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The minimum value of function y = x2 in the interval [1, 5] is           (A) 0 (B) 1           (C) 25 (D) undefined The vec...

Mathematics: Quick recap(questions)






  • The minimum value of function y = x2 in the interval [1, 5] is
          (A) 0 (B) 1

          (C) 25 (D) undefined


  • The vector field is F = xi - yj (where i and j are unit vector) is
      (A) divergence free, but not irrotational
      (B) irrotational, but not divergence free
      (C) divergence free and irrotational
      (D) neither divergence free nor irrational


  • From a pack of regular playing cards, two cards are drawn at random. What is the probability that both cards will be Kings, if first card in NOT replaced ?
          (A) 1/26
          (B) 1/52
          (C)1/169
          (D) 1/221

Answer:
1.(B)
2.(C)
3.(D)

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GATE cut off marks varies with time, check out a short history here.

GATE: CUTOFF


GATE cut off marks varies with time, check out a short history here.

2011 Click Here 2012 Click Here 2013 Click Here 2014 Set 1 Click Here 2014 Set 2 Click Here 2014 Set 3 Click Here 2014 Set...

GATE:Previous year mechanical question paper

GATE 2016 topper reveals success mantra to crack the exam: Read to know Khantesh Mohanbhai Agrawal's inspirational story  INDIATOD...

GATE-MECHANICAL ENGG.[A story]



GATE 2016 topper reveals success mantra to crack the exam: Read to know Khantesh Mohanbhai Agrawal's inspirational story 
INDIATODAY.IN NEW DELHI, APRIL 5, 2016


Q. Did you take any coaching classes? Are they important for preparations?
Khantesh: Yes, I did enroll for GATEFORUM Distance Learning Program (DLP) and EII online Test Series, but I hardly used any of them since the major chunk of my preparation was self-study, solving problems from www.unitoperation.com and discussing doubts with friends. Joining coaching classes is a subjective question and varies from person to person and his prior knowledge in subjects. If you have studied decently during your graduation, there is not much need of coaching, although a test series may help you to manage time. However, there are no good test series available in Chemical Engineering.
Read the whole story from Nptel website link(Click here).

1. If the duration of activity f alone is changed from 9 to 10 days, then the (A) critical path remains the same and the total duration t...

INDUSTRIAL ENGINEERING: Quick recap(questions)

1. If the duration of activity f alone is changed from 9 to 10 days, then the
(A) critical path remains the same and the total duration to complete the project changes to 19 days.
(B) critical path and the total duration to complete the project remains the same.
(C) critical path changes but the total duration to complete the project remains the same.
(D) critical path changes and the total duration to complete the project changes to 17 days


2.For the standard transportation linear programme with m source and n destinations and total supply equaling total demand, an optimal solution (lowest cost) with the smallest number of non-zero xij values (amounts from source i to destination j ) is desired. The best upper bound for this number is
(A) mn                                                              (B) 2(m + n)
(C) m + n                                                          (D) m + n - 1


3.A company produces two types of toys : P and Q. Production time of Q is twice that of P and the company has a maximum of 2000 time units per day. The supply of raw material is just sufficient to produce 1500 toys (of any type) per day. Toy type Q requires an electric switch which is available @ 600 pieces per day only. The company makes a profit of Rs. 3 and Rs. 5 on type P and Q respectively. For maximization of profits, the daily production quantities of P and Q toys should respectively be
(A) 1000, 500                                                    (B) 500, 1000
(C) 800, 600                                                      (D) 1000, 1000



Answer:
1. (A)
2. (D)
3. (A)

For the same inlet and outlet temperatures of hot and cold fluids, the Log mean Temperature Difference (LMTD) is           (A) greater...

Heat Transfer:Quick recap(questions)

  • For the same inlet and outlet temperatures of hot and cold fluids, the Log mean Temperature Difference (LMTD) is
          (A) greater for parallel flow heat exchanger than for counter flow heat
          exchanger
          (B) greater for counter flow heat exchanger than for parallel flow heat
          exchanger
          (C) same for both parallel and counter flow heat exchangers
          (D) dependent on the properties of the fluids.

