Ultimate Quant Marathon Blog For IIM CAT

If we define P(x)=1+x+x^2+..+x^6. Then what will be the remainder when P(x^7) is divided by P(x)?

a) 0        b)  1      c)   7     d) 49         e) none of these

254) If x^2-y^2=a where x,y are positive integers and a is an odd integer. If (x,y) has only one solution then a is
a) prime
b) composite
c) prime square
d) a ,b,c
e) a,c

255) If m^2+24m+21 has 3 factors for a natural number m, find the sum of all such m’s

256) Find the number of pairs of positive numbers (x,y) such that x^3-y^3=100 and (x-y) and xy are integers.

a) 0          b) 1                 c) 2                d) 4                e) none of these