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 531-540 of 590 questions.
What is the simplified form of ( \frac{(n+6)!-(n+5)!}{(n+4)!} )?
A. ( (n+5)2 )
((n+6)!-(n+5)!=(n+5)!((n+6)-1)) है। इसलिए उत्तर ((n+5)2) है। / ((n+6)!-(n+5)!=(n+5)!((n+6)-1)). Therefore the answer is ((n+5)2).
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If ( \frac{(n+6)!-(n+5)!}{(n+4)!}=196 ), what is the value of (n)?
B. (9)
सरल रूप ((n+5)2) है। (n+5=14), इसलिए (n=9)। / The simplified form is ((n+5)2). Since (n+5=14), (n=9).
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What is the simplified form of ( \frac{(n+7)!}{(n+4)!}-\frac{(n+6)!}{(n+3)!} )?
B. (4(n+6)(n+5))
सामान्य ((n+6)(n+5)) निकालें। अंतर ((n+7)-(n+4)=3) नहीं, क्योंकि दूसरा पद ((n+6)(n+5)(n+4)) है और अंतर (3(n+6)(n+5)) है। / Take common ((n+6)(n+5)). The difference is ((n+7)-(n+4)=3), so the correct form is (3(n+6)(n+5)).
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If ( \frac{(n+7)!}{(n+4)!}-\frac{(n+6)!}{(n+3)!}=720 ), what is the value of (n)?
A. (9)
सरल रूप (3(n+6)(n+5)) है। \(3\cdot15\cdot14=630\) नहीं, इसलिए सही विकल्प नहीं है। / The simplified form is (3(n+6)(n+5)). Since \(3\cdot15\cdot14=630\), no option is correct.
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If ( \frac{(n!)2}{(n-1)!(n+1)!}=\frac{13}{14} ), what is the value of (n)?
B. (13)
सरल रूप \( \frac{n}{n+1} \) है। \( \frac{n}{n+1}=\frac{13}{14} \), इसलिए (n=13)। / The simplified form is \( \frac{n}{n+1} \). Since \( \frac{n}{n+1}=\frac{13}{14} \), (n=13).
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What is the simplified value of \( \frac{19!}{15!\cdot4!}\div\frac{18!}{14!\cdot4!} \)?
B. \( \frac{19}{15} \)
दोनों पदों का अनुपात सीधे \( \frac{19}{15} \) बनता है। बड़े मान निकालने के बजाय फैक्टोरियल काटें। / The ratio of the two terms directly becomes \( \frac{19}{15} \). Cancel factorials instead of finding large values.
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What is the simplified form of ( \frac{(n+3)!}{n!}+\frac{(n+1)!}{(n-2)!} )?
A. \(2n^3+6n^2+4n+6\)
पहला पद ((n+3)(n+2)(n+1)) और दूसरा ((n+1)n(n-1)) है। जोड़ने पर \(2n^3+6n^2+4n+6\) मिलता है। / The first term is ((n+3)(n+2)(n+1)) and the second is ((n+1)n(n-1)). Adding gives \(2n^3+6n^2+4n+6\).
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If ( \frac{(n+3)!}{n!}+\frac{(n+1)!}{(n-2)!}=546 ), what is the value of (n)?
A. (6)
(n=6) रखने पर \(9\cdot8\cdot7+7\cdot6\cdot5=504+210=714\) नहीं मिलता। इसलिए यह समीकरण विकल्पों से मेल नहीं खाता। / Putting (n=6) gives \(9\cdot8\cdot7+7\cdot6\cdot5=504+210=714\). Therefore the equation does not match the options.
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What is the value of \( \frac{13!}{6!\cdot7!}-\frac{12!}{6!\cdot6!} \)?
A. (792)
पहला पद (1716) और दूसरा (924) है। अंतर (792) है। / The first term is (1716) and the second is (924). The difference is (792).
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What is the simplified form of ( \frac{(n+4)!}{(n+1)!}+\frac{(n+3)!}{n!} )?
C. ( (n+3)(n+2)(2n+5) )
दोनों पदों में ( (n+3)(n+2) ) सामान्य है। इसलिए सरल रूप ( (n+3)(n+2)(2n+5) ) मिलता है। / The common factor in both terms is ( (n+3)(n+2) ). Therefore the simplified form is ( (n+3)(n+2)(2n+5) ).
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