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 81-90 of 588 questions.
If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,2,3,4\}\), what is the smallest number in (A')?
C. (5)
(A') में (5,6,7,8) हैं। इनमें सबसे छोटी संख्या (5) है। / (A') contains (5,6,7,8). The smallest among them is (5).
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If \(A=\{a,b,c\}\), why will ({a,c}) be in (\mathcal{P}(A))?
A. क्योंकि यह (A) का उपसमुच्चय हैbecause it is a subset of (A)
({क,ग}) के सभी तत्व (A) में हैं इसलिए यह उपसमुच्चय है। घात समुच्चय के तत्व उपसमुच्चय होते हैं। / All elements of ({a,c}) are in (A), so it is a subset. Elements of a power set are subsets.
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If \(U=\{1,2,3,4,5\}\) and \(A=\{1,2,3,4,5\}\), how many elements are in (A')?
A. (0)
जब (A=U) हो तो पूरक रिक्त होता है। इसलिए (A') में (0) तत्व हैं। / When (A=U), the complement is empty. Therefore (A') has (0) elements.
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If \(U=\{1,2,3,4\}\) and \(A=\emptyset\), how many elements will be in (\mathcal{P}(A'))?
D. (16)
जब \(A=\emptyset\) हो तो (A'=U) होता है। यहां (U) में (4) तत्व हैं इसलिए \(2^4=16\) तत्व मिलेंगे। / When \(A=\emptyset\), (A'=U). Here (U) has (4) elements so the power set has \(2^4=16\) elements.
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If \(A=\{1,2,3\}\), how many sets in (\mathcal{P}(A)) contain (1)?
C. (4)
(1) को स्थिर रखकर बाकी (2) तत्वों को चुनने या न चुनने के \(2^2=4\) तरीके हैं। इसलिए ऐसे (4) उपसमुच्चय हैं। / Keep (1) fixed and choose or not choose the remaining (2) elements in \(2^2=4\) ways. So there are (4) such subsets.
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If \(U=\{black,white,red,yellow\}\) and \(A=\{black,yellow\}\), what is (A')?
B. ({सफेद,लाल})({white,red})
(A) के रंग हटाने पर (U) में सफेद और लाल बचते हैं। इसलिए (A'={सफेद,लाल}) है। / After removing the colors of (A), white and red remain in (U). Hence (A'={white,red}).
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If \(A=\{5,10,15\}\), how many subsets in (\mathcal{P}(A)) do not contain (15)?
C. (4)
(15) को न लेकर बाकी (2) तत्वों से \(2^2=4\) उपसमुच्चय बनते हैं। परीक्षा में हटे हुए तत्व के बाद बचे तत्व गिनें। / Without (15), the remaining (2) elements form \(2^2=4\) subsets. In exams count the elements left after removing the fixed element.
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If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(M=\{2,4,6,8,10\}\), which element will be in (M')?
C. (9)
(9) (U) में है लेकिन (M) में नहीं है। इसलिए (9) (M') में होगा। / (9) is in (U) but not in (M). So (9) will be in (M').
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If \(A=\{a,e,i\}\), how many three element subsets are in (\mathcal{P}(A))?
A. (1)
तीन तत्वों वाले समुच्चय का तीन तत्व वाला उपसमुच्चय केवल वही पूरा समुच्चय होता है। इसलिए संख्या (1) है। / The only three element subset of a three element set is the whole set itself. So the number is (1).
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If \(A=\{1,2\}\), which statement is correct?
A. \({1}\subseteq A\) और \({1}\in\mathcal{P}(A)\)\({1}\subseteq A\) and \({1}\in\mathcal{P}(A)\)
({1}) (A) का उपसमुच्चय है इसलिए वह घात समुच्चय का तत्व है। सीधे (1) को (\mathcal{P}(A)) का तत्व न मानें। / ({1}) is a subset of (A), so it is an element of the power set. Do not treat direct (1) as an element of (\mathcal{P}(A)).
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