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 561-570 of 590 questions.
If (\frac{n!}{(n-2)!}=132) then what is the value of (n)?
C. (12)
समीकरण (n(n-1)=132) बनता है। \(12\times11=132\) इसलिए (n=12) है। / The equation becomes (n(n-1)=132). Since \(12\times11=132\), (n=12).
Login to save your score, XP, coins and progress.
If (\frac{(n+4)!}{(n+2)!}=156) then what is the value of (n)?
B. (9)
((n+4)(n+3)=156) मिलता है। \(13\times12=156\) इसलिए (n=9) है। / We get ((n+4)(n+3)=156). Since \(13\times12=156\), (n=9).
Login to save your score, XP, coins and progress.
What is the least (n) for which (n!) is divisible by (72)?
B. (6)
\(72=2^3\times3^2\) है और (6!) में ये सभी गुणनखंड हैं। ऐसे प्रश्नों में अभाज्य गुणनखंड पहले लिखें। / \(72=2^3\times3^2\) and (6!) contains all these factors. In such questions write prime factors first.
Login to save your score, XP, coins and progress.
What is the least (n) for which (n!) is divisible by (125)?
B. (15)
\(125=5^3\) है और (15!) में (5,10,15) से तीन (5) मिलते हैं। इसलिए न्यूनतम (n=15) है। / \(125=5^3\) and (15!) gives three factors of (5) from (5,10,15). So the least (n=15).
Login to save your score, XP, coins and progress.
How many trailing zeros are there in (50!)?
C. (12)
शून्य की संख्या \(\left\lfloor\frac{50}{5}\right\rfloor+\left\lfloor\frac{50}{25}\right\rfloor=10+2=12\) है। (5) की घात गिनना सबसे तेज तरीका है। / The number of zeros is \(\left\lfloor\frac{50}{5}\right\rfloor+\left\lfloor\frac{50}{25}\right\rfloor=10+2=12\). Counting powers of (5) is the fastest method.
Login to save your score, XP, coins and progress.
What is the highest power of (5) in (100!)?
C. (24)
घात \( \left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24\) है। उच्च घात के लिए भागफल जोड़ें। / The exponent is \(\left\lfloor\frac{100}{5}\right\rfloor+\left\lfloor\frac{100}{25}\right\rfloor=20+4=24\). For highest power add the quotients.
Login to save your score, XP, coins and progress.
What is the highest power of (7) in (80!)?
B. (12)
घात \( \left\lfloor\frac{80}{7}\right\rfloor+\left\lfloor\frac{80}{49}\right\rfloor=11+1=12\) है। अभाज्य की घातों तक ही जोड़ें। / The exponent is \(\left\lfloor\frac{80}{7}\right\rfloor+\left\lfloor\frac{80}{49}\right\rfloor=11+1=12\). Add only up to powers of the prime.
Login to save your score, XP, coins and progress.
Which value is equal to \(\frac{25!}{23!}\)?
B. (600)
\(\frac{25!}{23!}=25\times24=600\) होता है। केवल बचे हुए दो पदों को गुणा करें। / \(\frac{25!}{23!}=25\times24=600\). Multiply only the two remaining terms.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{16!}{14!\times 8}\)?
B. (30)
\(\frac{16!}{14!\times8}=\frac{16\times15}{8}=30\) है। पहले (16) को (8) से काटें। / \(\frac{16!}{14!\times8}=\frac{16\times15}{8}=30\). First cancel (16) with (8).
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+3)!}{(n+1)!}-\frac{(n+2)!}{n!})?
A. (2(n+2))
पहला पद ((n+3)(n+2)) और दूसरा ((n+2)(n+1)) है। अंतर (2(n+2)) है। / The first term is ((n+3)(n+2)) and the second is ((n+2)(n+1)). The difference is (2(n+2)).
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.