Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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If \(x=\frac{8!}{6!}\) and \(y=\frac{5!}{3!}\), what is the value of (x+y)?
C. (76)
\(x=8\times7=56\) और \(y=5\times4=20\)। इसलिए (x+y=76) है। / \(x=8\times7=56\) and \(y=5\times4=20\). Therefore (x+y=76).
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What is the simplified form of (\frac{(n+5)!}{(n+3)!})?
A. ((n+5)(n+4))
((n+5)!=(n+5)(n+4)(n+3)!)। इसलिए सरल रूप ((n+5)(n+4)) है। / ((n+5)!=(n+5)(n+4)(n+3)!). Therefore the simplified form is ((n+5)(n+4)).
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What is the value of \(\frac{11!-10!}{9!}\)?
C. (100)
अंश (10!(11-1)=10\cdot10!) है। \(\frac{10\cdot10!}{9!}=10\times10=100\) है। / The numerator is (10!(11-1)=10\cdot10!). Thus \(\frac{10\cdot10!}{9!}=10\times10=100\).
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What is the value of \(\frac{9!}{7!}\div\frac{6!}{5!}\)?
B. (12)
\(\frac{9!}{7!}=72\) और \(\frac{6!}{5!}=6\)। इसलिए भागफल (12) है। / \(\frac{9!}{7!}=72\) and \(\frac{6!}{5!}=6\). Therefore the quotient is (12).
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If (\frac{(n+1)!}{(n-1)!}=72), what is the value of (n)?
C. (8)
अनुपात (n(n+1)) के बराबर है। \(8\times9=72\), इसलिए (n=8) है। / The ratio equals (n(n+1)). Since \(8\times9=72\), (n=8).
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What is the value of \(\frac{5!,3!}{2!,4!}\)?
C. (15)
\(\frac{5!}{4!}=5\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(5\times3=15\) है। / \(\frac{5!}{4!}=5\) and \(\frac{3!}{2!}=3\). Hence the value is \(5\times3=15\).
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What is the value of \(\frac{8!}{5!}+\frac{6!}{4!}-4!\)?
D. (342)
\(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\) और (4!=24)। इसलिए (336+30-24=342) है। / \(\frac{8!}{5!}=336\), \(\frac{6!}{4!}=30\), and (4!=24). Thus (336+30-24=342).
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How many consecutive factors remain in (\frac{(n+5)!}{(n+2)!})?
B. (3)
(\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3))। इसलिए तीन क्रमागत गुणक बचते हैं। / (\frac{(n+5)!}{(n+2)!}=(n+5)(n+4)(n+3)). Therefore three consecutive factors remain.
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If (\frac{(n+3)!}{(n+1)!}=90), what is the value of (n)?
B. (7)
(\frac{(n+3)!}{(n+1)!}=(n+3)(n+2))। \(10\times9=90\), इसलिए (n=7) है। / (\frac{(n+3)!}{(n+1)!}=(n+3)(n+2)). Since \(10\times9=90\), (n=7).
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What is the value of \(\frac{13!}{11!,2!}-\frac{6!}{4!,2!}\)?
C. (63)
पहला पद (78) और दूसरा पद (15) है। अंतर (78-15=63) है। / The first term is (78) and the second term is (15). The difference is (78-15=63).
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