Coefficient of x2 in the expansion of (1+x)2+(1+x)3+....(1+x)49+(1+mx)50is 2C2+3C2+.......49C2+50C2m2=(3n+1)51C3 3C3+3C2+......+49C2+50C2m2=(3n+1)51C3 50C3+50C2m2=(3n+1)51C3
50.49.48
6
+
50.49
2
m2=(3n+1)
51.50.49
6
m2=51n+1 must be a prefect quuared ⇒ n = 5 and m =16 Ans.⇒ 5