The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is :

The value of $$3 + {1 \over {4 + {1 \over {3 + {1 \over {4 + {1 \over {3 + ....\infty }}}}}}}}$$ is equal to

The number of times the digit 3 will be written when listing the integers from 1 to 1000 is :

Let the plane ax + by + cz + d = 0 bisect the line joining the points (4, $$-$$3, 1) and (2, 3, $$-$$5) at the right angles. If a, b, c, d are integers, then the
minimum value of (a² + b² + c² + d²) is _________.