factorial_notation se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
348 questions tagged with factorial_notation.
Which expression is equal to \(\frac{12!}{9!}\)?
B. \(12\times11\times10\)
\(\frac{12!}{9!}=12\times11\times10\)। हर में (9!) होने से (9!) तक का भाग कट जाता है। / \(\frac{12!}{9!}=12\times11\times10\). Since the denominator is (9!), the part up to (9!) cancels.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{11!}{9!,2!}\)?
B. (55)
\(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\)। बड़े फैक्टोरियल को (9!) तक लिखें। / \(\frac{11!}{9!,2!}=\frac{11\times10}{2}=55\). Write the larger factorial up to (9!).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{8!}{4!}-\frac{7!}{4!}\)?
B. (1470)
(\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470)। समान हर होने पर अंश मिलाकर देखें। / (\frac{8!-7!}{4!}=\frac{7!(8-1)}{4!}=7\times7\times6\times5=1470). With a common denominator, combine the numerator.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{5!+3!}{4!}\)?
C. \(\frac{21}{4}\)
अंश (120+6=126) है और (4!=24)। इसलिए मान \(\frac{126}{24}=\frac{21}{4}\) है। / The numerator is (120+6=126) and (4!=24). Hence the value is \(\frac{126}{24}=\frac{21}{4}\).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{9!}{6!,3!}-\frac{7!}{5!,2!}\)?
A. (63)
\(\frac{9!}{6!,3!}=84\) और \(\frac{7!}{5!,2!}=21\), इसलिए अंतर (63) है। दोनों संयोजन-जैसे पद अलग निकालें। / \(\frac{9!}{6!,3!}=84\) and \(\frac{7!}{5!,2!}=21\), so the difference is (63). Evaluate both combination-like terms separately.
Login to save your score, XP, coins and progress.
If (\frac{(n+2)!}{n!}=30), what is the value of (n)?
B. (4)
(\frac{(n+2)!}{n!}=(n+2)(n+1))। \(6\times5=30\), इसलिए (n=4)। / (\frac{(n+2)!}{n!}=(n+2)(n+1)). Since \(6\times5=30\), (n=4).
Login to save your score, XP, coins and progress.
What is the simplified form of (\frac{(n+3)!}{n!})?
A. ((n+3)(n+2)(n+1))
((n+3)!=(n+3)(n+2)(n+1)n!), इसलिए (n!) कट जाता है। क्रम से तीन गुणक बचते हैं। / ((n+3)!=(n+3)(n+2)(n+1)n!), so (n!) cancels. Three consecutive factors remain.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{7!-6!}{6!}\)?
B. (6)
\(7!=7\times6!\), इसलिए (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6)। समान फैक्टोरियल बाहर लें। / Since \(7!=7\times6!\), (\frac{7!-6!}{6!}=\frac{6!(7-1)}{6!}=6). Take the common factorial out.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{10!}{8!}+\frac{4!}{2!}\)?
C. (102)
\(\frac{10!}{8!}=90\) और \(\frac{4!}{2!}=12\), इसलिए योग (102) है। समान फैक्टोरियल भाग काटें। / \(\frac{10!}{8!}=90\) and \(\frac{4!}{2!}=12\), so the sum is (102). Cancel common factorial parts.
Login to save your score, XP, coins and progress.
If (\frac{n!}{(n-2)!}=42), what is the value of (n)?
B. (7)
(\frac{n!}{(n-2)!}=n(n-1)), इसलिए (n(n-1)=42)। \(7\times6=42\), अतः (n=7)। / (\frac{n!}{(n-2)!}=n(n-1)), so (n(n-1)=42). Since \(7\times6=42\), (n=7).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{8!}{5!,3!}+\frac{6!}{4!,2!}\)?
C. (71)
\(\frac{8!}{5!,3!}=56\) और \(\frac{6!}{4!,2!}=15\), इसलिए कुल (71) है। दोनों पदों को अलग हल करें। / \(\frac{8!}{5!,3!}=56\) and \(\frac{6!}{4!,2!}=15\), so the total is (71). Solve both terms separately.
