GATE CSE 2006

Consider the polynomial p(x)=a_{0}+a_{1}x+a_{2}x^{2} + a_{3}x^{3}, where a_{i}\neq 0,\forall i. The minimum number of multiplications needed to evaluate p on an input x is:

Let X, Y, Z be sets of sizes x, y and z respectively. Let W=X\timesY and E be the set of all subsets of W. The number of functions from Z to E is

The set {1, 2, 3, 5, 7, 8, 9} under multiplication modulo 10 is not a group. Given below are four plausible reasons. Which one of them is false?

A relation R is defined on ordered pairs of integers as follows:
(x,y)R(u,v) if x\ltu and y\gtv. Then R is

For which one of the following reason does Internet Protocol (IP) use the timeto-live (TTL) field in the IP datagram header?

Consider three CPU-intensive processes, which require 10,20 and 30 time units and arrive at times 0,2, and 6, respectively. How many context switches are needed if the operating system implements a shortes remaining time first scheduling algorithm? Do not count the context switches at time zero and at the end

Consider the following grammar.
S \rightarrow S * E
S \rightarrow E
E \rightarrow F + E
E \rightarrow F
F F \rightarrow id
Consider the following LR(0) items corresponding to the grammar above.
(i) S \rightarrow S * .E
(ii) E \rightarrow F. + E
(iii) E \rightarrow F + .E
Given the items above, which two of them will appear in the same set in the canonical sets-of-items for the grammar?

You are given a free running clock with a duty cycle of 50% and a digital waveform f which changes only at the negative edge of the clock. Which one of the following circuits (using clocked D flip flops) will delay the phase of f by 180^{\circ} ?

A CPU has 24-bit instructions. A program starts at address 300 (in decimal). Which one of the following is a legal program counter (all values in decimal)?

In a binary max heap containing n numbers, the smallest element can be found in time