Year-wise GATE papers

GATE 2017

16 questions and papers

GATE CS 2017 Set 2 — Question 30

Numerical answer 1 mark Theory of Computation GATE CS — Computer Science & IT

Consider the language \(L\) given by the regular expression \((a+b)^*b(a+b)\) over the alphabet \(\{a,b\}\). The smallest number of states needed in a deterministic finite-state automaton (DFA) accepting \(L\)…

GATE CS 2017 Set 1 — Question 29

Multiple choice 2 marks Probability and Statistics GATE CS — Computer Science & IT

\(P\) and \(Q\) are considering to apply for a job. The probability that \(P\) applies for the job is \(\dfrac{1}{4}\), the probability that \(P\) applies for the job given that \(Q\) applies for the job is \(\dfrac{1}{2}\), and the probability that \(Q\) applies for the…

GATE CS 2017 Set 2 – Question 51

Numerical answer 2 marks Operating Systems GATE CS — Computer Science & IT

Consider the following CPU processes with arrival times (in milliseconds) and length of CPU bursts (in milliseconds) as given below:ProcessArrival timeBurst timeP107P233P355P462If the pre-emptive shortest remaining time first…

GATE CS 2017 Set 1 — Question 47

Numerical answer 2 marks Engineering Mathematics GATE CS — Computer Science & IT

If the characteristic polynomial of a \(3\times 3\) matrix \(M\) over \(\mathbb{R}\) (the set of real numbers) is \(\lambda^{3} - 4\lambda^{2} + a\lambda + 30\), \(a \in \mathbb{R}\), and one eigenvalue of \(M\) is \(2\), then the largest among the absolute values of the eigenvalues of \(M\) is ______.

GATE CS 2017 Set 1 — Question 30

Multiple choice 2 marks Engineering Mathematics GATE CS — Computer Science & IT

If \(f(x) = R\sin\left(\dfrac{\pi x}{2}\right) + S\), \(f'\left(\dfrac{1}{2}\right) = \sqrt{2}\) and \(\displaystyle\int_{0}^{1} f(x)\,dx = \dfrac{2R}{\pi}\), then the constants \(R\) and \(S\) are respectively