Question

how many 4 digit numbers can be formed by using 0,1,2,3,4,5. divisible by 4.

Answer 1

Digits = 0, 1, 2, 3, 4, 5.
conditions for divisible by 4. 
1). Last two digits should be divisible by 4.
2). or last two digit be 0, 0.
so we can take these two digits  from 0, 2 and 4
case.(1)
no. of 4 digit's number divisible by 4,if their last digit(unit place) be 0.
option for put the number at  tens place = 3 :   (0, 2 & 4)......{If repetition is allowed}
option for 100s place = 6  :  (0, 1, 2, 3, 4, 5)
option for 100s place = 5  :  (1, 2, 3, 4, 5)
no. of 4 digit's numbers divisible by for, their last digit be Zero. = 3 × 6 × 5 = 90

case.(2)
no. of 4 digit's numbers divisible by 4, if last digit be 2 .
option for put the digit at tens place = 3      :  (1,3 & 5)
options for hundreds place = 6                    :(0, 1, 2, 3, 4 & 5) 
options for 1000s place = 5                          :  (1, 2, 3, 4 & 5) 
No. of 4 digit's numbers divisible by 4, their last digit be 2. = 3 × 6 × 5 = 90
 
case.(3)
no. of 4 digit's numbers divisible by 4, if last digit be 4.
option for tens place =   3        :  (0, 2 & 4)
options for 100s place = 6      : (0, 1, 2, 3, 4 & 5)
options for 1000s place =   5    :  (1, 2, 3, 4 & 5)
no of 4 digit's numbers divisible by 4, their last digit be 4. = 3 × 6 ×5 = 90

From case (1), (2 ) and (3)----
Total no. of 4 digit's  numbers , divisible by 4 formed by digits 0, 1, 2, 3, 4 &5 .=   90 + 90 + 90 = 270

NOTE; Here repetition is allowed. take in care .