CAT Exam

find the no of solutions of 3^x + x^2 =5

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CAT Other Question

let n!=1*2*3*---*n for integer n>=1.If p=1!+(2*2!)+(3*3!)+----+(10*10!),then p+2 when divided by 11! leaves a remainder of
1) 10
2) 0
3) 7
4) 1 There are how many integral solution pairs are possible for

(3x^2 + y^2 - 4y - 17)^3 - (2x^2 + 2y^2 - 4y - 6)^3 = (x^2 - y^2 - 11)^3

a. 6
b. 8
c.10
d.12
e. None of These