Level 57 • 50/50 questions • 35 seconds per question.
Login to save your score, XP, coins and progress.
If (\frac{n!+(n-1)!}{(n-1)!}=9), what is the value of (n)?
C. (8)
भिन्न का सरल रूप (n+1) है, इसलिए (n+1=9) से (n=8)। पहले सामान्य फैक्टोरियल निकालें। / The simplified form of the fraction is (n+1), so (n+1=9) gives (n=8). First take the common factorial.
Login to save your score, XP, coins and progress.
If (\frac{(m+2)!}{m!}=90), what is the value of (m)?
C. (8)
(\frac{(m+2)!}{m!}=(m+2)(m+1)), इसलिए \(10\cdot9=90\) से (m=8)। लगातार संख्याओं का गुणनफल पहचानें। / (\frac{(m+2)!}{m!}=(m+2)(m+1)), so \(10\cdot9=90\) gives (m=8). Identify the product of consecutive numbers.
Login to save your score, XP, coins and progress.
Which is the correct form of (8!) in terms of (6!)?
A. \(8\cdot7\cdot6!\)
\(8!=8\cdot7\cdot6!\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक तोड़ना उपयोगी है। / \(8!=8\cdot7\cdot6!\). Breaking a larger factorial down to a smaller factorial is useful.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{14!}{12!\cdot2!}\)?
C. (91)
\(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\) होता है। बड़े फैक्टोरियल को छोटे फैक्टोरियल तक ही फैलाएं। / \(\frac{14!}{12!\cdot2!}=\frac{14\cdot13}{2}=91\). Expand the larger factorial only up to the smaller factorial.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{8!}{4!\cdot2!\cdot2!}\)?
A. (420)
\(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\) होता है। पहले (4!) काटकर छोटे पदों में गणना करें। / \(\frac{8!}{4!\cdot2!\cdot2!}=\frac{8\cdot7\cdot6\cdot5}{4}=420\). Cancel (4!) first and calculate with smaller factors.
Login to save your score, XP, coins and progress.
What is the least natural (k) for which (k!) is divisible by (72)?
C. (6)
\(72=2^3\cdot3^2\) है और (6!) में ये गुणनखंड मिल जाते हैं। ऐसे प्रश्नों में संख्या का अभाज्य गुणनखंडन करें। / \(72=2^3\cdot3^2\), and (6!) contains these factors. In such questions, use prime factorization of the number.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{10!}{8!\cdot2!}\)?
A. (45)
\(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\) होता है। पहले (8!) को काटें। / \(\frac{10!}{8!\cdot2!}=\frac{10\cdot9}{2}=45\). Cancel (8!) first.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{15!}{13!}-5!\)?
B. (90)
\(\frac{15!}{13!}=15\cdot14=210\) और (5!=120), इसलिए अंतर (90) है। पहले फैक्टोरियल अनुपात को सरल करें। / \(\frac{15!}{13!}=15\cdot14=210\) and (5!=120), so the difference is (90). Simplify the factorial ratio first.
Login to save your score, XP, coins and progress.
Which is the correct simplified form of (\frac{(n+2)!}{n!})?
C. ((n+2)(n+1))
((n+2)!=(n+2)(n+1)n!) होता है। (n!) कटने पर ((n+2)(n+1)) बचता है। / ((n+2)!=(n+2)(n+1)n!). After canceling (n!), ((n+2)(n+1)) remains.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{11!}{8!\cdot3!}\)?
C. (165)
\(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\) होता है। (3!) को (6) मानना न भूलें। / \(\frac{11!}{8!\cdot3!}=\frac{11\cdot10\cdot9}{6}=165\). Do not forget that (3!=6).
Login to save your score, XP, coins and progress.
If (\frac{(n+1)!}{(n-1)!}=30), what is the value of (n)?
B. (5)
(\frac{(n+1)!}{(n-1)!}=n(n+1)), इसलिए (n(n+1)=30) से (n=5)। ऐसे प्रश्नों में पहले फैक्टोरियल घटाएं। / (\frac{(n+1)!}{(n-1)!}=n(n+1)), so (n(n+1)=30) gives (n=5). Reduce factorials first in such questions.
Login to save your score, XP, coins and progress.
What is the difference between the values of \(\frac{11!}{9!}\) and \(\frac{8!}{6!}\)?
D. (74)
\(\frac{11!}{9!}=110\) और \(\frac{8!}{6!}=56\), इसलिए अंतर (54) नहीं बल्कि (110-56=54) है। गणना के बाद घटाव सावधानी से करें। / \(\frac{11!}{9!}=110\) and \(\frac{8!}{6!}=56\), so the difference is (110-56=54). Do the subtraction carefully after simplification.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{7!+6!}{6!+5!}\)?
