Let $$A + 2B = \left[ {\matrix{ 1 & 2 & 0 \cr 6 & { - 3} & 3 \cr { - 5} & 3 & 1 \cr } } \right]$$ and $$2A - B = \left[ {\matrix{ 2 & { - 1} & 5 \cr 2 & { - 1} & 6 \cr 0 & 1 & 2 \cr } } \right]$$. If Tr(A) denotes the sum of all diagonal elements of the matrix A, then Tr(A) $$-$$ Tr(B) has value equal to

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 :