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 151-160 of 600 questions.
A. ({1,5,7,11})
(A^c\cap B^c=\(A\cup B\)^c) होता है। \(A\cup B={2,3,4,6,8,9,10,12}\), इसलिए बचे तत्व उत्तर हैं। / (A^c\cap B^c=\(A\cup B\)^c). Since \(A\cup B={2,3,4,6,8,9,10,12}\), the remaining elements are the answer.
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A. ({1,2,3,6,7,8,9,10})
(A^c\cup B^c=\(A\cap B\)^c) होता है। \(A\cap B={4,5}\), इसलिए (U) से इसे हटाने पर उत्तर मिलता है। / (A^c\cup B^c=\(A\cap B\)^c). Since \(A\cap B={4,5}\), remove it from (U) to get the answer.
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A. (12)
(1) से (20) तक (8) अभाज्य संख्याएं हैं, इसलिए (n\(A^c\)=20-8=12)। (1) को अभाज्य न मानें। / There are (8) primes from (1) to (20), so (n\(A^c\)=20-8=12). Do not treat (1) as prime.
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If \(U={x:x\in\mathbb{Z},-4\le x\le 4}\) and \(A={x:x^2\le 4}\), what is \(A^c\)?
A. ({-4,-3,3,4})
\(x^2\le 4\) से \(A=\{-2,-1,0,1,2\}\) मिलता है। (U) के बाकी तत्व \(A^c\) बनाते हैं। / From \(x^2\le 4\), \(A=\{-2,-1,0,1,2\}\). The remaining elements of (U) form \(A^c\).
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If (U=[-2,6]) and (A=(1,4]), what is \(A^c\)?
A. ([-2,1]\cup(4,6])
(1) (A) में नहीं है, इसलिए पूरक में शामिल होगा। (4) (A) में है, इसलिए पूरक (4) के बाद शुरू होगा। / (1) is not in (A), so it is included in the complement. (4) is in (A), so the complement starts after (4).
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If (U=(-5,5]) and (A=[-1,3)), what is \(A^c\)?
A. \((-5,-1)\cup[3,5]\)
(-1) (A) में है, इसलिए पूरक में नहीं आएगा। (3) (A) में नहीं है, इसलिए पूरक में शामिल होगा। / (-1) is in (A), so it is not in the complement. (3) is not in (A), so it is included in the complement.
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If \(A\subseteq B\subseteq U\), which of the following is always true?
A. \(B^c\subseteq A^c\)
पूरक लेने पर समावेशन का क्रम उलट जाता है। इसलिए \(A\subseteq B\) से \(B^c\subseteq A^c\) मिलता है। / The order of inclusion reverses after taking complements. Thus \(A\subseteq B\) gives \(B^c\subseteq A^c\).
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If \(A^c\subseteq B^c\), which conclusion is correct?
A. \(B\subseteq A\)
पूरकों में समावेशन उलटा होता है। इसलिए \(A^c\subseteq B^c\) से \(B\subseteq A\) मिलेगा। / Inclusion reverses for complements. Therefore \(A^c\subseteq B^c\) implies \(B\subseteq A\).
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If (n(U)=80), (n(A)=50), (n(B)=45), and (n\(A\cap B\)=25), what is (n(\(A\cup B\)^c))?
A. (10)
(n\(A\cup B\)=50+45-25=70) है। इसलिए (n(\(A\cup B\)^c)=80-70=10) होगा। / (n\(A\cup B\)=50+45-25=70). Hence (n(\(A\cup B\)^c)=80-70=10).
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If (n(U)=100), (n\(A^c\)=40), (n\(B^c\)=55), and (n\(A^c\cap B^c\)=20), what is (n\(A\cap B\))?
A. (25)
\(A^c\cup B^c\) की संख्या (40+55-20=75) है। डी मॉर्गन से (A^c\cup B^c=\(A\cap B\)^c), इसलिए (n\(A\cap B\)=25)। / The number in \(A^c\cup B^c\) is (40+55-20=75). By De Morgan, (A^c\cup B^c=\(A\cap B\)^c), so (n\(A\cap B\)=25).
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