Practice focused topic-wise MCQs with answers and explanations for quick revision and exam preparation.
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Showing 431-440 of 590 questions.
By how much is \( \frac{10!}{8!} \) greater than \( \frac{9!}{7!} \)?
D. (18)
पहला मान (90) और दूसरा (72) है। अंतर (18) है। / The first value is (90) and the second is (72). The difference is (18).
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Which factor will not appear in the expansion of ( \frac{(n+4)!}{n!} )?
D. (n)
विस्तार ((n+4)(n+3)(n+2)(n+1)) है, इसलिए (n) शामिल नहीं है। हर वाले (n!) तक कटौती हो जाती है। / The expansion is ((n+4)(n+3)(n+2)(n+1)), so (n) is not included. Cancellation stops at the denominator (n!).
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When (n=4), what is the value of ( \frac{(n+4)!}{n!} )?
A. (1680)
(n=4) रखने पर \( \frac{8!}{4!}=8\cdot7\cdot6\cdot5=1680 \) मिलता है। मान रखने से पहले सामान्य रूप समझें। / Putting (n=4) gives \( \frac{8!}{4!}=8\cdot7\cdot6\cdot5=1680 \). Understand the general form before substituting.
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What is the value of \( \frac{14!}{10!\cdot4!}-\frac{13!}{10!\cdot3!} \)?
B. (715)
पहला पद (1001) और दूसरा (286) है, इसलिए अंतर (715) है। ऐसे प्रश्नों में दोनों पद अलग-अलग निकालकर घटाएं। / The first term is (1001) and the second is (286), so the difference is (715). In such questions, calculate both terms separately and subtract.
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What is the simplified form of ( \frac{\frac{(n+4)!}{n!}}{\frac{(n+3)!}{(n-1)!}} )?
D. \( \frac{n+4}{n} \)
ऊपर और नीचे के समान गुणक कटने पर \( \frac{n+4}{n} \) बचता है। बड़े अनुपात को पहले गुणनफल में बदलें। / After canceling the common factors in numerator and denominator, \( \frac{n+4}{n} \) remains. First convert large ratios into products.
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What is the highest power of (2) that divides (14!)?
C. (11)
घात \( \left\lfloor\frac{14}{2}\right\rfloor+\left\lfloor\frac{14}{4}\right\rfloor+\left\lfloor\frac{14}{8}\right\rfloor=11 \) है। अभाज्य घात निकालते समय सभी भागफल जोड़ें। / The exponent is \( \left\lfloor\frac{14}{2}\right\rfloor+\left\lfloor\frac{14}{4}\right\rfloor+\left\lfloor\frac{14}{8}\right\rfloor=11 \). Add all quotients while finding a prime exponent.
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What is the smallest positive (n) for which (n!) is divisible by (1008)?
B. (7)
\(1008=2^4\cdot3^2\cdot7\) है और (7!) में ये सभी गुणक मिल जाते हैं। विभाज्यता में अभाज्य गुणनखंडों की जरूरत पूरी करें। / \(1008=2^4\cdot3^2\cdot7\), and (7!) contains all these factors. For divisibility, satisfy all prime factor requirements.
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What is the simplified form of ( \frac{(n+4)!+(n+3)!}{(n+2)!} )?
A. ( (n+3)(n+5) )
((n+3)!) सामान्य लेने पर ऊपर ((n+3)!(n+5)) बनता है। भाग देने पर ((n+3)(n+5)) मिलता है। / Taking ((n+3)!) common gives ((n+3)!(n+5)) in the numerator. Dividing gives ((n+3)(n+5)).
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If ( \frac{(n+4)!+(n+3)!}{(n+2)!}=120 ), what is the value of (n)?
B. (7)
सरल रूप ((n+3)(n+5)) है, इसलिए ((n+3)(n+5)=120)। \(10\cdot12=120\), इसलिए (n=7)। / The simplified form is ((n+3)(n+5)), so ((n+3)(n+5)=120). Since \(10\cdot12=120\), (n=7).
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What is the value of \( \frac{12!}{9!}-2\cdot\frac{11!}{8!} \)?
D. (660)
पहला पद (1320) और दूसरा \(2\cdot330=660\) है, इसलिए अंतर (660) है। गुणांक वाले पद में पहले गुणा पूरा करें। / The first term is (1320) and the second is \(2\cdot330=660\), so the difference is (660). Complete the multiplication in the coefficient term first.
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