1
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Let $$f\left( n \right) = n$$ and $$g\left( n \right) = {n^{\left( {1 + \sin \,\,n} \right)}},$$ where $$n$$ is a positive integer. Which of the following statements is/are correct?

$$\eqalign{ & \,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = O\left( {g\left( n \right)} \right) \cr & \,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,f\left( n \right) = \Omega \left( {g\left( n \right)} \right) \cr} $$

A
Only $${\rm I}$$
B
Only $${\rm I}$$$${\rm I}$$
C
both $${\rm I}$$ and $${\rm I}$$$${\rm I}$$
D
Neither $${\rm I}$$ nor $${\rm I}$$$${\rm I}$$
2
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Among simple $$LR (SLR) ,$$ canonical $$LR,$$ and look-ahead $$LR$$ $$(LALR),$$ which of the following pairs identify the method that is very easy to implement and the method that is the most powerful , in that order?
A
$$SLR, LALR$$
B
Canonical $$LR,$$ $$LALR$$
C
$$SLR,$$ canonical $$LR$$
D
$$LALR,$$ canonical $$LR$$
3
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+2
-0.6
Consider the following grammar $$G$$

$$\eqalign{ & \,\,\,\,\,\,\,S \to \,\,\,\,\,\,\,F|H \cr & \,\,\,\,\,\,F \to \,\,\,\,\,\,\,p|c \cr & \,\,\,\,\,\,H \to \,\,\,\,\,\,\,d|c \cr} $$

where $$S, F$$ and $$H$$ are non-terminal symbols, $$p, d,$$ and $$c$$ are terminal symbols. Which of the following statement(s) is/are correct?

$$\,\,\,\,\,\,\,S1.\,\,\,\,\,\,\,LL\left( 1 \right)\,\,$$ can parse all strings that are generated using grammar $$G$$
$$\,\,\,\,\,\,\,S2.\,\,\,\,\,\,\,LR\left( 1 \right)\,\,$$ can parse all strings that are generated using grammar $$G$$

A
Only $$S1$$
B
Only $$S2$$
C
both $$S1$$ and $$S2$$
D
Neither $$S1$$ nor $$S2$$
4
GATE CSE 2015 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider a CSMA/CD network that transmits data at a rate of 100 Mbps (108 bits second) over a 1 km(kilometer) cable with no repeaters. If the minimum frame size required for this network is 1250 bytes, what is the signal speed (km/sec) in the cable?
A
8000
B
10000
C
16000
D
20000
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