GATE CSE 2017 SET-1
Q31.
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 ?Q33.
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.Q34.
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}Q35.
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}) isQ36.
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?Q37.
Consider the following grammar. P\rightarrowxQRS Q\rightarrowyz|zR\rightarroww|\varepsilon S\rightarrowyWhat is FOLLOW (Q) ?Q38.
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 ?Q39.
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.Q40.
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)