The number of rational terms in the expansion of (1+2+53)6 is

A term in the expansion of (1+2+53)6 isof the form6!r!s!(6−r−s)!(1)6−r−s(2)r(53)s=6!r!s!(6−r−s)!2r/25s/3This term will be rational if 2r/2 and  5s/3 are both rational numbers. This is possible if and only if  r is a multiple of 2 and s is a multiple of 3. Possible values of r are 0, 2, 4 and 6 whereas the possible values of s are  0, 3 6 and  Also note that 0≤r+s≤6For r=0,s can take value 0, 3 or 6For r = 2, s can take value 0 or 3For r = 4, s can take value 0For r = 6, s can take value 0.Thus, the number of rational terms is  3+2+1+1=7