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 ?Q23.
The number of integers between 1 and 500 (both inclusive) that are divisible by 3 or 5 or 7 is ______________.Q24.
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}) isQ25.
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}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?Q27.
Consider the following grammar. P\rightarrowxQRS Q\rightarrowyz|zR\rightarroww|\varepsilon S\rightarrowyWhat is FOLLOW (Q) ?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 ?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.Q30.
A computer network uses polynomials over GF(2) for error checking with 8 bits as information bits and uses x^{3}+x+1 as the generator polynomial to generate the check bits. In this network, the message 01011011 is transmitted as