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 511-520 of 600 questions.
If \(U={x:x \in \mathbb{Z},-6\le x\le 12}\) and \(A={x:x \in U,2x-3<7}\), what is (A')?
A. ({5,6,7,8,9,10,11,12})
(2x-3<7) से (x<5) मिलता है। इसलिए पूरक में \(x\ge 5\) वाले सदस्य आएंगे।
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\(If (U={1,2,\ldots,25}), (A={x:x \in U,5\) is a divisor of x}), how many prime numbers are in (A')?
A. (7)
(25) तक अभाज्य संख्याएं (9) हैं और उनमें (5) को हटाना होगा। (A') में (5) के गुणज नहीं आते, इसलिए (7) अभाज्य बचते हैं। / There are (9) primes up to (25), and (5) must be removed. Multiples of (5) are not in (A'), so (7) primes remain.
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If \(A\cap B'=A\), which conclusion must be true?
A. \(A\subseteq B'\)
\(A\cap B'=A\) तभी होता है जब (A) का हर सदस्य (B') में हो। अतः \(A\subseteq B'\) है। / \(A\cap B'=A\) occurs only when every element of (A) is in (B'). Hence \(A\subseteq B'\).
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If \(U={1,2,\ldots,70}\), \(A={x:x \in U,2\mid x}\), \(B={x:x \in U,7\mid x}\), what is (n((A-B)'))?
A. (40)
(A-B) में वे सम संख्याएं हैं जो (7) से विभाज्य नहीं हैं, उनकी संख्या (35-5=30) है। इसलिए पूरक (70-30=40) है। / (A-B) contains even numbers not divisible by (7), and their count is (35-5=30). Therefore the complement has (70-30=40) elements.
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If \(U=\mathbb{R}\) and \(A={x:x \in \mathbb{R},x^2-6x+8>0}\), what is (A')?
A. ([2,4])
\(x^2-6x+8>0\) का हल (x<2) या (x>4) है। इसलिए पूरक में \(2\le x\le 4\) आएगा। / The solution of \(x^2-6x+8>0\) is (x<2) or (x>4). Thus the complement is \(2\le x\le 4\).
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A. ({1,2,3,4,5,7,8,9,10,11,13,14,15,16,17})
(A'\cup B'=\(A\cap B\)') है। \(A\cap B={6,12,18}\), इसलिए इन्हें (U) से हटाएं। / (A'\cup B'=\(A\cap B\)'). Since \(A\cap B={6,12,18}\), remove these from (U).
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A. (17)
\(A'\cap B'\) का अर्थ विषम और वर्ग नहीं संख्याएं हैं। (40) तक (20) विषम संख्याओं में (1,9,25) वर्ग हैं, इसलिए (17) बचते हैं। / \(A'\cap B'\) means odd and non-square numbers. Among (20) odd numbers up to (40), (1,9,25) are squares, so (17) remain.
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If \(U=\{p,q,r,s,t,u,v\}\), (A'={q,s,u}), and \(B=\{p,q,t,v\}\), what is \(A\cap B\)?
A. ({p,t,v})
पहले (A=U-A'={p,r,t,v}) लिखें। फिर (B) से प्रतिच्छेद लेने पर ({p,t,v}) मिलता है। / First write (A=U-A'={p,r,t,v}). Intersecting with (B) gives ({p,t,v}).
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If \(U=\mathbb{R}\), (A=\(-3,\infty\)), and (B=\(-\infty,5]\), what is (\(A\cap B\)')?
A. ((-\infty,-3]\cup\(5,\infty\))
(A\cap B=(-3,5]) है। इसका पूरक ((-\infty,-3]\cup\(5,\infty\)) होगा। / (A\cap B=(-3,5]). Its complement is ((-\infty,-3]\cup\(5,\infty\)).
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A. (87)
\(A\cap B\) में (30) के गुणज होंगे, जो (90) तक (3) हैं। इसलिए पूरक में (90-3=87) सदस्य हैं। / \(A\cap B\) contains multiples of (30), and there are (3) up to (90). So the complement has (90-3=87) elements.
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