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 221-230 of 600 questions.
A. \(^{5}C_2\times{}^{6}C_3\)
ठीक (2) girls और (3) boys चुनने हैं। परीक्षा में exact condition में केवल वही case लें। / Exactly (2) girls and (3) boys must be selected. In exams take only that case for exact conditions.
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Which sum is correct for a (5)-member committee with at least (3) boys from (6) boys and (5) girls?
A. \(^{6}C_3{}^{5}C_2+^{6}C_4{}^{5}C_1+^{6}C_5{}^{5}C_0\)
Boys की संख्या (3), (4) या (5) हो सकती है। परीक्षा में at least condition में सभी valid cases जोड़ें। / The number of boys can be (3), (4), or (5). In exams add all valid cases in at least conditions.
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A. \(^{8}C_5\times5!\)
पहले (5) letters चुनते हैं और फिर उन्हें (5!) तरीकों से जमाते हैं। परीक्षा में word में order महत्वपूर्ण होता है। / First choose (5) letters and then arrange them in (5!) ways. In exams order is important in a word.
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If a (5)-letter word is made from (8) distinct letters with repetition allowed, what is the count?
C. \(8^5\)
हर स्थान पर (8) choices फिर से उपलब्ध हैं। परीक्षा में repetition allowed हो तो power rule \(n^r\) लगाएँ। / Each position has (8) choices available again. In exams use the power rule \(n^r\) when repetition is allowed.
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A. \(6\times7^3\)
पहला digit (0) नहीं हो सकता इसलिए (6) choices हैं और बाकी तीन स्थानों पर (7) choices हैं। परीक्षा में leading zero को अलग देखें। / The first digit cannot be (0), so there are (6) choices and (7) choices for each remaining place. In exams treat leading zero separately.
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B. \(6\times{}^{6}P_3\)
पहले स्थान के लिए (6) non-zero choices हैं और फिर बाकी (3) स्थान (6) बची digits से भरते हैं। परीक्षा में पहले स्थान को अलग handle करें। / There are (6) non-zero choices for the first place and then (3) places are filled from the remaining (6) digits. In exams handle the first place separately.
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If \(^{n}C_r=^{n}C_{r-2}\) and the lower indices are different, which relation is correct for (n)?
A. (n=2r-2)
अलग lower indices पूरक होंगे इसलिए (r+(r-2)=n) है। परीक्षा में equal combination को complement rule से हल करें। / Different lower indices are complementary, so (r+(r-2)=n). In exams solve equal combinations using the complement rule.
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If \(\frac{^{n}C_{r+1}}{^{n}C_r}=2\), which equation is formed?
A. (n-r=2(r+1))
अनुपात \(\frac{n-r}{r+1}\) है और उसे (2) के बराबर रखा गया है। परीक्षा में ratio formula से सीधे equation बनाएं। / The ratio is \(\frac{n-r}{r+1}\) and it is set equal to (2). In exams form the equation directly from the ratio formula.
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If \(\frac{^{n}C_r}{^{n}C_{r-1}}=3\), which equation is correct?
A. (n-r+1=3r)
अनुपात \(\frac{n-r+1}{r}\) होता है। इसे (3) के बराबर रखने पर (n-r+1=3r) मिलता है। / The ratio is \(\frac{n-r+1}{r}\). Setting it equal to (3) gives (n-r+1=3r).
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B. \(^{10}C_4\)
Quadrilateral के लिए (4) points का unordered selection चाहिए। परीक्षा में shape बनाते समय points का order न गिनें। / A quadrilateral needs an unordered selection of (4) points. In exams do not count the order of points when forming a shape.
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