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 311-320 of 559 questions.
If \(U=\{a,b,c,d,e,f\}\), (A'={b,d,f}), what is (A)?
A. ({a,c,e})
(A), (U) में (A') के बाहर बचे तत्वों का समुच्चय है। इसलिए \(A=\{a,c,e\}\)। / (A) is the set of elements left in (U) outside (A'). Therefore \(A=\{a,c,e\}\).
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If \(A=\{1,2,3,4,5\}\), how many elements of (\mathcal{P}(A)) have even cardinality?
B. (16)
(5) तत्वों वाले समुच्चय के कुल (32) उपसमुच्चय हैं। इनमें आधे यानी (16) सम आकार के होते हैं। / A set with (5) elements has (32) subsets. Half of them, (16), have even cardinality.
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If \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,4,9\}\), what is the correct description of (A')?
B. (U) में अपूर्ण वर्ग संख्याएँNon-perfect-square numbers in (U)
(A) में (U) के पूर्ण वर्ग (1,4,9) हैं। पूरक में (U) की बाकी अपूर्ण वर्ग संख्याएँ होंगी। / (A) contains the perfect squares (1,4,9) in (U). Its complement contains the remaining non-perfect-square numbers in (U).
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If \(A=\{a,b,c\}\), how many elements of (\mathcal{P}(A)) are supersets of ({a,b})?
B. (2)
({a,b}) को रखना जरूरी है और (c) वैकल्पिक है। इसलिए ({a,b}) और ({a,b,c}), कुल (2) हैं। / ({a,b}) must be included and (c) is optional. Thus ({a,b}) and ({a,b,c}), total (2), work.
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If (U) is the set of all digits and \(A=\{0,2,4,6,8\}\), what is (A')?
A. ({1,3,5,7,9})
सभी अंक (0) से (9) तक होते हैं। (A) सम अंकों का समुच्चय है, इसलिए पूरक विषम अंक हैं। / All digits are from (0) to (9). (A) is the set of even digits, so the complement is the odd digits.
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If \(A=\{1,2,3,4\}\), how many elements of (\mathcal{P}(A)) contain exactly one of (1) and (2)?
C. (8)
(1,2) में से ठीक एक चुनने के (2) तरीके हैं। शेष (3,4) के लिए \(2^2\) तरीके, इसलिए कुल (8) हैं। / There are (2) ways to choose exactly one of (1,2). The remaining (3,4) give \(2^2\) choices, so total (8).
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If \(U=\mathbb{N}\) and \(A={x:x\in \mathbb{N}, x\le 100}\), what is (A')?
A. \({x:x\in \mathbb{N}, x>100}\)
(A) में (100) तक की प्राकृतिक संख्याएँ हैं। \(\mathbb{N}\) में पूरक (100) से बड़ी प्राकृतिक संख्याएँ हैं। / (A) contains natural numbers up to (100). In \(\mathbb{N}\), the complement is natural numbers greater than (100).
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If \(A=\{1,2,3\}\), how many elements are in \(\mathcal{P}(A)\setminus{\emptyset,A}\)?
C. (6)
(\mathcal{P}(A)) में \(2^3=8\) तत्व हैं। \(\emptyset\) और (A) हटाने पर (6) तत्व बचते हैं। / (\mathcal{P}(A)) has \(2^3=8\) elements. Removing \(\emptyset\) and (A) leaves (6) elements.
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If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\) and \(B=\{3,4,5,6\}\), what is \(A'\cup B'\)?
A. ({1,2,5,6,7,8})
(A'={5,6,7,8}) और (B'={1,2,7,8}) है। उनका संघ ({1,2,5,6,7,8}) है। / (A'={5,6,7,8}) and (B'={1,2,7,8}). Their union is ({1,2,5,6,7,8}).
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If \(A=\{x,y,z,w\}\), how many elements of (\mathcal{P}(A)) are disjoint from ({x,z})?
B. (4)
असंयुक्त उपसमुच्चय में (x) और (z) नहीं आ सकते। केवल (y,w) चुने जा सकते हैं, इसलिए \(2^2=4\) हैं। / A disjoint subset cannot contain (x) or (z). Only (y,w) may be chosen, so there are \(2^2=4\).
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