Login to save your score, XP, coins and progress.
What is the simplified value of (\frac{(n+2)!}{(n+1)!}-\frac{n!}{(n-1)!})?
B. (2)
पहला अनुपात (n+2) और दूसरा (n) है। अंतर ((n+2)-n=2) होगा। / The first ratio is (n+2) and the second is (n). The difference is ((n+2)-n=2).
Login to save your score, XP, coins and progress.
What is the value of \(\frac{5!}{3!}+\frac{5!}{4!}\)?
B. (25)
\(\frac{5!}{3!}=20\) और \(\frac{5!}{4!}=5\), इसलिए योग (25) है। हर अनुपात अलग-अलग सरल करें। / \(\frac{5!}{3!}=20\) and \(\frac{5!}{4!}=5\), so the sum is (25). Simplify each ratio separately.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{6!}{3!}+4!\)?
C. (144)
\(\frac{6!}{3!}=120\) और (4!=24), इसलिए कुल (144) है। पहले भिन्न को सरल करें। / \(\frac{6!}{3!}=120\) and (4!=24), so the total is (144). Simplify the fraction first.
Login to save your score, XP, coins and progress.
If ((n+1)!=720), what is the value of (n)?
B. \(5\)
ज्ञात है कि \(6!=6\times5\times4\times3\times2\times1=720\)। अतः \((n+1)!=6!\), इसलिए \(n+1=6\) और \(n=5\)। \(n=6\) लेने पर \((n+1)!=7!=5040\) होगा, जो 720 नहीं है। परीक्षा टिप: \(5!=120\), \(6!=720\) और \(7!=5040\) जैसे छोटे फैक्टोरियल मान याद रखें। / We know that \(6!=6\times5\times4\times3\times2\times1=720\). Hence, \((n+1)!=6!\), so \(n+1=6\) and \(n=5\). If \(n=6\), then \((n+1)!=7!=5040\), not 720. Exam tip: Memorise small factorial values such as \(5!=120\), \(6!=720\), and \(7!=5040\).
Login to save your score, XP, coins and progress.
If (n=3), what will be the value of (\frac{(n+2)!}{n!})?
B. (20)
(n=3) रखने पर \(\frac{5!}{3!}=5\times4=20\)। पहले चर का मान रखें। / Putting (n=3), \(\frac{5!}{3!}=5\times4=20\). Substitute the variable first.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{9!}{7!}-5!\)?
A. (-48)
\(\frac{9!}{7!}=9\times8=72\) और (5!=120), इसलिए मान (-48) है। घटाव में चिह्न ध्यान से रखें। / \(\frac{9!}{7!}=9\times8=72\) and (5!=120), so the value is (-48). Keep the sign carefully in subtraction.
Login to save your score, XP, coins and progress.
If (\frac{(n+1)!}{n!}=8), what is the value of (n)?
B. (7)
(\frac{(n+1)!}{n!}=n+1), इसलिए (n+1=8) और (n=7)। पहले फैक्टोरियल अनुपात सरल करें। / (\frac{(n+1)!}{n!}=n+1), so (n+1=8) and (n=7). Simplify the factorial ratio first.
Login to save your score, XP, coins and progress.
What is \(\frac{8!}{8}\) equal to?
B. (7!)
\(8!=8\times7!\), इसलिए \(\frac{8!}{8}=7!\) है। सामान्य गुणक काटकर उत्तर मिल जाता है। / \(8!=8\times7!\), so \(\frac{8!}{8}=7!\). Cancel the common factor to get the answer.
Login to save your score, XP, coins and progress.
What is the value of \(3!+4!\times0!\)?
A. (30)
(0!=1), इसलिए \(4!\times0!=24\) और (3!+24=30)। गुणा को जोड़ से पहले करें। / (0!=1), so \(4!\times0!=24\) and (3!+24=30). Do multiplication before addition.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{10!}{8!,2!}\)?
