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 251-260 of 590 questions.
If (\frac{n!+(n-1)!}{(n-1)!}=9), what is the value of (n)?
C. (8)
भिन्न का सरल रूप (n+1) है, इसलिए (n+1=9) से (n=8)। पहले सामान्य फैक्टोरियल निकालें। / The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.
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If (\frac{(m+2)!}{m!}=90), what is the value of (m)?
C. (8)
(\frac{(m+2)!}{m!}=(m+2)(m+1)), इसलिए \(10\cdot9=90\) से (m=8)। लगातार संख्याओं का गुणनफल पहचानें। / (\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.
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Which is the correct form of (8!) in terms of (6!)?
A. \(8\cdot7\cdot6!\)
\(8!=8\cdot7\cdot6!\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ना उपयोगी है। / \(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
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What is the value of \(\frac{14!}{12!\cdot2!}\)?
C. (91)
\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक ही फैलाएं। / \(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.
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What is the value of \(\frac{8!}{4!\cdot2!\cdot2!}\)?
A. (420)
\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\) होता है। पहले (4!) काटकर छोटे पदों में गणना करें। / \(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.
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What is the least natural (k) for which (k!) is divisible by (72)?
C. (6)
\(72=2^3\cdot3^2\) है और (6!) में ये गुणनखंड मिल जाते हैं। ऐसे प्रश्नों में संख्या का अभाज्य गुणनखंडन करें। / \(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.
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What is the value of \(\frac{10!}{8!\cdot2!}\)?
A. (45)
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\) होता है। पहले (8!) को काटें। / \(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
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What is the value of \(\frac{15!}{13!}-5!\)?
B. (90)
\(\frac{15!}{13!}=15\cdot14=210\) और (5!=120), इसलिए अंतर (90) है। पहले फैक्टोरियल अनुपात को सरल करें। / \(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.
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Which is the correct simplified form of (\frac{(n+2)!}{n!})?
C. ((n+2)(n+1))
((n+2)!=(n+2)(n+1)n!) होता है। (n!) कटने पर ((n+2)(n+1)) बचता है। / ((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
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What is the value of \(\frac{11!}{8!\cdot3!}\)?
C. (165)
\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\) होता है। (3!) को (6) मानना न भूलें। / \(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).
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