JEE Mains Model Paper 2

tr+1 , the (r + 1)th in the expansion of (516+2

1

8

)100 is given by
tr+1 =

100

‌

Cr (5

1

6

)100−t (2

1

8

)r
As 5 and 2 are relatively prime , Tr+1 will be rational if

100−r

6

and

r

8

are both integers i.e. if 100 - r is a multiple of 6 and r is a multiple of 8. As 0 ≤ r ≤ 100, multiples of 8 upto 100 and corresponding value of 100 - r are
r = 0 , 8 , 16 , 24 , ..... , 88 , 96
100 - r = 100 , 92 , 84 , 76 , 12 , 4
Out of 100 - r, multiples of 6 are 84 , 60 , 36 , 12
∴ There are just four rational terms
⇒ number of irrational terms is 101 - 4 = 97