## GATE CSE 2016 Set 2

Exam Held on Thu Jan 01 1970 00:00:00 GMT+0000 (Coordinated Universal Time)
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## Algorithms

Assume that the algorithms considered here sort the input sequences in ascending...
The Floyd-Warshall algorithm for all-pair shortest paths computation is based on...
A complete binary min-heap is made by including each integer in $$[1,1023]$$ exa...
Let, $${x_1} \oplus {x_2} \oplus {x_3} \oplus {x_4} = 0$$ where $${x_1},\,{x_2},... Let$$X$$be the number of distinct$$16$$-bit integers in$$2’s$$complement re... ## Discrete Mathematics Consider the system, each consisting of m linear equations in$$n$$variables. ... Suppose that the eigen values of matrix$$A$$are$$1, 2, 4.$$The determinant o... Let$${A_1},\,{A_2},\,{A_3}$$and$${A_4}$$be four matrices of dimensions$$10 ...
Suppose that a shop has an equal number of <b>LED</b> bulbs of two different typ...
Consider the following expressions: <br>$$\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$(i)$$ $... Let $$f(x)$$ be a polynomial and $$g\left( x \right) = f'\left( x \right)$$ be i... The minimum number of colours that is sufficient to vertex-colour any planar gra... A binary relation $$R$$ on $$N \times N$$ is defined as follows: $$(a,b)R(c,d)$$... Consider a set $$U$$ of $$23$$ different compounds in a Chemistry lab. There is ... Which one of the following well-formed formulae in predicate calculus is <b>NOT<... The value of the expression $${13^{99}}$$ ($$mod$$ $$17$$), in the range $$0$$ t... ## General Aptitude The man who is now Municipal Commissioner worked as ____________________. Find the odd one in the following group of words <p>mock, deride, praise, jeer<... Nobody knows how the Indian cricket team is going to <u>cope with</u> the diffic... Pick the odd one from the following options. In a quadratic function, the value of the product of the roots $$\left( {\alpha ... Among$$150$$faculty members in an institute,$$55$$are connected with each ot... All hill-stations have a lake. Ooty has two lakes. <p>Which of the statement(s) ... Computers were invented for performing only high-end useful computations. Howeve... <img class="question-image" src="https://gateclass.static.cdn.examgoal.com/54lQq... In a$$2 \times 4$$rectangle grid shown below, each cell is a rectangle. How ma... ## Operating Systems In which one of the following page replacement algorithms it is possible for the... Consider the following processes, with the arrival time and the length of the C... Consider a non-negative counting semaphore$$S.$$The operation$$P(S)$$decreme... ## Theory of Computation The number of states in the minimum sized$$DFA$$that accepts the language defi... Language$${L_1}$$is defined by the grammar:$$S{}_1 \to a{S_1}b|\varepsilon $$... Consider the following types of languages:$${L_1}:$$Regular,$${L_2}:$$Contex... Consider the following two statements: <p>$$\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,$$I... Consider the following languages:$$$\eqalign{ & {L_1} = \left\{ {{a^n}{b^m}...
Consider the following languages. <p>$$\,\,\,\,\,\,\,\,\,\,\,\,$$ {L_1} = \lef...