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 281-290 of 590 questions.
What is the value of \(\frac{9!}{6!\cdot3!}\)?
C. (84)
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\) होता है। पहले (6!) काटने से हल छोटा होता है। / \(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
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What is the value of \(\frac{6!}{4!}-2!\)?
B. (28)
\(\frac{6!}{4!}=30\) और (2!=2), इसलिए मान (28) है। भाग और घटाव का क्रम ध्यान रखें। / \(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.
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(\frac{(n+1)!}{(n-1)!}) is equal to which expression?
B. (n(n+1))
((n+1)!=(n+1)n(n-1)!) होता है। इसलिए भाग देने पर (n(n+1)) मिलता है। / ((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
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What is the value of \(\frac{4!\cdot5}{5!}\)?
A. (1)
क्योंकि \(5!=5\cdot4!\), इसलिए \(\frac{4!\cdot5}{5!}=1\)। फैक्टोरियल को निकट छोटे फैक्टोरियल से लिखें। / Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.
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What is the value of \(3!\cdot4!\)?
C. (144)
(3!=6) और (4!=24), इसलिए गुणनफल (144) है। छोटे फैक्टोरियल याद रखें। / (3!=6) and (4!=24), so the product is (144). Memorize small factorials.
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What is the value of \(\frac{8!}{5!\cdot3!}\)?
C. (56)
\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\) होता है। पहले समान फैक्टोरियल काटें। / \(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.
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If (n!=120), what is the value of ((n-2)!)?
C. (6)
(120=5!), इसलिए (n=5) और ((n-2)!=3!=6)। पहले (n) पहचानें। / (120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.
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What is the value of \(\frac{7!}{3!\cdot4!}\)?
C. (35)
\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\) होता है। (4!) काटकर गणना करें। / \(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.
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What is the value of \(\frac{5!}{2!}+1!\)?
C. (61)
\(\frac{5!}{2!}=60\) और (1!=1), इसलिए मान (61) है। (1!) और (0!) दोनों (1) होते हैं। / \(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).
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What is the simplified form of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
B. (2)
पहला पद (n+2) और दूसरा (n) है, इसलिए अंतर (2) है। अलग-अलग सरलीकरण करने से गलती कम होती है। / The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.
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