Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 221-230 of 590 questions.
What is the simplified form of (\frac{(n+2)!-n!}{n!})?
B. \(n^2+3n+1\)
(\frac{(n+2)!}{n!}=(n+2)(n+1)), फिर (1) घटेगा। सरल रूप \(n^2+3n+1\) है। / (\frac{(n+2)!}{n!}=(n+2)(n+1)), then (1) is subtracted. The simplified form is \(n^2+3n+1\).
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What is the value of \(\frac{10!}{8!}+\frac{7!}{6!}+0!\)?
C. (98)
\(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\) और (0!=1)। कुल (98) है। / \(\frac{10!}{8!}=90\), \(\frac{7!}{6!}=7\), and (0!=1). The total is (98).
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What is the simplified form of \(\frac{n!}{(n-1)!}\times\frac{(n+1)!}{n!}\)?
C. (n(n+1))
पहला अनुपात (n) और दूसरा (n+1) है। इसलिए गुणनफल (n(n+1)) है। / The first ratio is (n) and the second is (n+1). Therefore the product is (n(n+1)).
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If (\frac{n!}{(n-3)!}=210), what is the value of (n)?
B. (7)
(\frac{n!}{(n-3)!}=n(n-1)(n-2))। \(7\times6\times5=210\), इसलिए (n=7) है। / (\frac{n!}{(n-3)!}=n(n-1)(n-2)). Since \(7\times6\times5=210\), (n=7).
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What is the value of \(\frac{9!+8!}{7!}\)?
B. (80)
अंश को (8!(9+1)) लिखा जा सकता है। \(\frac{10\cdot8!}{7!}=10\times8=80\) है। / The numerator can be written as (8!(9+1)). Thus \(\frac{10\cdot8!}{7!}=10\times8=80\).
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What is the value of \(\frac{6!}{3!,3!}+\frac{7!}{5!,2!}\)?
C. (41)
पहला पद (20) और दूसरा (21) है। दोनों का योग (41) होगा। / The first term is (20) and the second is (21). Their sum is (41).
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What is the simplified form of (\frac{\frac{(n+4)!}{n!}}{\frac{(n+2)!}{n!}})?
B. ((n+4)(n+3))
यह भाग (\frac{(n+4)!}{(n+2)!}) बन जाता है। इसलिए सरल रूप ((n+4)(n+3)) है। / This division becomes (\frac{(n+4)!}{(n+2)!}). Hence the simplified form is ((n+4)(n+3)).
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If \(a=\frac{7!-5!}{5!}\), what is the value of (a)?
B. (41)
\(\frac{7!}{5!}=42\) और \(\frac{5!}{5!}=1\)। इसलिए (a=42-1=41) है। / \(\frac{7!}{5!}=42\) and \(\frac{5!}{5!}=1\). Therefore (a=42-1=41).
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If (\frac{(n+1)!}{(n-2)!}=60), what is the value of (n)?
B. (4)
(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1))। \(5\times4\times3=60\), इसलिए (n=4) है। / (\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).
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What is the value of \(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\)?
C. (22)
ऊपर का पद (220) और नीचे का पद (10) है। भाग देने पर (22) मिलता है। / The numerator term is (220) and the denominator term is (10). Dividing gives (22).
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