$$\int\limits_0^{\pi /4} {\left( {1 - \tan x} \right)/\left( {1 + \tan x} \right)dx} $$ $$\,\,\,\,\,\,$$ evaluates to

An unbalanced dice (with 6 faces, numbered from 1 to 6) is thrown. The probability that the face value is odd is 90% of the probability that the face valueis even. The probability of getting any even bnumbered face is the same.

If the probability that the face is even given that it is greater than 3 is 0.75, which one of the following options is closest to the probability that the face value exceeds 3?

A multilevel page table is preferred in comparison to a single level page table for translating virtual address to physical address because.

Consider the virtual page reference string $$$1,2,3,2,4,1,3,2,4,1$$$
On a demand paged virtual memory system running on a computer system that has main memory size of $$3$$ page frames which are initially empty. Let $$LRU,$$ $$FIFO$$ and $$OPTIMAL$$ denote the number of page faults under the corresponding page replacement policy. Then