JEE Advanced Model Paper 15 with solutions for online practice

n (S) =

20

‌

C3
Number of A.P’s with c.d’s 1,2,3,.........,9
are respectively 18, 16, 14,............, 2
Total no. of A.P’s = 2 + 4 + 6 +..........+ 18 = 2(1 + 2 + 3 +..................+ 9) = 90
No. of A.P’s with odd c.d. = 18 + 14+ 10 + 6 + 2 = 50 Sum = even => (3 nos. are even) or (1 even, 2 odd)
No. of fav. Case -

10

‌

C3 + (

10

‌

C1×

10

‌

C2) = 120 + 450 = 70
Prob (product is odd) = (

10 ‌ C3

20 ‌ C3

) =

2

19