  • In a counter flow heat exchanger, for the hot fluid the heat capacity = 2 kJ/kgK, mass flow rate= 5 kg/s, inlet temperature = 150cC, outlet temperature = 100cC. For the cold fluid, heat capacity = 4 kJ/kgK, mass flow rate = 10 kg/s, inlet temperature = 20cC. Neglecting heat transfer to the surroundings, the outlet temperature of the cold fluid in cC is                            (A) 7.5
    (B) 32.5
    (C) 45.5
    (D) 70.0
  •  The logarithmic mean temperature difference (LMTD) of a counter flow heat exchanger is 20cC. The cold fluid enters at 20cC and the hot fluid enters at 100cC. Mass flow rate of the cold fluid is twice that of the hot fluid. Specific heat at constant pressure of the hot fluid is twice that of the cold fluid. The exit temperature of the cold fluid
    (A) is 40cC
    (B) is 60cC
    (C) is 80cC
    (D) cannot be determined




Answers:
1. (C)
2. (B)
3. (C)

A butt weld joint is developed on steel plates having yield and ultimate tensile strength of 500 MPa and 700 MPa, respectively. The thi...

Machine design: Quick recap(questions)


  • A butt weld joint is developed on steel plates having yield and ultimate tensile strength of 500 MPa and 700 MPa, respectively. The thickness of the plates is 8 mm and width is 20 mm. Improper selection of welding parameters caused an undercut of 3 mm depth along the weld. The maximum transverse tensile load (in kN) carrying capacity of the developed weld joint is?
  • A metric thread of pitch 2 rnrn and thread angle 60 degree is inspected for its pitch diameter using 3 wire method. The diameter of the best size wire in mm  is 
           (a) 0.866  (b) 1.000  (c)1.154  (d)2.000






Answers:
1.70KN
2. (c)


1. The definition of 1 K as per the internationally accepted temperature scale is (a) 1/100th the difference between normal boiling p...

Thermodynamics: Quick recap(questions)


1. The definition of 1 K as per the internationally accepted temperature scale is
(a) 1/100th the difference between normal boiling point and normal freezing point of water
(b) 1/273.15th the normal freezing point of water
(c) 100 times the difference between the triple point of water and the normal freezing point ‘ of water
(d) 1/273.16‘“ of the triple point of water

2.The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is 2.87 m3 and 300 K. respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is 0.5 bar. If the gas constant of air is R = 287 J/kgK and the atmospheric pressure is 1 bar, the mass of air (in kg) in the vessel is
(a) 1.67
(b) 3.33
(C) 5-00
(d) 6.66

3.Air expands steadily through a turbine from 6 bar, 800 to 1 bar, 520 K. During the expansion, heat transfer from air to the surroundings at 300 K is 10 kj/kg air. Neglect the changes in kinetic and potential energies and evaluate the irreversibiiity per kg air. Assume air to behave as an ideai gas with Cp=1.0 kj/kgk and R=0.3/KgK




Ans:
1.(d)
2.(c)
3. 42.03 kj/kg

Section 1: Engineering Mathematics  Linear Algebra : Matrix algebra, systems of linear equations, eigenvalues and eigenvectors. Calc...

Syllabus: GATE(mechanical engg.)


Section 1:
Engineering Mathematics 
Linear Algebra: Matrix algebra, systems of linear equations, eigenvalues and eigenvectors.
Calculus:Functions of single variable, limit, continuity and differentiability, mean value theorems, indeterminate forms; evaluation of definite and improper integrals; double and triple integrals; partial derivatives, total derivative, Taylor series (in one and two variables), maxima and minima, Fourier series; gradient, divergence and curl, vector identities, directional derivatives, line, surface and volume integrals, applications of Gauss, Stokes and Green’s theorems.
Differential equations: First order equations (linear and nonlinear); higher order linear differential equations with constant coefficients; Euler-Cauchy equation; initial and boundary value problems; Laplace transforms; solutions of heat, wave and Laplace's equations.
Complex variables: Analytic functions; Cauchy-Riemann equations; Cauchy’s integral theorem and integral formula; Taylor and Laurent series. Probability and Statistics: Definitions of probability, sampling theorems, conditional probability; mean, median, mode and standard deviation; random variables, binomial, Poisson and normal distributions.
Numerical Methods: Numerical solutions of linear and non-linear algebraic equations; integration by trapezoidal and Simpson’s rules; single and multi-step methods for differential equations.


