Latest TCS Aptitude Question SOLUTION: for which of the following n is the number (2^74)+(2^2058)+(2^2n) a perfect square.. a. 2010 b. 2011 c. 2012 d. 2100

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for which of the following n is the number (2^74)+(2^2058)+(2^2n) a perfect square..
a. 2010
b. 2011
c. 2012
d. 2100

Asked In TCS (12 years ago)

Unsolved Read Solution (4)

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Mrinal Singh  (12 years ago)

we know (a+b)^2= (a^2)+(b^2)+2ab
form the question,
a^2=(2^74), a=(2^37), 2ab=2^2058, b^2=(2^2n)
therefore,2ab=2*(2^37)*(2^x)
find the value of x. 2ab=(2^((1+37+x)=2058)
solving this we get, x=2020.
2^(b^2)=(2^(2020)^2).
2^2n=(2^2(2020))
so n=2020.
no option is given. so it is a dummy question.

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Garima  (12 years ago)

none of given options

(2^74)+(2^2058)+(2^2n)

here for perfect square
2^2058 = 2*(2^37)* 2^n= 2*(2^37)* 2^2020

so n=2020

Is this solution Helpfull? Yes (8) | No (2)  

aishwarya kumar  (12 years ago)

it is a dummy question.
no answer matches.
to solve it we know that a perfect square should have 1, 6 ,4, 9 at the last digit. so find last digit of first two terms like this 2^5 gives 2 at units place so uptill 2^70 it will be 2 and then find for rest 4 it gives 6 so unit place digit for 1st term is 6*2=12...take only first digit..solve second term like this and then by putting options in the third term you will find that all options are wrong.

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sagar  (12 years ago)

2020 is the right ans

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