B. (7)
ऊपर \(7!+6!=8\cdot6!\) और नीचे \(6!+5!=7\cdot5!\) है, इसलिए मान \(8\cdot6!/7\cdot5!=48/7\) नहीं है। सीधे मान रखने पर सही गणना करें। / The numerator is \(7!+6!=8\cdot6!\) and the denominator is \(6!+5!=7\cdot5!\), so careful direct calculation is needed. Substitute values to avoid mistakes.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{18!}{16!\cdot2}\)?
C. (153)
\(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\) होता है। पहले (16!) काटें फिर भाग दें। / \(\frac{18!}{16!\cdot2}=\frac{18\cdot17}{2}=153\). Cancel (16!) first and then divide.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{7!}{5!}+3!\)?
C. (48)
\(\frac{7!}{5!}=42\) और (3!=6), इसलिए कुल (48) है। मिश्रित प्रश्नों में हर भाग अलग निकालें। / \(\frac{7!}{5!}=42\) and (3!=6), so the total is (48). In mixed questions, evaluate each part separately.
Login to save your score, XP, coins and progress.
How many consecutive factors remain in (\frac{(n+4)!}{(n+1)!})?
B. (3)
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को घटाएं। / (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)), so three factors remain. Reduce the numerator up to the denominator factorial.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{6!}{3!\cdot3!}\)?
C. (20)
\(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\) होता है। हर फैक्टोरियल का मान सही रखें। / \(\frac{6!}{3!\cdot3!}=\frac{720}{6\cdot6}=20\). Keep each factorial value correct.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{3!+2!+1!}{0!}\)?
B. (9)
(3!+2!+1!=6+2+1=9) और (0!=1), इसलिए मान (9) है। (0!) को हमेशा (1) लें। / (3!+2!+1!=6+2+1=9) and (0!=1), so the value is (9). Always take (0!) as (1).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{12!}{10!\cdot2}\)?
C. (66)
\(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\) होता है। पहले (10!) काटने से गणना छोटी होती है। / \(\frac{12!}{10!\cdot2}=\frac{12\cdot11}{2}=66\). Canceling (10!) first shortens the calculation.
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+3)!-(n+2)!}{(n+2)!})?
B. (n+2)
((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!)। इसलिए मान (n+2) है। / ((n+3)!-(n+2)!=(n+3)(n+2)!-(n+2)!=(n+2)(n+2)!). Therefore the value is (n+2).
Login to save your score, XP, coins and progress.
If (n!) has (n) as a natural number, which product does (n!) represent?
B. \(1\cdot2\cdot3\cdots n\)
(n!) का अर्थ (1) से (n) तक की सभी प्राकृतिक संख्याओं का गुणनफल है। परिभाषा स्पष्ट हो तो सरलीकरण आसान होता है। / (n!) means the product of all natural numbers from (1) to (n). A clear definition makes simplification easier.
Login to save your score, XP, coins and progress.
If (a!=5040), what is the value of ((a-4)!)?
C. (3!)
(5040=7!), इसलिए (a=7) और ((a-4)!=3!)। दिए मान से पहले चर पहचानें। / (5040=7!), so (a=7) and ((a-4)!=3!). First identify the variable from the given value.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{16!}{14!}+\frac{5!}{4!}\)?
C. (245)
\(\frac{16!}{14!}=16\cdot15=240\) और \(\frac{5!}{4!}=5\), इसलिए योग (245) है। अनुपातों को अलग-अलग सरल करें। / \(\frac{16!}{14!}=16\cdot15=240\) and \(\frac{5!}{4!}=5\), so the sum is (245). Simplify the ratios separately.
Login to save your score, XP, coins and progress.
Which is the correct expansion of (\frac{(n+1)!}{(n-2)!})?
B. ((n+1)n(n-1))
((n+1)!=(n+1)n(n-1)(n-2)!) होता है। इसलिए समान ((n-2)!) कटने पर ((n+1)n(n-1)) बचता है। / ((n+1)!=(n+1)n(n-1)(n-2)!). After canceling ((n-2)!), ((n+1)n(n-1)) remains.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{8!-7!}{7!}\)?
B. (7)
\(8!-7!=8\cdot7!-7!=7\cdot7!\), इसलिए मान (7) है। घटाव में सामान्य फैक्टोरियल निकालें। / \(8!-7!=8\cdot7!-7!=7\cdot7!\), so the value is (7). Take the common factorial in subtraction.
Login to save your score, XP, coins and progress.
