Q13/067) Let x be a real number and let M=(3x−1)/(1+x) – ((√(∣x∣−2) +√(2−∣x∣))/ √∣2−x∣.

We are taking square root of |x| - 2 and its –ve so it has to be zero

So |x| - 2 = 0 or x = 2 or – 2

x cannot be 2 as 2-x is in denominator

so x = - 2 

hence putting the value x = -2 we get M = 7

as M^4 =  1 mod 10   

M^2000 = 1 mod 10 or M^2003 = M^3 mod 10 = 343 mod 10 or 3

3 is the unit digit