B

A number is divisible by 4 when its last two digits are divisible by 4
For this the numbers should have their last two digits as 00, 04, 08, 12, 16, … 96
By the formula, [latex]{a}_{n}[/latex] = a + (n - 1)d
96 = 0 + (n - 1) × 4
n = 25
So there are 25 choices for last 2 digits and 9 choices (1-9) for the 1st digit
So total 9 × 25 = 225

C

Total 15 people, and a particular woman is to be taken to form a group of 5, so choice is to be done from 14 people of 4 people
Ways are [latex]^{14}{C}_{4}[/latex] = 1768

B

0 cannot be on first place for it to be a 4 digit number.
So for 1st digit 4 choices, for second also 4 (because 0 can be placed here), then 3 for third place, 2 for fourth place
Total numbers = 4 × 4 × 3 × 2 = 96

D

For [latex]{1}^{st}[/latex] prize there are 8 choices, for [latex]{2}^{nd}[/latex] prize, 7 choices, and for [latex]{3}^{rd}[/latex] prize – 6 choices left
So total ways = 8 × 7 × 6 = 336

C

[latex]{2}^{4} - 1[/latex] = 16 - 1 = 15
[latex]{2}^{5} - 1[/latex] = 32 - 1 = 31
15 × 31 = 465