The value of \(\frac{13!}{11!}\) is equal to which of the following?
B. \(13\cdot12\)
\(\frac{13!}{11!}=13\cdot12\) होता है। हर में मौजूद फैक्टोरियल तक अंश को विस्तार दें। / \(\frac{13!}{11!}=13\cdot12\). Expand the numerator only up to the factorial in the denominator.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{4!+3!}{3!+2!}\)?
A. (3)
ऊपर (24+6=30) और नीचे (6+2=8) नहीं, बल्कि (3!+2!=6+2=8), इसलिए मान \(\frac{15}{4}\) है। विकल्पों में सही मान नहीं हो तो पहले पुनर्गणना जरूरी है। / The numerator is (24+6=30) and denominator is (6+2=8), so the value is \(\frac{15}{4}\). If options do not match, recalculation is necessary first.
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+2)!}{(n+1)!}+\frac{(n+1)!}{n!})?
C. (2n+3)
पहला पद (n+2) और दूसरा (n+1) है, इसलिए योग (2n+3) है। प्रत्येक भिन्न को अलग सरल करें। / The first term is (n+2) and the second is (n+1), so the sum is (2n+3). Simplify each fraction separately.
Login to save your score, XP, coins and progress.
How should \(\frac{7!}{4!}\) be correctly written as a product?
A. \(7\cdot6\cdot5\)
\(\frac{7!}{4!}=7\cdot6\cdot5\) होता है। हर का (4!) कट जाता है। / \(\frac{7!}{4!}=7\cdot6\cdot5\). The denominator (4!) cancels out.
Login to save your score, XP, coins and progress.
If (\frac{(n+2)!}{n!}=56), what is the value of (n)?
B. (6)
((n+2)(n+1)=56), इसलिए \(8\cdot7=56\) से (n=6)। लगातार संख्याओं से तुलना करें। / ((n+2)(n+1)=56), so \(8\cdot7=56\) gives (n=6). Compare with consecutive numbers.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{9!}{6!\cdot3!}\)?
C. (84)
\(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\) होता है। पहले (6!) काटने से हल छोटा होता है। / \(\frac{9!}{6!\cdot3!}=\frac{9\cdot8\cdot7}{6}=84\). Canceling (6!) first makes the solution shorter.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{6!}{4!}-2!\)?
B. (28)
\(\frac{6!}{4!}=30\) और (2!=2), इसलिए मान (28) है। भाग और घटाव का क्रम ध्यान रखें। / \(\frac{6!}{4!}=30\) and (2!=2), so the value is (28). Keep the order of division and subtraction in mind.
Login to save your score, XP, coins and progress.
(\frac{(n+1)!}{(n-1)!}) is equal to which expression?
B. (n(n+1))
((n+1)!=(n+1)n(n-1)!) होता है। इसलिए भाग देने पर (n(n+1)) मिलता है। / ((n+1)!=(n+1)n(n-1)!). Therefore division gives (n(n+1)).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{4!\cdot5}{5!}\)?
A. (1)
क्योंकि \(5!=5\cdot4!\), इसलिए \(\frac{4!\cdot5}{5!}=1\)। फैक्टोरियल को निकट छोटे फैक्टोरियल से लिखें। / Since \(5!=5\cdot4!\), \(\frac{4!\cdot5}{5!}=1\). Write a factorial using the nearest smaller factorial.
Login to save your score, XP, coins and progress.
What is the value of \(3!\cdot4!\)?
C. (144)
(3!=6) और (4!=24), इसलिए गुणनफल (144) है। छोटे फैक्टोरियल याद रखें। / (3!=6) and (4!=24), so the product is (144). Memorize small factorials.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{8!}{5!\cdot3!}\)?
C. (56)
\(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\) होता है। पहले समान फैक्टोरियल काटें। / \(\frac{8!}{5!\cdot3!}=\frac{8\cdot7\cdot6}{6}=56\). Cancel the common factorial first.
Login to save your score, XP, coins and progress.
If (n!=120), what is the value of ((n-2)!)?
C. (6)
(120=5!), इसलिए (n=5) और ((n-2)!=3!=6)। पहले (n) पहचानें। / (120=5!), so (n=5) and ((n-2)!=3!=6). Identify (n) first.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{7!}{3!\cdot4!}\)?
C. (35)
\(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\) होता है। (4!) काटकर गणना करें। / \(\frac{7!}{3!\cdot4!}=\frac{7\cdot6\cdot5}{6}=35\). Cancel (4!) and calculate.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{5!}{2!}+1!\)?
