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 321-330 of 559 questions.
A. ({2,4,5,6,8,10})
(A) में (1,3,7,9) हैं। इसलिए पूरक (2) या (5) से विभाज्य तत्व ({2,4,5,6,8,10}) हैं। / (A) contains (1,3,7,9). So the complement is the elements divisible by (2) or (5): ({2,4,5,6,8,10}).
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If \(A=\{2,4,6,8,10\}\), how many elements of (\mathcal{P}(A)) contain only even numbers?
C. (32)
(A) के सभी तत्व सम हैं, इसलिए (\mathcal{P}(A)) के हर उपसमुच्चय में केवल सम संख्याएँ होंगी। कुल संख्या \(2^5=32\) है। / All elements of (A) are even, so every subset in (\mathcal{P}(A)) contains only even numbers. The total number is \(2^5=32\).
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B. (3)
(1) निश्चित है और (2) नहीं लेना है, इसलिए (3,4,5) में से (2) तत्व चुनने होंगे। संख्या \(\binom{3}{2}=3\) है। / (1) is fixed and (2) is excluded, so choose (2) elements from (3,4,5). The count is \(\binom{3}{2}=3\).
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If (|A|=6), how many elements of (\mathcal{P}(A)) have size (2) or (4)?
B. (30)
ऐसे उपसमुच्चयों की संख्या \(\binom{6}{2}+\binom{6}{4}=15+15=30\) है। आकार आधारित प्रश्नों में संयोजन लगाएँ। / The number is \(\binom{6}{2}+\binom{6}{4}=15+15=30\). Use combinations for size-based subset questions.
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C. (20)
\(A\cap B\) में (6) के गुणज (6,12,18,24) हैं, इसलिए इसमें (4) तत्व हैं। पूरक में (24-4=20) तत्व होंगे। / \(A\cap B\) contains the multiples of (6): (6,12,18,24), so it has (4) elements. The complement has (24-4=20) elements.
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\(If (U={1,2,3,4,5,6,7,8,9,10,11,12}) and (A={x:x\in U, x\) is divisible by 4}), what is (A')?
A. ({1,2,3,5,6,7,9,10,11})
(4) से विभाज्य तत्व (4,8,12) हैं। पूरक में (U) के बाकी तत्व आएँगे। / The elements divisible by (4) are (4,8,12). The complement contains the remaining elements of (U).
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If \(A={\emptyset,{a},b}\), which of the following is an element of (\mathcal{P}(A))?
A. \({\emptyset,{a}}\)
\({\emptyset,{a}}\), (A) का उपसमुच्चय है। घात समुच्चय में हमेशा मूल समुच्चय के उपसमुच्चय आते हैं। / \({\emptyset,{a}}\) is a subset of (A). A power set always contains subsets of the original set.
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A. \({x:x\in \mathbb{Z}, x<-2\) या (x>3})\({x:x\in \mathbb{Z}, x<-2\) or (x>3})
पूरक में वे पूर्णांक होंगे जो दिए गए अंतराल के बाहर हैं। सीमा मान (-2) और (3) (A) में हैं इसलिए पूरक में नहीं होंगे। / The complement contains integers outside the given interval. The endpoints (-2) and (3) are in (A), so they are not in the complement.
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If (\mathcal{P}(A)) has (256) elements, how many elements are in (\mathcal{P}(\mathcal{P}(A)))?
B. \(2^{256}\)
(\mathcal{P}(A)) स्वयं (256) तत्वों वाला समुच्चय है। इसलिए उसके घात समुच्चय में \(2^{256}\) तत्व होंगे। / (\mathcal{P}(A)) itself is a set with (256) elements. Its power set therefore has \(2^{256}\) elements.
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If \(A=\{1,2,3,4,5,6\}\), how many elements of (\mathcal{P}(A)) contain (1) and do not contain (6)?
B. (16)
(1) निश्चित है और (6) निषिद्ध है। शेष चार तत्व स्वतंत्र हैं, इसलिए \(2^4=16\) उपसमुच्चय होंगे। / (1) is fixed and (6) is forbidden. The remaining four elements are free, so there are \(2^4=16\) subsets.
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