C. (45)
\(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\)। पहले (8!) काटें और फिर (2!) से भाग दें। / \(\frac{10!}{8!,2!}=\frac{10\times9}{2}=45\). First cancel (8!) and then divide by (2!).
Login to save your score, XP, coins and progress.
How can (15!) be written using (14!)?
B. \(15\times14!\)
\(15!=15\times14!\) होता है। यह ((n)!=n(n-1)!) का सीधा प्रयोग है। / \(15!=15\times14!\). This is a direct use of ((n)!=n(n-1)!).
Login to save your score, XP, coins and progress.
If (m=2!) and (n=4!), what is the value of (m+n)?
C. 26
क्रमगुणित के अनुसार 2! = 2 तथा 4! = 4 × 3 × 2 × 1 = 24। अतः m + n = 2 + 24 = 26, इसलिए सही उत्तर विकल्प C है। 24 केवल n का मान है, m + n का नहीं। परीक्षा टिप: पहले प्रत्येक क्रमगुणित का मान निकालें, फिर दिए गए व्यंजक में प्रतिस्थापित करें। / Using factorials, 2! = 2 and 4! = 4 × 3 × 2 × 1 = 24. Therefore, m + n = 2 + 24 = 26, so option C is correct. Note that 24 is only the value of n, not of m + n. Exam tip: Evaluate each factorial first, then substitute the values into the given expression.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{4!+1!}{5}\)?
C. (5)
(4!+1!=24+1=25), और \(\frac{25}{5}=5\)। अंश को पहले सरल करें। / (4!+1!=24+1=25), and \(\frac{25}{5}=5\). Simplify the numerator first.
Login to save your score, XP, coins and progress.
Which expansion correctly starts (9!)?
A. \(9\times8\times7\times\cdots\times1\)
(9!) में (9) से (1) तक गुणा होता है। क्रमगुणित में जोड़ या घटाव नहीं होता। / In (9!), numbers from (9) down to (1) are multiplied. Factorial does not use addition or subtraction.
Login to save your score, XP, coins and progress.
A. (696)
(6!=720) और (4!=24), इसलिए अंतर (696) है। सीधे घटाने से पहले दोनों क्रमगुणित निकालें। / (6!=720) and (4!=24), so the difference is (696). Find both factorials before subtracting directly.
Login to save your score, XP, coins and progress.
What is the simplified form of \(\frac{(n+3)!}{(n+1)!}\)?
B. ((n+3)(n+2))
\((n+3)!=(n+3)(n+2)(n+1)!\), इसलिए शेष ((n+3)(n+2)) है। समान क्रमगुणित भाग काटें। / \((n+3)!=(n+3)(n+2)(n+1)!\), so the remaining part is ((n+3)(n+2)). Cancel the common factorial part.
Login to save your score, XP, coins and progress.
What is the value of \(\frac{6!}{3!}\div5\)?
B. (24)
\(\frac{6!}{3!}=6\times5\times4=120\), और \(120\div5=24\)। भागों को क्रम से सरल करें। / \(\frac{6!}{3!}=6\times5\times4=120\), and \(120\div5=24\). Simplify the operations in order.
Login to save your score, XP, coins and progress.
What is the last factor in (5!)?
B. (1)
\(5!=5\times4\times3\times2\times1\), इसलिए अंतिम गुणक (1) है। क्रमगुणित हमेशा (1) तक जाता है। / \(5!=5\times4\times3\times2\times1\), so the last factor is (1). A factorial always goes down to (1).
Login to save your score, XP, coins and progress.
What is the difference between \(7!\div5!\) and (2!)?
B. (40)
\(7!\div5!=42\) और (2!=2), इसलिए अंतर (40) है। पहले दोनों भागों के मान निकालें। / \(7!\div5!=42\) and (2!=2), so the difference is (40). First find the values of both parts.
Login to save your score, XP, coins and progress.
Use Google login or mobile OTP. Admin can block users and control login providers.