CS and IT GATE 2016 Set-1 Questions with Answer

Ques 53 Mathematics

A function f : N⁺ → N⁺, defined on the set of positive integers N⁺, satisfies the following

properties:
f(n) = f(n/2) if nis even
f(n) = f(n+5) if nis odd

Let R = {i|∃ j : f(j) = i} be the set of distinct values that f takes. The maximum possible size of R is .

Ques 54 Mathematics

The coefficient of x¹² in (x³ + x⁴ + x⁵ + x⁶ + ...)³ is_________

Ques 55 Mathematics

Two eigenvalues of a 3 x 3 real matrix P are (2 + √ -1) and 3. The determinant of P is _____

Ques 56 Mathematics

A probability density function on the interval [a, 1] is given by 1 / x² and outside this interval the value of the function is zero. The value of a is :

Ques 57 Mathematics

If f(x) = 2x⁷ + 3x - 5 Which of the following is a factor of f(x)?

Ques 58 Operating System

Consider a computer system with ten physical page frames. The system is provided with an access sequence a₁, a₂, ..., a₂₀, a₁, a₂, ..., a₂₀), where each ai number. The difference in the number of page faults between the last-in-first-out page replacement policy and the optimal page replacement policy is __________

Ques 59 Operating System

Consider a disk queue with requests for I/O to blocks on cylinders 47, 38, 121, 191, 87, 11, 92, 10. The C-LOOK scheduling algorithm is used. The head is initially at cylinder number 63, moving towards larger cylinder numbers on its servicing pass. The cylinders are numbered from 0 to 199. The total head movement (in number of cylinders) incurred while servicing these requests is______

Ques 60 Operating System

Consider a computer system with 40-bit virtual addressing and page size of sixteen kilobytes. If the computer system has a one-level page table per process and each page table entry requires 48 bits, then the size of the per-process page table is _________megabytes.

Ques 61 Operating System

Consider an arbitrary set of CPU-bound processes with unequal CPU burst lengths submitted at the same time to a computer system. Which one of the following process scheduling algorithms would minimize the average waiting time in the ready queue?