Section 2:
Applied Mechanics and Design 
Engineering Mechanics:
Free-body diagrams and equilibrium; trusses and frames; virtual work; kinematics and dynamics of particles and of rigid bodies in plane motion; impulse and momentum (linear and angular) and energy formulations, collisions.
Mechanics of Materials / Strength of Material: Stress and strain, elastic constants, Poisson's ratio; Mohr’s circle for plane stress and plane strain; thin cylinders; shear force and bending moment diagrams; bending and shear stresses; deflection of beams; torsion of circular shafts; Euler’s theory of columns; energy methods; thermal stresses; strain gauges and rosettes; testing of materials with universal testing machine; testing of hardness and impact strength.
Theory of Machines: Displacement, velocity and acceleration analysis of plane mechanisms; dynamic analysis of linkages; cams; gears and gear trains; flywheels and governors; balancing of reciprocating and rotating masses; gyroscope.
Vibrations: Free and forced vibration of single degree of freedom systems, effect of damping; vibration isolation; resonance; critical speeds of shafts.
Machine Design: Design for static and dynamic loading; failure theories; fatigue strength and the S-N diagram; principles of the design of machine elements such as bolted, riveted and welded joints; shafts, gears, rolling and sliding contact bearings, brakes and clutches, springs.


Section 3:
Fluid Mechanics and Thermal Sciences 
Fluid Mechanics: Fluid properties; fluid statics, manometry, buoyancy, forces on submerged bodies, stability of floating bodies; control-volume analysis of mass, momentum and energy; fluid acceleration; differential equations of continuity and momentum; Bernoulli’s equation; dimensional analysis; viscous flow of incompressible fluids, boundary layer, elementary turbulent flow, flow through pipes, head losses in pipes, bends and fittings.
Heat-Transfer: Modes of heat transfer; one dimensional heat conduction, resistance concept and electrical analogy, heat transfer through fins; unsteady heat conduction, lumped parameter system, Heisler's charts; thermal boundary layer, dimensionless parameters in free and forced convective heat transfer, heat transfer correlations for flow over flat plates and through pipes, effect of turbulence; heat exchanger performance, LMTD and NTU methods; radiative heat transfer, Stefan-Boltzmann law, Wien's displacement law, black and grey surfaces, view factors, radiation network analysis.
Thermodynamics: Thermodynamic systems and processes; properties of pure substances, behaviour of ideal and real gases; zeroth and first laws of thermodynamics, calculation of work and heat in various processes; second law of thermodynamics; thermodynamic property charts and tables, availability and irreversibility; thermodynamic relations.
Applications: Power Engineering: Air and gas compressors; vapour and gas power cycles, concepts of regeneration and reheat. I.C. Engines: Air-standard Otto, Diesel and dual cycles. Refrigeration and air-conditioning: Vapour and gas refrigeration and heat pump cycles; properties of moist air, psychrometric chart, basic psychrometric processes. Turbomachinery: Impulse and reaction principles, velocity diagrams, Pelton-wheel, Francis and Kaplan turbines.


Section 4:
Materials, Manufacturing and Industrial Engineering 
Engineering Materials: Structure and properties of engineering materials, phase diagrams, heat treatment, stress-strain diagrams for engineering materials.
Casting, Forming and Joining Processes:Different types of castings, design of patterns, moulds and cores; solidification and cooling; riser and gating design. Plastic deformation and yield criteria; fundamentals of hot and cold working processes; load estimation for bulk (forging, rolling, extrusion, drawing) and sheet (shearing, deep drawing, bending) metal forming processes; principles of powder metallurgy. Principles of welding, brazing, soldering and adhesive bonding.
Machining and Machine Tool Operations: Mechanics of machining; basic machine tools; single and multi-point cutting tools, tool geometry and materials, tool life and wear; economics of machining; principles of non-traditional machining processes; principles of work holding, design of jigs and fixtures.
Metrology and Inspection: Limits, fits and tolerances; linear and angular measurements; comparators; gauge design; interferometry; form and finish measurement; alignment and testing methods; tolerance analysis in manufacturing and assembly.
Computer Integrated Manufacturing: Basic concepts of CAD/CAM and their integration tools. Production Planning and Control: Forecasting models, aggregate production planning, scheduling, materials requirement planning.
Inventory Control: Deterministic models; safety stock inventory control systems.
Operations Research: Linear programming, simplex method, transportation, assignment, network flow models, simple queuing models, PERT and CPM.

source: http://www.gate.iitg.ac.in/Syllabi/ME_Mechanical-Engineering.pdf
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