Latest TCS Aptitude Question SOLUTION: In this question, A^B means A raised to the power B. let f(X) = 1 + X + X^2 +…..X^6. The remainder when f(X^7) is divided by f(X) is : o 7 o 0 o 6 o None of the other 3 choices

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In this question, A^B means A raised to the power B. let f(X) = 1 + X + X^2 +…..X^6. The remainder when f(X^7) is divided by f(X) is :
o 7
o 0
o 6
o None of the other 3 choices

Asked In TCS Nakshatra Mukhopadhyay (8 years ago)

Unsolved Read Solution (3)

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Read Solution (3) :

milan jena  (8 years ago)

It is given f(x)=1+x+x^2+.........+x^6
So f(x^7)=1+(x^7)+(x^7)^2+.......+(x^6)^7
=1+x^7+x^14+............+x^42
=1+(X^7 - 1)+(x^14 - 1)+..............+(x^42 - 1) + 6

We know that (x^7 - 1)=(x-1)(x^6 + x^5 +x^4 + .....+1)
So here (x^7 - 1) is divisible by f(x), because value of f(x) is (x^6 + x^5 +x^4 + .....+1)
Simillarly (x^14 - 1),(x^21 - 1),......(x^42 - 1) ,all are divisible by f(x), because all of these contain
(x^6 + x^5 +x^4 + .....+1).
so f(x^7)/f(x)=

={1+(X^7 - 1)+(x^14 - 1)+..............+(x^42 - 1) + 6}/f(x)=1+x+x^2+.........+x^6
so all term except 1 and 6 is divisible by f(x).
so remainder is 1+6=7.

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Goutham  (8 years ago)

0
SUB 1 IN F(X) AND F(X^7)

Is this solution Helpfull? Yes (3) | No (7)  

Mahima Goyal  (5 years ago)

7 is the corret answer.
bcz f(x^7)=7

Is this solution Helpfull? Yes (1) | No   

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