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If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of
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04 May 2021, 03:27
04 May 2021, 03:27
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Question Stats:
71% (02:15) correct
28% (00:41) wrong based on 7 sessions
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If \(a=\frac{13!^1^6-13!^8}{13!^8+13!^4}\) what is the unit digit of \(\frac{a}{13!^4}\)?
A. 0
B. 1
C. 9
D. 4
E. 6
A. 0
B. 1
C. 9
D. 4
E. 6
Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of
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04 May 2021, 06:18
04 May 2021, 06:18
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a = 13!^8-13!^4
a/13!^4 = 13!^4-1
Units digit = 1 - 1 = 0 (3^4 unit digit is 1)
Answer A - 0
a/13!^4 = 13!^4-1
Units digit = 1 - 1 = 0 (3^4 unit digit is 1)
Answer A - 0
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Re: If a=(13!^1^6-13!^8)/(13!^8+13!^4) hat is the unit digit of
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04 May 2021, 08:35
04 May 2021, 08:35
1
GeminiHeat wrote:
If \(a=\frac{13!^1^6-13!^8}{13!^8+13!^4}\) what is the unit digit of \(\frac{a}{13!^4}\)?
A. 0
B. 1
C. 9
D. 4
E. 6
A. 0
B. 1
C. 9
D. 4
E. 6
\(a = \frac{13!^{16} - 13!^8}{13!^8 + 13!^4}\)
Let, \(13! = x\)
\(a = \frac{(x^8 - x^4)(x^8 + x^4)}{(x^8 + x^4)}\)
\(a = x^8 - x^4\)
Now, \(\frac{a}{x^2} = x^2 - 1\)
Since we have \(13!\), we will have a \(10\) in it which makes it's unit digit as \(0\)
Therefore, \((13!)^2\) will have units digit as \(0\)
Our Answer would be \(.....0 - 1 = 9\)
Hence, option C
