Question

Numbers greater than $1000$ but not greater than $4000$ which can be formed with the digits $0,1,2,3,4$ (repetiion of digits is allowed) are

• A. $350$
• B. $374$
• C. $450$
• D. $575$

Answer 1

The correct option is B $374$

We need to form numbers that are $>1000$ and $<4000$ using $0,1,2,3,4$

The first digit can only be $1,2,3$

The rest of the digits can be any of the $5$ ( Since repetition is allowed ).

$\Rightarrow$ Total $=3\times 5\times 5\times 5=3\times 5^3$

$=375$

But $1000$ is also included in the above calculation.

$\therefore 375-1=374$ numbers possible.

Hence, the answer is $374.$