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 191-200 of 600 questions.
If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A^c={1,4,9}\), how many elements are in (A)?
A. (7)
(U) में (10) तत्व हैं और \(A^c\) में (3) तत्व हैं। इसलिए (n(A)=10-3=7) होगा। / (U) has (10) elements and \(A^c\) has (3) elements. Therefore (n(A)=10-3=7).
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If (n(U)=64) and (n(A)=3n\(A^c\)), what is (n\(A^c\))?
A. (16)
मान लें (n\(A^c\)=x), तब (n(A)=3x)। इसलिए (3x+x=64) से (x=16) मिलता है। / Let (n\(A^c\)=x), then (n(A)=3x). Thus (3x+x=64), giving (x=16).
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If (n(U)=54) and (n\(A^c\)=2n(A)), what is (n(A))?
A. (18)
मान लें (n(A)=x), तब (n\(A^c\)=2x)। इसलिए (x+2x=54) से (x=18) है। / Let (n(A)=x), then (n\(A^c\)=2x). Hence (x+2x=54), so (x=18).
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\(If (A\subseteq U) and (A^c={x:x\in U\) and \(x\notin A}), why is (A\cap A^c) empty\)?
A. क्योंकि कोई तत्व एक साथ (A) में और (A) में नहीं हो सकताbecause no element can be both in (A) and not in (A)
पूरक की परिभाषा में \(x\notin A\) शर्त होती है। इसलिए वही तत्व (A) में भी नहीं हो सकता। / The definition of complement has the condition \(x\notin A\). So the same element cannot also be in (A).
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If \(U=\{1,2,3,4,5,6,7,8\}\) and \(A=\{1,2,3\}\), which (B) is not the complement of (A)?
A. ({4,5,6,7})
सही पूरक ({4,5,6,7,8}) है। विकल्प ({4,5,6,7}) में (8) छूट गया है। / The correct complement is ({4,5,6,7,8}). The option ({4,5,6,7}) misses (8).
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A. (90)
(1) से (100) तक (10) के (10) गुणज हैं। इसलिए पूरक में (100-10=90) तत्व होंगे। / There are (10) multiples of (10) from (1) to (100). Therefore the complement has (100-10=90) elements.
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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 \(A\cup B\)?
A. (U)
यदि \(B=A^c\), तो \(A\cup B=A\cup A^c=U\) होगा। यह पूरक का सीधा गुण है। / If \(B=A^c\), then \(A\cup B=A\cup A^c=U\). This is a direct property of complement.
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If \(U=\{1,2,3,4,5,6,7,8,9,10\}\), \(A=\{2,4,6,8,10\}\), and \(B=A^c\), what is \(A\cap B\)?
A. \(\varnothing\)
यदि \(B=A^c\), तो \(A\cap B=A\cap A^c=\varnothing\) होगा। पूरक समुच्चय हमेशा असंबद्ध होते हैं। / If \(B=A^c\), then \(A\cap B=A\cap A^c=\varnothing\). Complementary sets are always disjoint.
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If \(U=\{1,2,3,4,5,6,7,8\}\), \(A=\{1,2,3,4\}\), and \(B=\{5,6,7,8\}\), what is (\(A\cup B\)^c)?
A. \(\varnothing\)
यहां \(A\cup B=U\) है। इसलिए (\(A\cup B\)^c=U^c=\varnothing) होगा। / Here \(A\cup B=U\). Therefore (\(A\cup B\)^c=U^c=\varnothing).
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If \(U=\{1,2,3,4,5,6\}\), \(A=\{1,2,3\}\), and \(B=\{4,5,6\}\), what is (\(A\cap B\)^c)?
A. (U)
यहां \(A\cap B=\varnothing\) है। इसलिए (\(A\cap B\)^c=\varnothing^c=U) होगा। / Here \(A\cap B=\varnothing\). Therefore (\(A\cap B\)^c=\varnothing^c=U).
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