GATE CSE 2006

Question 1
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:
A
3
B
5
C
6
D
9
Engineering Mathematics   Linear Algebra
Question 2
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
A
Z^{2xy}
B
Z*2^{xy}
C
Z^{2x+y}
D
2^{xyz}
Discrete Mathematics   Set Theory
Question 3
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
It is not closed
B
2 does not have an inverse
C
3 does not have an inverse
D
8 does not have an inverse
Discrete Mathematics   Group Theory
Question 4
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
A
Neither a Partial Order nor an Equivalence Relation
B
A Partial Order but not a Total Order
C
A Total Order
D
An Equivalence Relation
Discrete Mathematics   Relation
Question 5
For which one of the following reason does Internet Protocol (IP) use the timeto-live (TTL) field in the IP datagram header?
A
Ensure packets reach destination within that time
B
Discard packets that reach later than that time
C
Prevent packets from looping indefinitely
D
Limit the time for which a packet gets queued in intermediate routers
Computer Network   Network Layer Protocol
Question 6
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
A
1
B
2
C
3
D
4
Operating System   CPU Scheduling
Question 7
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?
A
(i) and (ii)
B
(ii) and (iii)
C
(i) and (iii)
D
None of these
Compiler Design   Parsing
Question 8
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
A
B
B
C
C
D
D
Digital Logic   Sequential Circuit
Question 9
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)?
A
400
B
500
C
600
D
700
Computer Organization   Machine Instruction
Question 10
In a binary max heap containing n numbers, the smallest element can be found in time
A
\Theta (n)
B
\Theta (logn)
C
\Theta (log logn)
D
\Theta (1)
Data Structure   Heap Tree
There are 10 questions to complete.

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