Write the greatest and the smallest 4-digit numbers using four different digits with the conditions as given:

(i) Digit 7 is always at units place.

(ii) Digit 4 is always at tens place.

(iii) Digit 9 is always at hundreds place.

(iv) Digit 2 is always at thousands place.

(i) Digit 7 is always at units place.

The number is of the form _ _ _ 7 (with all four digits different).

For the greatest 4-digit number, the remaining three digits should be as large as possible (different from 7 and from each other). The largest such digits are 9, 8 and 6.

Greatest 4-digit number = 9867.

For the smallest 4-digit number, the thousands place cannot be 0. The smallest non-zero digit (other than 7) is 1. Then the remaining digits are 0 and 2 (smallest available, different from 1 and 7).

Smallest 4-digit number = 1027.

Hence, the greatest 4-digit number is 9,867 and the smallest 4-digit number is 1,027.

(ii) Digit 4 is always at tens place.

The number is of the form _ _ 4 _ (with all four digits different).

For the greatest 4-digit number, fill the remaining places with the largest distinct digits other than 4. Use 9 at thousands, 8 at hundreds and 7 at units.

Greatest 4-digit number = 9847.

For the smallest 4-digit number, the thousands place cannot be 0. Place 1 at thousands, 0 at hundreds, 4 at tens and 2 at units.

Smallest 4-digit number = 1042.

Hence, the greatest 4-digit number is 9,847 and the smallest 4-digit number is 1,042.

(iii) Digit 9 is always at hundreds place.

The number is of the form _ 9 _ _ (with all four digits different).

For the greatest 4-digit number, fill the remaining places with the largest distinct digits other than 9. Use 8 at thousands, 7 at tens and 6 at units.

Greatest 4-digit number = 8976.

For the smallest 4-digit number, the thousands place cannot be 0. Place 1 at thousands, 9 at hundreds, 0 at tens and 2 at units.

Smallest 4-digit number = 1902.

Hence, the greatest 4-digit number is 8,976 and the smallest 4-digit number is 1,902.

(iv) Digit 2 is always at thousands place.

The number is of the form 2 _ _ _ (with all four digits different).

For the greatest 4-digit number, fill the remaining places with the largest distinct digits other than 2. Use 9 at hundreds, 8 at tens and 7 at units.

Greatest 4-digit number = 2987.

For the smallest 4-digit number, fill the remaining places with the smallest distinct digits other than 2 (since 2 is already at thousands). Use 0 at hundreds, 1 at tens and 3 at units.

Smallest 4-digit number = 2013.

Hence, the greatest 4-digit number is 2,987 and the smallest 4-digit number is 2,013.