GATE CSE 2017 SET-1


Q21.

Let u and v be two vectors in R^{2} whose Euclidean norms satisfy ||u||=2|| v|| . What is the value of \alpha such that w=u+\alphav bisects the angle between u and v ?
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Q22.

The value of \lim_{x\rightarrow 1}\frac{x^{7}-2x^{5}+1}{x^{3}-3x^{2}+2}
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Q23.

The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.
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Q24.

Consider the following languages over the alphabet \Sigma = \{a, b,c\}. Let L_{1}=\{a^{n}b^{n}c^{m}|m,n\geq 0\} and L_{2}=\{a^{m}b^{n}c^{n}|m,n\geq 0\} Which of the following are context-free languages ? I. L_{1}\cup L_{2} II. L_{1}\cap L_{2}
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Q25.

Consider the context-free grammars over the alphabet {a,b,c} given below. S and T are non-terminals G_{1}:S\rightarrow aSb|T, T\rightarrow cT|\epsilon G_{2}:S\rightarrow bSa|T,T\rightarrow cT|\epsilon The language L(G_{1})\cap L(G_{2}) is
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Q26.

If G is grammar with productions S\rightarrow SaS|aSb|bSa|SS|\epsilon where S is the start variable, then which one of the following is not generated by G?
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Q27.

Consider the following grammar. P\rightarrowxQRS Q\rightarrowyz|zR\rightarroww|\varepsilon S\rightarrowyWhat is FOLLOW (Q) ?
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Q28.

Consider the following context-free grammar over the alphabet \sum = {a,b,c} with S as the start symbol. S\rightarrowabScT|abcT T\rightarrowbT|b Which one of the following represents the language generated by the above grammar ?
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Q29.

Consider the following CPU processes with arrival times (in milliseconds) and length of CPU burst (in milliseconds) as given below: If the pre-emptive shortest remaining time first scheduling algorithm is used to schedule the processes., then the average waiting time across all processes is ________ milliseconds.
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Q30.

The values of parameters for the Stop-and-Wait ARQ protocol are as given below: Bit rate of the transmission channel = 1Mbps Propagation delay from sender to receiver = 0.75 ms Time to process a frame = 0.25ms Number of bytes in the information frame =1980 Number of bytes in the acknowledge frame = 20 Number of overhead bytes in the information frame = 20 Assume that there are no transmission errors. Then the transmission efficiency ( expressed in percentage) of the Stop-and - Wait ARQ protocol for the above parameters is _________( correct to 2 decimal places)
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