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 511-520 of 590 questions.
What is the simplified form of ( \frac{(n+6)!}{(n+4)!}+\frac{(n+5)!}{(n+3)!} )?
A. (2(n+5)2)
दोनों पद ((n+6)(n+5)) और ((n+5)(n+4)) हैं। समान ((n+5)) निकालने पर (2(n+5)2) मिलता है। / The two terms are ((n+6)(n+5)) and ((n+5)(n+4)). Taking common ((n+5)) gives (2(n+5)2).
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If ( \frac{(n+6)!}{(n+4)!}+\frac{(n+5)!}{(n+3)!}=338 ), what is the value of (n)?
A. (8)
सरल रूप (2(n+5)2) है। (2(n+5)2=338) से (n+5=13), इसलिए (n=8)। / The simplified form is (2(n+5)2). From (2(n+5)2=338), (n+5=13), so (n=8).
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What is the value of \( \frac{13!}{7!\cdot6!}+\frac{13!}{8!\cdot5!} \)?
B. (3432)
दोनों पद (1716) और (1287) नहीं, सही योग (3003) है। / The two terms are (1716) and (1287), so the correct sum is (3003).
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What is the value of \( \frac{12!}{6!\cdot6!}\times\frac{3}{11} \)?
C. (252)
पहला भाग (924) है। \(924\cdot\frac{3}{11}=252\) मिलता है। / The first part is (924). Then \(924\cdot\frac{3}{11}=252\).
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What is the value of \( \frac{14!}{11!}-3\cdot\frac{13!}{11!} \)?
B. (1716)
पहला पद \(14\cdot13\cdot12=2184\) और दूसरा \(3\cdot13\cdot12=468\) है। अंतर (1716) है। / The first term is \(14\cdot13\cdot12=2184\) and the second is \(3\cdot13\cdot12=468\). The difference is (1716).
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What is the value of \( \frac{10!+3\cdot9!}{8!} \)?
B. (117)
\( \frac{10!}{8!}=90 \) और \( \frac{3\cdot9!}{8!}=27 \) है। कुल (117) है। / \( \frac{10!}{8!}=90 \) and \( \frac{3\cdot9!}{8!}=27 \). The total is (117).
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What is the simplified form of ( \frac{(n+4)!}{(n-1)!(n+3)(n+2)} )?
B. ( (n+1)(n+4) )
ऊपर ((n+4)(n+3)(n+2)(n+1)n(n-1)!) है। काटने पर (n(n+1)(n+4)) बचेगा। / The numerator is ((n+4)(n+3)(n+2)(n+1)n(n-1)!). After cancellation (n(n+1)(n+4)) remains.
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If ( \frac{(n+4)!}{(n-1)!(n+3)(n+2)}=990 ), what is the value of (n)?
B. (9)
सरल रूप (n(n+1)(n+4)) है। \(9\cdot10\cdot13=1170\) नहीं, इसलिए सही विकल्पों में मान नहीं है। / The simplified form is (n(n+1)(n+4)). Since \(9\cdot10\cdot13=1170\), no given option satisfies the equation.
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If ( \frac{(n+4)!}{(n-1)!(n+3)(n+2)}=840 ), what is the value of (n)?
B. (8)
सरल रूप (n(n+1)(n+4)) है। \(8\cdot9\cdot12=864\) नहीं, इसलिए समीकरण त्रुटिपूर्ण है। / The simplified form is (n(n+1)(n+4)). Since \(8\cdot9\cdot12=864\), the equation is invalid.
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What is the highest power of (3) that divides (35!)?
B. (15)
घात \( \left\lfloor\frac{35}{3}\right\rfloor+\left\lfloor\frac{35}{9}\right\rfloor+\left\lfloor\frac{35}{27}\right\rfloor=15 \) है। उच्च घातों का योगदान जोड़ना न भूलें। / The exponent is \( \left\lfloor\frac{35}{3}\right\rfloor+\left\lfloor\frac{35}{9}\right\rfloor+\left\lfloor\frac{35}{27}\right\rfloor=15 \). Do not forget the contribution of higher powers.
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