I don't think your approach is right. Here is what i would do.

p( getting correct answer ) = 0.25

q = 1 - 0.25 = 0.75

P( of getting none correct ) = 10C0 x (0.25)^0 x (0.75)^10

b.) More than 7 corrects

p( more than 7 corrects ) = P(x=8) + P(x=9) + P(x=10)

= 10C8 x (0.25)^8 x (0.75)^2 + 10C9 x (0.25)^9 x (0.75)^1 + 10C10 x (0.25)^10 x (0.75)^0