Questions

The term derivative indicates that it has no independent value that is its value is entirely derived from the values of the underlying assets. The underlying asset can be securities, commodities , bullion, currency, livestock or anything else.

Kachchh district is the largest in India in terms of territorial extent, located in the state of Gujarat.
The second largest district is Leh in Jammu & Kashmir.

From the hints,

Only two options for 1st and 2nd digits => 4,2 and 9,3 since it is single digits

Sum of second and third digit  = 10 

If 2 => 3rd digit = 8

If 3 => 3rd digit = 7

4th digit = 2nd digit + 1 => (2+1 =3) or (3+1 = 4)

Sum of all digits = 30

Let 5th digit be x

=> 1st possibility = 4 + 2 + 8 + 3 + x = 30 => x = 13 (Not possible since it has 2 digits)

=> 2nd possibility = 9 + 3 + 7 + 4 + x = 30 => x = 7

Therefore, the PIN is 93747 

First nationalisation of commercial banks in India took place in 1969 and second time in 1980.