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.
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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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What is the simplified form of (\frac{(n+4)!}{(n+2)!}-\frac{(n+3)!}{(n+1)!})?
A. (2(n+3))
पहला पद ((n+4)(n+3)) और दूसरा ((n+3)(n+2)) है। अंतर लेने पर (2(n+3)) मिलता है। / The first term is ((n+4)(n+3)) and the second is ((n+3)(n+2)). Taking the difference gives (2(n+3)).
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If (\frac{(n+4)!}{(n+1)!}=504), what is the value of (n)?
B. (5)
(\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2))। \(9\times8\times7=504\), इसलिए (n=5) है। / (\frac{(n+4)!}{(n+1)!}=(n+4)(n+3)(n+2)). Since \(9\times8\times7=504\), (n=5).
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What is the value of \(\frac{15!-12!}{12!}\)?
B. (2729)
\(\frac{15!}{12!}=15\times14\times13=2730\) और \(\frac{12!}{12!}=1\)। इसलिए मान (2730-1=2729) है। / \(\frac{15!}{12!}=15\times14\times13=2730\) and \(\frac{12!}{12!}=1\). Therefore the value is (2730-1=2729).
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What is the value of \(\frac{10!}{6!,4!}+\frac{10!}{7!,3!}\)?
D. (330)
पहला पद (210) और दूसरा पद (120) है। दोनों का योग (330) है। / The first term is (210) and the second term is (120). Their sum is (330).
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What is the simplified form of (\frac{\frac{(n+3)!}{n!}}{\frac{(n+2)!}{n!}})?
C. (n+3)
भिन्न को सरल करने पर (\frac{(n+3)!}{(n+2)!}) मिलता है। इसका मान (n+3) है। / Simplifying the fraction gives (\frac{(n+3)!}{(n+2)!}). Its value is (n+3).
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If (\frac{(n+2)!-(n+1)!}{n!}=36), what is the value of (n)?
B. (5)
सरल रूप ((n+1)2) है। ((n+1)2=36) से (n+1=6) और (n=5) है। / The simplified form is ((n+1)2). From ((n+1)2=36), (n+1=6) and (n=5).
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What is the value of \(\frac{14!}{12!}-\frac{13!}{11!}\)?
B. (26)
\(\frac{14!}{12!}=14\times13=182\) और \(\frac{13!}{11!}=13\times12=156\)। अंतर (26) है। / \(\frac{14!}{12!}=14\times13=182\) and \(\frac{13!}{11!}=13\times12=156\). The difference is (26).
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What is the value of \(\frac{6!}{2!,4!}\times\frac{4!}{3!}\)?
D. (60)
पहला पद (15) और दूसरा (4) है। गुणनफल \(15\times4=60\) है। / The first term is (15) and the second is (4). The product is \(15\times4=60\).
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If (n=5), what is the value of (\frac{(n+3)!}{(n+1)!}-\frac{(n+1)!}{n!})?
C. (50)
(n=5) पर पहला पद \(\frac{8!}{6!}=56\) और दूसरा \(\frac{6!}{5!}=6\) है। अंतर (50) है। / For (n=5), the first term is \(\frac{8!}{6!}=56\) and the second is \(\frac{6!}{5!}=6\). The difference is (50).
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What is the simplified form of (\frac{n!+(n-1)!}{(n-1)!})?
B. (n+1)
(n!=n(n-1)!), इसलिए अंश ((n-1)!(n+1)) है। भाग देने पर (n+1) मिलेगा। / Since (n!=n(n-1)!), the numerator is ((n-1)!(n+1)). Dividing gives (n+1).
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What is the value of \(\frac{9!-7!}{7!}\)?
C. (71)
\(\frac{9!}{7!}=72\) और \(\frac{7!}{7!}=1\)। इसलिए (72-1=71) है। / \(\frac{9!}{7!}=72\) and \(\frac{7!}{7!}=1\). Hence (72-1=71).
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What is the value of \(\frac{8!,3!}{6!,2!}\)?
C. (168)
\(\frac{8!}{6!}=56\) और \(\frac{3!}{2!}=3\)। इसलिए मान \(56\times3=168\) है। / \(\frac{8!}{6!}=56\) and \(\frac{3!}{2!}=3\). Therefore the value is \(56\times3=168\).
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What is the simplified form of \(\frac{(n+2)!}{(n+1)!}\times\frac{(n+1)!}{n!}\)?
B. ((n+2)(n+1))
पहला अनुपात (n+2) और दूसरा (n+1) है। गुणनफल ((n+2)(n+1)) होगा। / The first ratio is (n+2) and the second is (n+1). The product is ((n+2)(n+1)).
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What is the value of \(\frac{7!}{5!}+\frac{5!}{2!,3!}+1!\)?
C. (53)
\(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\) और (1!=1)। कुल (53) है। / \(\frac{7!}{5!}=42\), \(\frac{5!}{2!,3!}=10\), and (1!=1). The total is (53).
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If (\frac{(n+4)!}{(n+2)!}=132), what is the value of (n)?
B. (8)
(\frac{(n+4)!}{(n+2)!}=(n+4)(n+3))। \(12\times11=132\), इसलिए (n=8) है। / (\frac{(n+4)!}{(n+2)!}=(n+4)(n+3)). Since \(12\times11=132\), (n=8).
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What is the simplified form of (\frac{(n+5)!}{(n+2)!})?
B. ((n+5)(n+4)(n+3))
((n+5)!=(n+5)(n+4)(n+3)(n+2)!)। इसलिए तीन गुणक बचते हैं। / ((n+5)!=(n+5)(n+4)(n+3)(n+2)!). Therefore three factors remain.
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What is the value of \(\frac{11!}{8!,3!}-\frac{9!}{7!,2!}\)?
C. (129)
पहला पद (165) और दूसरा (36) है। अंतर (129) मिलेगा। / The first term is (165) and the second is (36). The difference is (129).
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What is the value of \(4!\times\frac{6!}{5!}-3!\)?
C. (138)
(4!=24), \(\frac{6!}{5!}=6\) और (3!=6)। इसलिए \(24\times6-6=138\) है। / (4!=24), \(\frac{6!}{5!}=6\), and (3!=6). Hence \(24\times6-6=138\).
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What is the value of \(\frac{10!-8!}{8!}\)?
C. (89)
\(\frac{10!}{8!}=90\) और \(\frac{8!}{8!}=1\)। इसलिए मान (90-1=89) है। / \(\frac{10!}{8!}=90\) and \(\frac{8!}{8!}=1\). Therefore the value is (90-1=89).
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What is the simplified form of (\frac{(n+3)!+(n+2)!}{(n+2)!})?
C. (n+4)
अंश ((n+2)![(n+3)+1]) है। इसलिए सरल रूप (n+4) है। / The numerator is ((n+2)![(n+3)+1]). Therefore the simplified form is (n+4).
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What is the value of \(\frac{\frac{12!}{9!,3!}}{\frac{5!}{3!,2!}}\)?
C. (22)
ऊपर का पद (220) और नीचे का पद (10) है। भाग देने पर (22) मिलता है। / The numerator term is (220) and the denominator term is (10). Dividing gives (22).
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If (\frac{(n+1)!}{(n-2)!}=60), what is the value of (n)?
B. (4)
(\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1))। \(5\times4\times3=60\), इसलिए (n=4) है। / (\frac{(n+1)!}{(n-2)!}=(n+1)n(n-1)). Since \(5\times4\times3=60\), (n=4).
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