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 441-450 of 590 questions.
What is the value of \( \frac{18!}{15!}-\frac{17!}{14!} \)?
B. (816)
पहला पद \(18\cdot17\cdot16=4896\) और दूसरा \(17\cdot16\cdot15=4080\) है। अंतर (816) है। / The first term is \(18\cdot17\cdot16=4896\) and the second is \(17\cdot16\cdot15=4080\). The difference is (816).
Login to save your score, XP, coins and progress.
What is the simplified value of \( \frac{15!}{11!\cdot4!} \)?
C. (1365)
\( \frac{15\cdot14\cdot13\cdot12}{4!}=1365 \) है। हर में (4!) का सही मान लगाएं। / \( \frac{15\cdot14\cdot13\cdot12}{4!}=1365 \). Use the correct value of (4!) in the denominator.
Login to save your score, XP, coins and progress.
If ( \frac{(n+4)!}{n!}=11880 ), what will be the value of (n)?
C. (8)
यह ((n+4)(n+3)(n+2)(n+1)=11880) है और \(12\cdot11\cdot10\cdot9=11880\)। इसलिए (n=8) है। / It is ((n+4)(n+3)(n+2)(n+1)=11880), and \(12\cdot11\cdot10\cdot9=11880\). So (n=8).
Login to save your score, XP, coins and progress.
If ( \frac{(n+2)!+(n+1)!}{(n+1)!}=14 ), what is the value of (n)?
C. (11)
सरल रूप (n+3) है। इसलिए (n+3=14) और (n=11)। / The simplified form is (n+3). Thus (n+3=14) and (n=11).
Login to save your score, XP, coins and progress.
What is the simplified form of ( \frac{(n+3)!-(n+2)!}{(n+1)!} )?
A. ((n+2)2)
((n+3)!-(n+2)!=(n+2)!((n+3)-1)) है। इससे ((n+2)2) मिलता है। / ((n+3)!-(n+2)!=(n+2)!((n+3)-1)). This gives ((n+2)2).
Login to save your score, XP, coins and progress.
If ( \frac{(n+3)!-(n+2)!}{(n+1)!}=121 ), what will be the value of (n)?
B. (9)
सरल रूप ((n+2)2) है। इसलिए (n+2=11) और (n=9)। / The simplified form is ((n+2)2). Therefore (n+2=11) and (n=9).
Login to save your score, XP, coins and progress.
If ( \frac{(n!)2}{(n-2)!(n+2)!}=\frac{10}{21} ), what is the value of (n)?
B. (5)
सरल रूप ( \frac{n(n-1)}{(n+1)(n+2)} ) है। (n=5) रखने पर \( \frac{20}{42}=\frac{10}{21} \) मिलता है। / The simplified form is ( \frac{n(n-1)}{(n+1)(n+2)} ). Putting (n=5) gives \( \frac{20}{42}=\frac{10}{21} \).
Login to save your score, XP, coins and progress.
What is the highest power of (2) that divides (20!)?
D. (18)
घात \( \left\lfloor\frac{20}{2}\right\rfloor+\left\lfloor\frac{20}{4}\right\rfloor+\left\lfloor\frac{20}{8}\right\rfloor+\left\lfloor\frac{20}{16}\right\rfloor=18 \) है। अभाज्य घात के लिए सभी भागफल जोड़ें। / The exponent is \( \left\lfloor\frac{20}{2}\right\rfloor+\left\lfloor\frac{20}{4}\right\rfloor+\left\lfloor\frac{20}{8}\right\rfloor+\left\lfloor\frac{20}{16}\right\rfloor=18 \). Add all quotients for a prime exponent.
Login to save your score, XP, coins and progress.
How many zeros will be at the end of (45!)?
A. (10)
शून्यों की संख्या \( \left\lfloor\frac{45}{5}\right\rfloor+\left\lfloor\frac{45}{25}\right\rfloor=10 \) है। (25) के योगदान को न भूलें। / The number of zeros is \( \left\lfloor\frac{45}{5}\right\rfloor+\left\lfloor\frac{45}{25}\right\rfloor=10 \). Do not forget the contribution of (25).
Login to save your score, XP, coins and progress.
What is the smallest positive (n) for which (n!) is divisible by (1440)?
C. (8)
\(1440=2^5\cdot3^2\cdot5\) है और यह जरूरत पहली बार (8!) में पूरी होती है। विभाज्यता में अभाज्य गुणनखंड जांचें। / \(1440=2^5\cdot3^2\cdot5\), and this requirement is first satisfied by (8!). For divisibility, check prime factors.
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.