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 571-580 of 600 questions.
C. (50)
वृत्तीय चयन में संख्या \(\frac{10}{10-3}\times{}^{7}C_{3}\) है। इसका मान (50) है। / For circular selection, the count is \(\frac{10}{10-3}\times{}^{7}C_{3}\). Its value is (50).
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How many non-negative integer solutions does (x+y+z=15) have?
A. (136)
स्टार और बार विधि से संख्या \(^{15+3-1}C_{3-1}=^{17}C_{2}\) है। इसका मान (136) है। / By the stars and bars method, the count is \(^{15+3-1}C_{3-1}=^{17}C_{2}\). Its value is (136).
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How many positive integer solutions does \(x_{1}+x_{2}+x_{3}+x_{4}+x_{5}=20\) have?
D. (3876)
धन पूर्णांक हलों के लिए पहले हर चर को (1) दें। संख्या \(^{19}C_{4}=3876\) है। / For positive integer solutions, give (1) to each variable first. The count is \(^{19}C_{4}=3876\).
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B. (104)
कुल \(^{16}C_{3}\) से \(x_i\geq6\) वाले मामले घटाकर दोहरे मामले जोड़ें। (560-480+24=104)। / Subtract cases with \(x_i\geq6\) from total \(^{16}C_{3}\) and add double-overlap cases. (560-480+24=104).
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How many non-negative integer solutions does (x+y+z=10) have if \(x\leq3\)?
C. (38)
कुल \(^{12}C_{2}=66\) हल हैं। \(x\geq4\) वाले \(^{8}C_{2}=28\) घटाने पर (38) मिलते हैं। / There are \(^{12}C_{2}=66\) total solutions. Subtract \(^{8}C_{2}=28\) cases with \(x\geq4\) to get (38).
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A. (5148)
पहले (4) सूटों में से सूट चुनें और फिर (13) में से (5) पत्ते चुनें। संख्या \(4\times{}^{13}C_{5}=5148\)। / First choose one of (4) suits and then choose (5) cards from (13). The number is \(4\times{}^{13}C_{5}=5148\).
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C. (712842)
दिल के (2) पत्ते \(^{13}C_{2}\) तरीकों से और बाकी (3) पत्ते \(^{39}C_{3}\) तरीकों से चुने जाएंगे। गुणन से (712842)। / Choose (2) hearts in \(^{13}C_{2}\) ways and the other (3) cards in \(^{39}C_{3}\) ways. Multiplication gives (712842).
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B. (886656)
कुल \(^{52}C_{5}\) से बिना इक्के वाले \(^{48}C_{5}\) हाथ घटाएं। उत्तर (886656) है। / Subtract hands with no ace \(^{48}C_{5}\) from total \(^{52}C_{5}\). The answer is (886656).
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C. (69184)
(4) रानियों में से (3) चुनें और बाकी (3) पत्ते (48) गैर-रानी पत्तों से चुनें। संख्या \(^{4}C_{3}\times{}^{48}C_{3}=69184\)। / Choose (3) queens from (4) and the other (3) cards from (48) non-queen cards. The number is \(^{4}C_{3}\times{}^{48}C_{3}=69184\).
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A. (66)
सम योग के लिए विषम अंकों की संख्या (0), (2), या (4) होनी चाहिए। गणना \(^{5}C_{0}{}^{4}C_{4}+^{5}C_{2}{}^{4}C_{2}+^{5}C_{4}{}^{4}C_{0}=66\)। / For an even sum, the number of odd digits must be (0), (2), or (4). The count is \(^{5}C_{0}{}^{4}C_{4}+^{5}C_{2}{}^{4}C_{2}+^{5}C_{4}{}^{4}C_{0}=66\).
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