Questions

Black soil coupled with favorable climatic conditions (Temperature of 21-320C and 30 -100 cm of rainfall) are responsible for cotton cultivation in Gujarat.

Red is deviated the least and violet the most

A solid sinks in a liquid if its density is greater than that of the liquid. if less, it floats

Facilitate means assist someone in their progress or work. Here Help is the only word which is similar in meaning with facilitate. Halt and check are antonyms i.e opposite in meaning of facilitate. 

Hence, facilitate is similar in meaning to help.

In 1814, George Stephenson developed steam engine to haul coal from mines to ports by railways. In 1830, the first railway train began to carry passengers and freight from Liverpool to Manchester.

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