Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 91-100 of 590 questions.
How can (5!) be written using (3!)?
A. \(5\times4\times3!\)
\(5!=5\times4\times3!\) होता है। बीच में रुककर छोटा क्रमगुणित लिखना सही है। / \(5!=5\times4\times3!\). It is correct to stop the expansion and write a smaller factorial.
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What is the value of \(\frac{11!}{10!}\)?
B. (11)
\(\frac{11!}{10!}=11\) क्योंकि \(11!=11\times10!\)। लगातार क्रमगुणित आसानी से कटते हैं। / \(\frac{11!}{10!}=11\) because \(11!=11\times10!\). Consecutive factorials cancel easily.
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What is the value of (6!+0!-1!)?
C. (720)
(6!=720), (0!=1) और (1!=1), इसलिए मान (720) है। (0!) और (1!) दोनों बराबर हैं। / (6!=720), (0!=1), and (1!=1), so the value is (720). (0!) and (1!) are equal.
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What is the simplified form of (\frac{(n+4)!}{(n+3)!})?
C. (n+4)
((n+4)!=(n+4)(n+3)!), इसलिए सरल रूप (n+4) है। क्रमगुणित में पास वाला भाग काटें। / ((n+4)!=(n+4)(n+3)!), so the simplified form is (n+4). Cancel the adjacent factorial part.
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What is the sum of \(4!\div2!\) and (3!)?
B. (18)
\(4!\div2!=12\) और (3!=6), इसलिए योग (18) है। भाग और क्रमगुणित दोनों को अलग-अलग सरल करें। / \(4!\div2!=12\) and (3!=6), so the sum is (18). Simplify the division and factorial separately.
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\(9\times8!\) is equal to which of the following?
C. (9!)
\(9!=9\times8!\), इसलिए दिया गया रूप (9!) है। यह क्रमगुणित की मूल पहचान है। / \(9!=9\times8!\), so the given form is (9!). This is a basic factorial identity.
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What is the value of \(\frac{5!}{2!,3!}\)?
C. (10)
\(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\)। हर क्रमगुणित का सही मान रखें। / \(\frac{5!}{2!,3!}=\frac{120}{2\times6}=10\). Keep the correct value of each factorial.
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C. (122)
(2!=2) और (5!=120), इसलिए योग (122) है। जोड़ते समय छोटे क्रमगुणित को न भूलें। / (2!=2) and (5!=120), so the sum is (122). Do not forget the smaller factorial while adding.
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How can (7!) be written using (5!)?
D. \(7\times6\times5!\)
\(7!=7\times6\times5!\) होता है। बड़े क्रमगुणित को छोटे क्रमगुणित तक विस्तार करें। / \(7!=7\times6\times5!\). Expand the larger factorial down to the smaller factorial.
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\(12\times11\times10!\) is equal to which of the following?
C. (12!)
\(12!=12\times11\times10!\), इसलिए दिया गया रूप (12!) है। क्रमगुणित विस्तार को छोटे क्रमगुणित तक पहचानें। / \(12!=12\times11\times10!\), so the given form is (12!). Recognize factorial expansion down to a smaller factorial.
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