GCET is the Goa Common Entrance Test, to be conducted by DTE Goa.

Schedule for the Goa CET 2016 is given below.
Event Dates
Start of receiving forms for GCET 28 Mar 2016
Last date for receiving applications and issue of admit cards 02 Apr 2016
Last date for receiving applications and issue of admit card
(with additional late fees of Rs. 1000/-) 29 Apr 2016
Date of GCET 10 May & 11 May 2016
Expected date of result of GCET 18 May 2016

As you have asked for the GCET old question paper for engineering students, I want to tell you that I was unable to find the old question paper.
But I am providing you with its syllabus, check below for the details

Physics
Unit, dimension, measurement
Kinematics
Newtons laws of motion
Circular motion
Work, power, energy
Momentum and collision
Centre of mass and Inertia
Rotational dynamics
Elasticity, Calorimetry, Thermal expansion
Ktg and thermodynamics
Simple Harmonic Motion
Mechanical Waves
Fluid Mechanics
Geometrical Optics
Wave Optics
Electrostatics
Gravitation
Current Electricity
Capacitance
Magnetic Effect of Current & Magnetism
Electromagnetic Induction & AC
Nuclear physics and radioactivity
Dual nature of matter and radiation
Electronic devices
Communication systems
Errors in Measurements & Instruments

Chemistry
Periodic table and properties
Mole concept
Nomenclature of organic compounds
Chemical bonding
Gaseous state
Electronic displacement effect
Atomic structure
Isomerism
Redox and equivalent concepts
Chemical and ionic equilibrium
Chemical kinetics
Nuclear chemistry (radioactivity)
Halogen Derivative
Co-ordination Compounds
Aliphatic Hydrocarbons
Aromatic Hydrocarbons
Liquid Solution & Surface Chemistry
Metallurgy
Alcohol & Ether
Phenol
Solid State
Qualitative Analysis
Carbonyl compounds
s, p, d & f block elements
Thermodynamics & Thermochemistry
Electrochemistry
Biomolecules
Polymers
Carboxylic acids & its derivative
Amines
Practical Organic Chemistry

Mathematics
Logarithms and related expressions
Compound angles
Quadratic equations and expressions
Sequence and progression
Trignometric functions, equations, inequations
Solutions of triangle
Straight line and pair of lines
Circles
Permutation and combination
Binomial Theorem
Sets, relations, functions
Mathematical induction and reasoning
Limit, Continuity, Derivability
Method of differentiation
Indefinite Integral
Definite Integral
Application of Derivatives
Determinant & Matrices
Vectors
3-dimensional geometry
Probability
Differential Equation
Area under curve
Parabola, Ellipse, Hyperbola
Complex Number
Statistics