Hi Ankita,

Approach for these type of questions, would be using slot method(Basic multiplication principle) to solve it.

Given,

1. we have to use digits 0,1,2,3,4 and 5

2. Form a 5 digit number. So first place(ten thousand’s place) cannot be 0.

3.  It has to be divisible by 4.

4. Digit should not repeat.

Lets understand first thing that, if a number has to be divisible by 4, then last two digit(ten’s place and unit’s place) has to be divisible by 4.

Also First it has to be even number, if it has to be divisible by 4. that is here number should end with 0, 2, or 4

So first case,

Number ending with “0”. If a number end with 0, its ten place has to be either 2 or 4 then only it will be divisible by 4. So the number of different ways would be,

4 * 3 * 2 * 2 * 1 = 48.

So here strike off answer choices A and B.

Second case:

Number ending with “2”. If a number end with 2, its ten place has to be either 1, 3 or 5 then only it will be divisible by 4. So the number of different ways would be,

3 * 3 * 2 * 3 * 1 = 54.

So here strike off answer choices C and D. Because case I and II itself gives the number of ways more than 100.

So answer has to be E-144.

Lets confirm it.

Third Case:

Number ending with “4”.  If a number end with 4, its ten place has to be either 0 or 2 then only it will be divisible by 4. So the number of different ways would be,

Here 2 – sub cases because we cannot have ten thousands place and ten place to be zero.

So number ending with  0 4.  The number of different ways are,

4 * 3 * 2 * 1 *1 = 24.

So number ending with 2 4. then number of different ways are,

3 * 3 * 2 * 1*1 = 18.

So third case total is 42.

So the entire total different ways is 144.

It might look like a lengthy explanation, but it took less than 90 secs to solve this question. Its easier one, if you know the basic rules and use the slot method.

Hope this helps.