AIEEE 2010 Solved Paper

Four numbers can be chosen ‌20C4 ways.
When common difference d=1 then the possible sets are (1,2,3,4)(2,3,4,5)(3,4,5,6) (17,18,19,20)=17 sets
So when d=1 then 17 different AP's are possible with 4 numbers.
Now let's create a table of all possible sets -∴ Total no of AP =17+14+11+8+5+2=57
∴ Required probability =‌

57

‌20C4

=‌

1

85

∴ Statement −1 : is true.
∴ Statement −2 : is false as common difference can also be ±6.