Q1:

n will be of the form 11ab, where a and b are odd numbers. We are looking for all n’s divisible by 3. ∴ 1 + 1 + a + b = 3 or 9 or 12 or 15 or 18 ∴ a + b = 1 or 4 or 7 or 10 or 13 or 16 ∴ a + b = 1 or 7 or 13 is not possible as the sum of two odd numbers cannot be odd. ∴ (a, b) = (1, 3), (3, 1), (1, 9), (3, 7), (5, 5), (7, 3), (9, 1), (7, 9), (9, 7) ∴ 9 elements of S are divisible by 3.

Hence, option 1.

Q2:

. g(x + 1) + g(x – 1) = g(x)

∴ g(x + 1) = g(x) – g(x – 1)

Now, let g(x − 1) = a and g(x) = b

g(x+1)=b-a

g(x+2)=b-a-b=-a

g(x+3)=-a-b+a=-b

g(x+4)=a-b

g(x+5)=g(x-1)

g(x+6)=g(x)

Hence option 4