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 281-290 of 600 questions.
If \(A^{c}=U\), which statement about (A) is correct?
B. \(A=\varnothing\)
यदि (A) का पूरक पूरा (U) है, तो (A) में कोई अवयव नहीं है। इसलिए \(A=\varnothing\) सही है। / If the complement of (A) is the whole (U), then (A) has no element. Thus, \(A=\varnothing\) is correct.
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If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A^{c}={1,4,7}\), what is (n(A))?
B. (5)
(n(A)=n(U)-n\(A^{c}\)=8-3=5)। यदि पूरक दिया हो तो कुल में से पूरक घटाएं। / (n(A)=n(U)-n\(A^{c}\)=8-3=5). If the complement is given, subtract it from the total.
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B. ({5,6,7,8,9,10})
\(A^{c}={5,6,7,8,9,10}\), और यह (B) का उपसमुच्चय है। इसलिए ये सभी अवयव (B) में होने जरूरी हैं। / \(A^{c}={5,6,7,8,9,10}\), and it is a subset of (B). Hence all these elements must be in (B).
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If \(U=\{1,2,3,4,5,6\}\) and \(A=\{2,3,5\}\), what is \(U\setminus A\) equal to?
B. \(A^{c}\)
\(U\setminus A\) का अर्थ है (U) से (A) हटाना, यही \(A^{c}\) है। पूरक को अंतर संकेत से भी लिखते हैं। / \(U\setminus A\) means removing (A) from (U), which is \(A^{c}\). Complement is also written using difference notation.
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If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{1,4,7\}\), how many elements are in \(A^{c}\cup A\)?
C. (7)
\(A^{c}\cup A=U\), इसलिए इसमें (7) अवयव हैं। सर्वसमिका को सीधे उपयोग करने से समय बचता है। / \(A^{c}\cup A=U\), so it has (7) elements. Using the identity directly saves time.
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If \(U=\{1,2,3,4,5,6,7\}\), \(A=\{2,4,6\}\), how many elements are in \(A^{c}\cap A\)?
A. (0)
(A) और \(A^{c}\) में कोई साझा अवयव नहीं होता, इसलिए प्रतिच्छेद खाली है। रिक्त समुच्चय की अवयव संख्या (0) होती है। / (A) and \(A^{c}\) are disjoint, so their intersection is empty. The cardinality of the empty set is (0).
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If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,5,8\}\), and \(C=\{3,4,6,7\}\), which statement is correct?
A. \(C=A^{c}\)
(A) के बाहर (U) में ({3,4,6,7}) बचते हैं, जो (C) है। पूरक पहचानने के लिए (U) से तुलना करें। / The elements left in (U) outside (A) are ({3,4,6,7}), which is (C). Compare with (U) to identify a complement.
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C. (14)
(20) के गुणनखंड ({1,2,4,5,10,20}) हैं, इसलिए (n(A)=6)। अतः (n\(A^{c}\)=20-6=14)। / The factors of (20) are ({1,2,4,5,10,20}), so (n(A)=6). Hence (n\(A^{c}\)=20-6=14).
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If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{1,3,5,7,9\}\), and \(B=A^{c}\), what is (B)?
A. ({2,4,6,8,10})
(A) विषम संख्याओं का समुच्चय है, इसलिए \(A^{c}\) सम संख्याएं ({2,4,6,8,10}) हैं। रूप देखकर भी उत्तर मिल सकता है। / (A) is the set of odd numbers, so \(A^{c}\) is the even numbers ({2,4,6,8,10}). The pattern can also help.
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If \(U={x:x \in \mathbb{Z}, -3\le x\le 3}\) and \(A=\{-3,-1,1,3\}\), what is \(A^{c}\)?
A. ({-2,0,2})
\(U=\{-3,-2,-1,0,1,2,3\}\), इसलिए (A) से बाहर ({-2,0,2}) हैं। ऋण संख्याओं और (0) को ध्यान से शामिल करें। / \(U=\{-3,-2,-1,0,1,2,3\}\), so the elements outside (A) are ({-2,0,2}). Include negative numbers and (0) carefully.
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