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 131-140 of 588 questions.
If \(U=\{3,6,9,12\}\) and (A=U), how many elements are in (A')?
A. (0)
जब (A=U) होता है तो (U) में (A) से बाहर कोई तत्व नहीं बचता। इसलिए (A') रिक्त है। / When (A=U), no element remains outside (A) in (U). Therefore (A') is empty.
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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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If \(U=\{blue,green,yellow,pink\}\) and \(A=\{green,pink\}\), what is (A')?
B. ({नीला,पीला})({blue,yellow})
(A) के रंग हटाने पर (U) में नीला और पीला बचते हैं। इसलिए (A'={नीला,पीला}) है। / After removing the colors of (A), blue and yellow remain in (U). Hence (A'={blue,yellow}).
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If \(A=\{12,24,36\}\), how many subsets in (\mathcal{P}(A)) do not contain (36)?
C. (4)
(36) को हटाकर बाकी (2) तत्वों से \(2^2=4\) उपसमुच्चय बनते हैं। ऐसे प्रश्नों में बचे तत्व गिनें। / After excluding (36), the remaining (2) elements form \(2^2=4\) subsets. Count the remaining elements in such questions.
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If \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(T=\{3,6,9\}\), which element will not be in (T')?
C. (6)
पूरक में मूल समुच्चय (T) के तत्व नहीं आते। इसलिए (6) (T') में नहीं होगा। / Elements of the original set (T) do not appear in the complement. So (6) will not be in (T').
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If \(A=\{o,u,i\}\), how many three element subsets are in (\mathcal{P}(A))?
A. (1)
तीन तत्वों वाले समुच्चय का तीन तत्व वाला उपसमुच्चय केवल पूरा समुच्चय होता है। इसलिए संख्या (1) है। / The only three element subset of a three element set is the whole set. So the number is (1).
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If \(A=\{5,6\}\), which statement is correct?
A. \({5}\subseteq A\) और \({5}\in\mathcal{P}(A)\)\({5}\subseteq A\) and \({5}\in\mathcal{P}(A)\)
({5}) (A) का उपसमुच्चय है इसलिए यह घात समुच्चय का तत्व है। सीधे (5) को घात समुच्चय का तत्व न मानें। / ({5}) is a subset of (A), so it is an element of the power set. Do not treat direct (5) as an element of the power set.
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If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,4,6,8\}\), how many elements of (A') are less than (5)?
B. (2)
(A'={2,3,5,7}) है। इनमें (5) से छोटे (2) और (3) हैं। / (A'={2,3,5,7}). Among these, (2) and (3) are less than (5).
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If \(A=\{4,5\}\), how many elements are in (\mathcal{P}(\mathcal{P}(A)))?
C. (16)
पहले (n(\mathcal{P}(A))=22=4) है। फिर (\mathcal{P}(\mathcal{P}(A))) में \(2^4=16\) तत्व होंगे। / First (n(\mathcal{P}(A))=22=4). Then (\mathcal{P}(\mathcal{P}(A))) has \(2^4=16\) elements.
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