TCS Company Numerical Ability

ages of two people has the ratio of 6.5. and by adding the ages we get 44.

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TCS Other 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

1)7 2)0 3)6 4)none of these
in how many ways can he letters of the english alphabet be arranged so that there are seven letters between the letters a and b and no letter is repeated

a)36*24!
b18*24!
c)24P7*2*18!
d)24P7*3*18!