C. (61)
\(\frac{5!}{2!}=60\) और (1!=1), इसलिए मान (61) है। (1!) और (0!) दोनों (1) होते हैं। / \(\frac{5!}{2!}=60\) and (1!=1), so the value is (61). Both (1!) and (0!) equal (1).
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
B. (2)
पहला पद (n+2) और दूसरा (n) है, इसलिए अंतर (2) है। अलग-अलग सरलीकरण करने से गलती कम होती है। / The first term is (n+2) and the second is (n), so the difference is (2). Simplifying separately reduces mistakes.
Login to save your score, XP, coins and progress.
For which value will ((n-3)!) be defined if (n) is an integer?
C. (n=3)
फैक्टोरियल गैर-ऋणात्मक पूर्णांक के लिए परिभाषित होता है, इसलिए \(n-3\ge0\)। दिए विकल्पों में (n=3) सही है। / Factorial is defined for non-negative integers, so \(n-3\ge0\). Among the given options, (n=3) is correct.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{9!}{8!}+\frac{6!}{5!}\)?
C. (15)
\(\frac{9!}{8!}=9\) और \(\frac{6!}{5!}=6\), इसलिए योग (15) है। सरल अनुपातों को तुरंत घटाएं। / \(\frac{9!}{8!}=9\) and \(\frac{6!}{5!}=6\), so the sum is (15). Reduce simple ratios quickly.
Login to save your score, XP, coins and progress.
What is the value of \(2!\cdot3!+4!\)?
B. (36)
\(2!\cdot3!=2\cdot6=12\) और (4!=24), इसलिए कुल (36) है। गुणा को जोड़ से पहले करें। / \(2!\cdot3!=2\cdot6=12\) and (4!=24), so the total is (36). Do multiplication before addition.
Login to save your score, XP, coins and progress.
Which is the complete expansion of (\frac{(n+3)!}{n!})?
C. ((n+3)(n+2)(n+1))
((n+3)!=(n+3)(n+2)(n+1)n!) होता है। इसलिए (n!) कटने पर तीन गुणनखंड बचते हैं। / ((n+3)!=(n+3)(n+2)(n+1)n!). After canceling (n!), three factors remain.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{10!}{7!\cdot3!}\)?
D. (120)
\(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\) होता है। बड़े फैक्टोरियल को तीन पदों तक घटाएं। / \(\frac{10!}{7!\cdot3!}=\frac{10\cdot9\cdot8}{6}=120\). Reduce the large factorial to three factors.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{6!-5!}{4!}\)?
C. (25)
\(6!-5!=6\cdot5!-5!=5\cdot5!\), और \(\frac{5\cdot5!}{4!}=25\)। पहले सामान्य फैक्टोरियल निकालें। / \(6!-5!=6\cdot5!-5!=5\cdot5!\), and \(\frac{5\cdot5!}{4!}=25\). Take the common factorial first.
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+2)!+(n+1)!}{(n+1)!})?
B. (n+3)
((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!)। इसलिए मान (n+3) है। / ((n+2)!+(n+1)!=(n+2)(n+1)!+(n+1)!=(n+3)(n+1)!). Therefore the value is (n+3).
Login to save your score, XP, coins and progress.
How many consecutive factors remain in \(\frac{12!}{9!}\)?
B. (3)
\(\frac{12!}{9!}=12\cdot11\cdot10\), इसलिए तीन गुणनखंड बचते हैं। हर के फैक्टोरियल तक अंश को काटें। / \(\frac{12!}{9!}=12\cdot11\cdot10\), so three factors remain. Cancel the numerator up to the denominator factorial.
Login to save your score, XP, coins and progress.
If (r!=24), what will be the value of ((r+1)!)?
D. (120)
(24=4!), इसलिए (r=4) और ((r+1)!=5!=120)। पहले दिए फैक्टोरियल से चर का मान निकालें। / (24=4!), so (r=4) and ((r+1)!=5!=120). First find the variable from the given factorial.
Login to save your score, XP, coins and progress.
What is the value of (\frac{(n+1)!}{(n+1)n!})?
B. (1)
((n+1)!=(n+1)n!), इसलिए पूरी भिन्न (1) बनती है। पहचान सूत्र याद रखने से समय बचता है। / ((n+1)!=(n+1)n!), so the whole fraction becomes (1). Remembering this identity saves time.
Login to save your score, XP, coins and progress.
This level is designed for 50 active questions. Currently 50 questions are available for the selected class and difficulty.
Yes, the timer uses 35 seconds per question for Medium difficulty and shows the total remaining time on the page.
Yes, every question has its own SEO-friendly page with answer, explanation and related practice links.
Use Google login or mobile OTP. Admin can block users and control login providers.