Question
What is the remainder when 120212 is divided by 1000?
Answer: Option D
:
D
Write (1202)12=(1200+2)12. In this expansion there will be 13 terms.
From the binomial theorem, the (r+1)th term is given as tr+1=nCran−rbr
The 13th term is 212=4096. 12th term is 12C11×12001×211=12−×12−00×2048−=−−−200.
When we add all 13th and 12th term, we get 296 as the last three digits.
The previous terms (1 to 11) will not make a difference to the answer as there will be a minimum of 12002 involved in the other terms, therefore the terms will end with more than 3 zeroes.
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:
D
Write (1202)12=(1200+2)12. In this expansion there will be 13 terms.
From the binomial theorem, the (r+1)th term is given as tr+1=nCran−rbr
The 13th term is 212=4096. 12th term is 12C11×12001×211=12−×12−00×2048−=−−−200.
When we add all 13th and 12th term, we get 296 as the last three digits.
The previous terms (1 to 11) will not make a difference to the answer as there will be a minimum of 12002 involved in the other terms, therefore the terms will end with more than 3 zeroes.
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