Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 21-30 of 590 questions.
What is the simplified form of (\frac{(n+1)!}{n!})?
B. (n+1)
((n+1)!=(n+1)n!), इसलिए भाग देने पर (n+1) बचता है। फैक्टोरियल पहचान को याद रखें। / ((n+1)!=(n+1)n!), so division leaves (n+1). Remember the factorial identity.
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What is the value of \(\frac{7!}{6!,1!}\)?
B. (7)
\(\frac{7!}{6!,1!}=\frac{7\times6!}{6!\times1}=7\)। (1!) का मान (1) होता है। / \(\frac{7!}{6!,1!}=\frac{7\times6!}{6!\times1}=7\). The value of (1!) is (1).
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B. (30)
(3!=6) और (4!=24), इसलिए योग (30) है। फैक्टोरियल को जोड़ने से पहले उसका मान निकालें। / (3!=6) and (4!=24), so the sum is (30). Find factorial values before adding them.
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What will be the value of (6!-5!)?
A. (600)
(6!=720) और (5!=120), इसलिए अंतर (600) है। बड़े फैक्टोरियल का मान ध्यान से लिखें। / (6!=720) and (5!=120), so the difference is (600). Write the value of the larger factorial carefully.
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What is the value of \(2!\times4!\)?
C. (48)
(2!=2) और (4!=24), इसलिए गुणनफल (48) है। पहले फैक्टोरियल मान निकालकर फिर गुणा करें। / (2!=2) and (4!=24), so the product is (48). First find factorial values and then multiply.
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What is the value of \(\frac{8!}{5!}\)?
A. (336)
\(\frac{8!}{5!}=8\times7\times6=336\)। छोटे फैक्टोरियल तक विस्तार करके काटें। / \(\frac{8!}{5!}=8\times7\times6=336\). Expand down to the smaller factorial and cancel.
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If (n=3), what is the value of ((n+2)!)?
B. (120)
(n+2=5), इसलिए ((n+2)!=5!=120)। पहले कोष्ठक का मान निकालें। / (n+2=5), so ((n+2)!=5!=120). First find the value inside the brackets.
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What is the simplified form of (\frac{(n+2)!}{n!})?
C. ((n+2)(n+1))
((n+2)!=(n+2)(n+1)n!), इसलिए (n!) कट जाएगा। शेष ((n+2)(n+1)) है। / ((n+2)!=(n+2)(n+1)n!), so (n!) cancels. The remaining part is ((n+2)(n+1)).
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Which is greater between (5!) and (4!)?
C. (5!)
(5!=120) और (4!=24), इसलिए (5!) बड़ा है। बड़े धनात्मक पूर्णांक का फैक्टोरियल सामान्यतः बड़ा होता है। / (5!=120) and (4!=24), so (5!) is greater. The factorial of a larger positive integer is generally larger.
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What is the value of \(\frac{4!+3!}{3!}\)?
B. (5)
\(\frac{4!+3!}{3!}=\frac{24+6}{6}=5\)। जोड़ वाले अंश को पहले सरल करें। / \(\frac{4!+3!}{3!}=\frac{24+6}{6}=5\). Simplify the numerator with addition first.
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