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 551-560 of 600 questions.
If \(^{n}C_{2}=105\), what is the value of \(^{n}C_{3}\)?
C. (455)
\(^{n}C_{2}=105\) से (n=15) मिलता है। इसलिए \(^{15}C_{3}=455\)। / From \(^{n}C_{2}=105\), we get (n=15). Therefore \(^{15}C_{3}=455\).
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If \(^{n}C_{5}:^{n}C_{4}=11:5\), what is the value of (n)?
B. (15)
\(\frac{^{n}C_{5}}{^{n}C_{4}}=\frac{n-4}{5}\) होता है। इसे \(\frac{11}{5}\) के बराबर रखने पर (n=15)। / \(\frac{^{n}C_{5}}{^{n}C_{4}}=\frac{n-4}{5}\). Equating it to \(\frac{11}{5}\) gives (n=15).
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If \(^{16}C_{r}=^{16}C_{2r+4}\), what is the value of (r)?
A. (4)
पूरक सूचकांकों का योग (16) होगा। इसलिए (r+2r+4=16) से (r=4)। / The complementary indices must add to (16). Thus (r+2r+4=16) gives (r=4).
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What is the value of \(^{13}C_{6}+^{13}C_{7}\)?
D. (3432)
पास्कल नियम से \(^{13}C_{6}+^{13}C_{7}=^{14}C_{7}\)। इसका मान (3432) है। / By Pascal's rule \(^{13}C_{6}+^{13}C_{7}=^{14}C_{7}\). Its value is (3432).
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A. (136)
निश्चित सदस्य को पहले चुन लें और बाकी (2) को (17) में से चुनें। संख्या \(^{17}C_{2}=136\) है। / Fix the required member first and choose the remaining (2) from (17). The number is \(^{17}C_{2}=136\).
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C. (350)
संभव मामले (2G3B) और (3G2B) हैं। योग \(^{5}C_{2}\times{}^{6}C_{3}+^{5}C_{3}\times{}^{6}C_{2}=350\)। / The possible cases are (2G3B) and (3G2B). The sum is \(^{5}C_{2}\times{}^{6}C_{3}+^{5}C_{3}\times{}^{6}C_{2}=350\).
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D. (5880)
ठीक (4) शिक्षक के लिए \(^{10}C_{4}\) और (2) छात्र के लिए \(^{8}C_{2}\) लें। गुणन से (5880) मिलता है। / Choose (4) teachers using \(^{10}C_{4}\) and (2) students using \(^{8}C_{2}\). Multiplication gives (5880).
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B. (378)
विशेष लोगों में से (1) और बाकी (4) लोगों को शेष (9) में से चुनें। संख्या \(^{3}C_{1}\times{}^{9}C_{4}=378\)। / Choose (1) special person and the remaining (4) people from the other (9). The number is \(^{3}C_{1}\times{}^{9}C_{4}=378\).
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C. (2541)
कुल चयन \(^{14}C_{6}\) हैं। कोई नामित विद्यार्थी न चुने जाने वाले \(^{11}C_{6}\) घटाने पर (2541) मिलता है। / Total selections are \(^{14}C_{6}\). Subtract selections with no named student \(^{11}C_{6}\) to get (2541).
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A. (6952)
वरिष्ठ सदस्यों की संख्या (2), (3), या (4) हो सकती है। योग \(^{4}C_{2}{}^{12}C_{5}+^{4}C_{3}{}^{12}C_{4}+^{4}C_{4}{}^{12}C_{3}=6952\)। / The number of senior members can be (2), (3), or (4). The sum is \(^{4}C_{2}{}^{12}C_{5}+^{4}C_{3}{}^{12}C_{4}+^{4}C_{4}{}^{12}C_{3}=6952\).
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