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: a)None of the other choices b)6 c)0 d)7

• Placement Papers
• /
• TCS
• /
• Category

TCS Question Papers: TCS Interview Experience(90) TCS Company Profile

(#M40039577) TCS Category question Keep an EYE

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:
a)None of the other choices b)6 c)0 d)7

Asked In TCS HARSHIT SHUKLA (9 years ago)

Unsolved Read Solution (16)

Is this Puzzle helpful?   (12)   (5) Submit Your Solution

Read Solution (16) :

Narasapu Hari prasad  (9 years ago)

hey guys it is given in Tcs correct ans is 7

Is this solution Helpfull? Yes (13) | No (4)  

chinmay  (9 years ago)

let x=0 then f(0)=1 and f(0^7)=1 then f(0^7)%f(0)=0 hence c)0 is correct

Is this solution Helpfull? Yes (9) | No (8)  

Narasapu Hari prasad  (9 years ago)

Ans is 7
f(x)=1+x+x^2....x^6
mathe matics rules
(x-1)(1+x+x^2...x^6)=x^7-1
so
f(x^7)=1+x^7+x^14.....x^42
f(x^7)%f(x)=1%f(x)+(x^7-1%f(x)+1%f(x)).............because
(x+1)%y=x%y+1%y
so
f(x^7)%f(x)=1+1+1+1+1+1+1=7
so ans is 7

Is this solution Helpfull? Yes (7) | No (8)  

M PRASANTH REDDY  (9 years ago)

option c is the Answer
f(x)=1+X+X^2+...X^6
then
f(x^7)= 1+ x^7 ( f(x)-x ).
so f(x^7)/f(x) reminder is 0.

by taking x=1 then
f(x^7)/f(x)= 1+ 1^7(7-1) / 7 =7/7 therefore reminder is 0.

by taking x=2 then
f(x^7)/f(x)= 1+ 2^7(127-1) / 127
=1+ 128(126) / 127
=16129/127
=127

by taking x=3 then
f(x^7)/f(x)= 1+ 3^7(1093-1) / 1093
=1+ 2187(1092) / 1093
=2388205/1093
=2185

therefore reminder is 0.

Is this solution Helpfull? Yes (6) | No (8)  

Chandu Muthyala  (9 years ago)

let say f(x) = y
f(x^7)= y^7
(y^7)%(y)=0

Is this solution Helpfull? Yes (3) | No (13)  

Hitender Singh  (9 years ago)

ans 7
wecant take x=0 as its nt natural nuber
take x=1
f(x)=7
f(x^7)=1
divide it you will get ans 7

Is this solution Helpfull? Yes (2) | No (9)  

M.Bhuvaneswari  (9 years ago)

ans) c.
f(x)=1+x+...x^6
let x=1
f(x)=7
f(x^7)= 1+x^7+(x^7)^2+...(x^7)^6
f(x^7)= 7
remainder= 0

Is this solution Helpfull? Yes (2) | No (5)  

Chandra chur anand  (9 years ago)

f(x)=1+x+x^2+...+x^6 put x=1 then
f(1)=7
and f(x^7)=7 because at x=1 f(1^7)=1
so f(x^7)%f(x)=7/7=1 hence remainder will be 0

Is this solution Helpfull? Yes (1) | No (1)  

kundan singh  (9 years ago)

f(x)=1+x+x^2+...+x^6 put x=1 then
f(1)=7
and f(x^7)=7 because at x=1 f(1^7)=1
so f(x^7)%f(x)=7/7=1 hence remainder will be 0

Is this solution Helpfull? Yes (1) | No (3)  

Raghav gupta  (9 years ago)

x^0+x^1+......+x^6
when divided by x^7 7 is prime gives 7

Is this solution Helpfull? Yes (1) | No   

neeraj  (8 years ago)

Let x =2 and x^7 = a
a=128
f(x)= 1+x^2....... x^6 putting x = 2 in this equation we get f(x) = 127
a%f(x) = 128%127 = 1
f(x^7) = 1 + (x^7)^2 + (x^7)^3+........ + (x^7)^6 = 1+a^2 + a^3 + ..... + a^6
f(x^7)/f(x) = 1/f(x)+a^2/f(x) + a^3/f(x) + ..... + a^6/f(x) = 1+1+1+1+1+1+1 = 7 ans

Is this solution Helpfull? Yes (1) | No   

  (6 years ago)

Consider f(x) series as GP.
For f(x), the common ratio is x
Sum of f(x)'s terms = (x^7 -1)/(x-1)
Now divide f(x) with each term of f(x^7)
1*(x-1)/(x^7 - 1) + x^7*(x-1)/(x^7 - 1).......
Now add +1 and -1 to each term except first and you will get the solution 7.

Suppose x^14/(x^7 - 1)
Now add +1 and -1,
( (x^7)^2 - 1^2 )/ (x^7 -1) + 1 and so on

Is this solution Helpfull? Yes (1) | No   

abhishek  (9 years ago)

let x=2
f(x)=127
f(x^7)=128
thus remainder is 1
it is valid for all integers
option a

Is this solution Helpfull? Yes | No (8)  

Ankit kumar  (9 years ago)

0,because each & every value of x,remainder will be zero.

Is this solution Helpfull? Yes | No   

aubrey  (9 years ago)

(x-1)(1+X+X^2+...X^6)=(x^7-1)
x^7= 1+(x-1)(1+X+X^2+...X^6)

let x^7 = A
and A%(1+X+X^2+...X^6)=1

f(x^7)=1+x7+x^14+x^21....+x^42

=1+A+A^2+A^3...+A^6
and when f(x^7)/f(x),the remainder from each term of f(x^7) is 1
hence 1+1+1+1+1+1+1=7
remainder is 7.

Is this solution Helpfull? Yes | No (3)  

Shashank Sourabh Singh  (8 years ago)

0 is correct ans

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.