) में हैं इसलिए यह उपसमुच्चय है। घात समुच्चय में सभी उपसमुच्चय आते हैं। / All elements of ({a,d}) are in (A), so it is a subset. A power set contains all subsets.
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If \(U=\{2,4,6\}\) and \(A=\emptyset\), how many elements will be in (\mathcal{P}(A'))?
C. (8)
जब \(A=\emptyset\) हो तो (A'=U) होता है। यहां (U) में (3) तत्व हैं इसलिए \(2^3=8\) तत्व मिलेंगे। / When \(A=\emptyset\), (A'=U). Here (U) has (3) elements so the power set has \(2^3=8\) elements.
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If \(A=\{2,5,8\}\), how many subsets in (\mathcal{P}(A)) contain (5)?
C. (4)
(5) को स्थिर रखकर बाकी (2) तत्वों के लिए \(2^2=4\) विकल्प हैं। इसलिए ऐसे (4) उपसमुच्चय होंगे। / Keep (5) fixed and choose from the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
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