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 481-490 of 590 questions.
If ( \frac{(n+5)!}{(n+2)!}-\frac{(n+4)!}{(n+1)!}=396 ), what is the value of (n)?
B. (8)
सरल रूप (3(n+4)(n+3)) है। \(3\cdot12\cdot11=396\), इसलिए (n=8)। / The simplified form is (3(n+4)(n+3)). Since \(3\cdot12\cdot11=396\), (n=8).
Login to save your score, XP, coins and progress.
If ( \frac{(n!)2}{(n-1)!(n+1)!}=\frac{11}{12} ), what is the value of (n)?
B. (11)
सरल रूप \( \frac{n}{n+1} \) है। \( \frac{n}{n+1}=\frac{11}{12} \) से (n=11) मिलता है। / The simplified form is \( \frac{n}{n+1} \). From \( \frac{n}{n+1}=\frac{11}{12} \), we get (n=11).
Login to save your score, XP, coins and progress.
What is the simplified value of \( \frac{18!}{14!\cdot4!}\div\frac{17!}{13!\cdot4!} \)?
A. \(\frac{153}{119}\)
दोनों पद (3060) और (2380) हैं। उनका अनुपात \( \frac{3060}{2380}=\frac{153}{119} \) है। / The two terms are (3060) and (2380). Their ratio is \( \frac{3060}{2380}=\frac{153}{119} \).
Login to save your score, XP, coins and progress.
What is the simplified form of ( \frac{(n+2)!}{n!}+\frac{n!}{(n-2)!} )?
B. \(2n^2+2n+2\)
पहला पद ((n+2)(n+1)) और दूसरा (n(n-1)) है। जोड़ने पर \(2n^2+2n+2\) मिलता है। / The first term is ((n+2)(n+1)) and the second is (n(n-1)). Adding gives \(2n^2+2n+2\).
Login to save your score, XP, coins and progress.
If ( \frac{(n+2)!}{n!}+\frac{n!}{(n-2)!}=114 ), what is the value of (n)?
B. (7)
सरल रूप \(2n^2+2n+2\) है। (n=7) रखने पर (98+14+2=114) मिलता है। / The simplified form is \(2n^2+2n+2\). Putting (n=7) gives (98+14+2=114).
Login to save your score, XP, coins and progress.
What is the value of \( \frac{12!}{6!\cdot6!}-\frac{11!}{5!\cdot6!} \)?
C. (462)
पहला पद (924) और दूसरा (462) है। अंतर (462) है। / The first term is (924) and the second is (462). The difference is (462).
Login to save your score, XP, coins and progress.
What is the simplified form of ( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!} )?
A. (4(n+5)(n+4)(n+3))
सामान्य ((n+5)(n+4)(n+3)) निकालने पर अंतर ((n+6)-(n+2)=4) है। पहले समान गुणकों को पहचानें। / Taking common ((n+5)(n+4)(n+3)), the difference is ((n+6)-(n+2)=4). Identify common factors first.
Login to save your score, XP, coins and progress.
If ( \frac{(n+6)!}{(n+2)!}-\frac{(n+5)!}{(n+1)!}=2880 ), what is the value of (n)?
B. (5)
सरल रूप (4(n+5)(n+4)(n+3)) है। \(4\cdot10\cdot9\cdot8=2880\), इसलिए (n=5)। / The simplified form is (4(n+5)(n+4)(n+3)). Since \(4\cdot10\cdot9\cdot8=2880\), (n=5).
Login to save your score, XP, coins and progress.
What is the smallest positive (n) for which (n!) is divisible by \(2^8\cdot3^2\cdot5^2\)?
C. (10)
(10!) में (2) की घात (8) और (5) की घात (2) मिलती है। (9!) में \(5^2\) नहीं आता, इसलिए (10) न्यूनतम है। / (10!) contains exponent (8) of (2) and exponent (2) of (5). (9!) does not contain \(5^2\), so (10) is minimum.
Login to save your score, XP, coins and progress.
What is the highest power of (7) that divides (100!)?
C. (16)
घात \( \left\lfloor\frac{100}{7}\right\rfloor+\left\lfloor\frac{100}{49}\right\rfloor=16 \) है। उच्च घातों जैसे (49) का योगदान जरूर जोड़ें। / The exponent is \( \left\lfloor\frac{100}{7}\right\rfloor+\left\lfloor\frac{100}{49}\right\rfloor=16 \). Always add the contribution of higher powers such as (49).
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.