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1

### AIEEE 2002

Number greater than 1000 but less than 4000 is formed using the digits 0, 1, 2, 3, 4 (repetition allowed). Their number is
A
125
B
105
C
374
D
625

## Explanation

There are 3 possible ways that we can make number greater than 1000 but less than 4000 using the digits 0, 1, 2, 3, 4 where repetition is allowed

Case 1 : First digit is 1 = 1 _ _ _

Possible numbers starting with 1 = 1$$\times$$5$$\times$$5$$\times$$5 = 125

But this includes 1000 also which does not satisfy the given condition of being greater than 1000. Hence there will be 124 numbers having 1 in the first place.

Case 2 : First digit is 2 = 2 _ _ _

Possible numbers starting with 2 = 1$$\times$$5$$\times$$5$$\times$$5 = 125

Case 3 : First digit is 3 = 3 _ _ _

Possible numbers starting with 3 = 1$$\times$$5$$\times$$5$$\times$$5 = 125

Total possible numbers = 124 + 125 + 125 = 374
2

### AIEEE 2002

Total number of four digit odd numbers that can be formed using 0, 1, 2, 3, 5, 7 (using repetition allowed) are
A
216
B
375
C
400
D
720

## Explanation

$$\therefore$$ Total no of ways = 5$$\times$$6$$\times$$6$$\times$$$${}^4{C_1}$$ = 720

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