Latest TCS Aptitude Question SOLUTION: For which of the following “n” is the number 2^74 + 2^2058 + 2^2n a perfect square? a. 2012 b. 2100 c. 2011 d. 2020

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For which of the following “n” is the number 2^74 + 2^2058 + 2^2n a perfect square?

a. 2012
b. 2100
c. 2011
d. 2020

Asked In TCS pernica bansal (10 years ago)

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Debolina Chakraborty  (10 years ago)

2^74+2^2058+2^2n= (2^37)^2+ (2^n)^2+ 2^2058
nw compare it wid (a+b)^2=a^2+b^2+2*a*b
a=2^37 and b=2^n
thus 2*(2^37)*(2^n)=2^(38+n)=2^2058
38+n=2058;
n=2020

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vikram kumar  (10 years ago)

ans will be option (c)
for the perfect square we have to check 74%4 then remainder will be 2
2058%4 remainder will be 2
we should put n= 2011,then 2n=4022,again dividing 4022%4,remainder will be 2
then for the perfect square we should take 2^2 common,which is to a perfect square

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Narendra kumar verma  (10 years ago)

make the exp in the form of a^2+b^2+2ab here a=2^37 and b=2^n then 2ab=2^2058 putting the the value of a and b. 2^n=(2^2058)/2^38 by comparing the power of n we get n=2020 ANS

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suparna das  (10 years ago)

ans is 2020

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