GATE ME 2007 | GATE ME Year Wise Previous Years Questions

GATE ME

1. If $$F(s)$$ is the Laplace transform of the function $$f(t)$$ then Laplace transform of $$\int\limits_0^t {f\left( x \ri 2. The solution of $${{d\,y} \over {d\,x}} = {y^2}$$ with initial value $$y(0)=1$$ is bounded in the interval is 3. Let $$X$$ and $$Y$$ be two independent random variables. Which one of the relations $$b/w$$ expectation $$(E),$$ varianc 4. The area of a triangle formed by the tips of vectors $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $ 5. $$\mathop {Lim}\limits_{x \to 0} {{{e^x} - \left( {1 + x + {{{x^2}} \over 2}} \right)} \over {{x^3}}} = $$ 6. If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________. 7. The minimum value of function $$\,\,y = {x^2}\,\,$$ in the interval $$\,\,\left[ {1,5} \right]\,\,$$ is 8. The number of linearly independent eigen vectors of $$\left[ {\matrix{ 2 & 1 \cr 0 & 2 \cr } } \righ 9. If a square matrix $$A$$ is real and symmetric then the eigen values 10. The partial differential equation $$\,\,{{{\partial ^2}\phi } \over {\partial {x^2}}} + {{{\partial ^2}\phi } \over {\pa 11. If $$\phi (x,y)$$ and $$\psi (x,y)$$ are function with continuous 2nd derivatives then $$\phi (x,y)\, + \,i\psi (x,y)$$ 12. A block of mass $$M$$ is related from point $$P$$ on a rough inclined plane with inclination angle $$\theta $$, shown in 13. During inelastic collision of two particles, which one of the following is conserved? 14. Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o 15. Consider a steady incompressible flow through a channel as shown below. The velocity profile is uniform with a value o 16. Consider an incompressible laminar boundary layer flow over a flat plate of length $$L$$, aligned with the direction of 17. Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of co 18. Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The 19. Which combination of the following statements about steady incompressible forced vortex flow is correct? P: Shear stres 20. In a steady flow through a nozzle, the flow velocity on the nozzle axis is given by $$u = {u_0}\left( {1 + 3x/L} \right) 21. Oil in a hydraulic cylinder is compressed from an initial volume $$2{m^3}$$ to $$1.96{m^3}$$. If the pressure of oil in 22. Newton's law of viscosity states that the shear stress in a fluid is proportional to : 23. The temp distribution within the Laminar thermal boundary layer over a heated isothermal flat plate is given by $$\left 24. In a counter flow heat exchanger, hot fluid enters at $${65^ \circ }C$$ and cold fluid leaves at $${30^ \circ }C.$$ mass 25. The average heat transfer coefficient on a thin hot vertical plate suspended in still air can be determined from observa 26. Building has to be maintained at $${21^ \circ }C$$ (dry bulb) and $${14.5^ \circ }C$$ (wet bulb). The dew point temp und 27. Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3 28. Consider steady one-dimensional heat flow in a plate of $$20mm$$ thickness with a uniform heat generation of $$80MW/{m^3 29. Capacities of production of an item over $$3$$ consecutive months in regular time are $$100,$$ $$100$$ and $$80$$ and in 30. In a machine shop, pins of $$15mm$$ diameter are produced at a rate of $$1000$$ per month and the same is consumed at a 31. The maximum level of inventory of item is $$100$$ and it is achieved with infinite replenishment rate. The inventory be 32. A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p 33. A block brake shows below has a free width of $$300$$ $$mm$$ and a mean coefficient of friction of $$0.25$$. For an acti 34. A natural feed journal bearing of diameter $$50mm$$ and length $$50mm$$ operating at $$20$$ revolutions/sec carries a lo 35. A ball bearing operating at a load $$F$$ has $$8000$$hours of life. The life of the bearing, in hours, when the load is 36. A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p 37. A gear set has a pinion with $$20$$ teeth and a gear with $$40$$ teeth. The pinion runs at $$30rev/s$$ and transmits a p 38. A bolted joint in shown below. The maximum shear stress, in $$MPa,$$ in bolts $$A$$ and $$B$$ respectively are 39. A thin spherical pressure vessel of $$200mm$$ diameter and $$1mm$$ thickness is subjected to an internal pressure varyin 40. Which of the following engineering materials is the most suitable candidate for hot chamber die casting 41. If a particular $$Fe$$-$$C$$ alloy contains less than $$0.83$$% carbon, it is called 42. A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in 43. Which type of motor is used in axial or spindle drives of $$CNC$$ m/c tools 44. A hole is specified as $${40^{\matrix{ {0.050} \cr {0.000} \cr } }}\,\,mm.$$ The mating shaft has a clearanc 45. The force requirement in a blanking operation of low carbon steel sheet is $$5.0$$ $$kN.$$ The thickness of the sheet is 46. In orthogonal turning of low carbon steel pipe with principal cutting edge angle of $$90,$$ the main cutting force is $$ 47. In orthogonal turning of medium carbon steel, the specific machining energy is $$2$$ $$kJ/m{m^3},$$ the cutting velocity 48. In orthogonal turning of a low carbon steel bar of diameter $$150mm$$ with uncoated carbide tool, the cutting velocity i 49. A low carbon steel bar of $$147$$ $$mm$$ diameter with length of $$630$$ $$mm$$ is being turned with uncoated carbide in 50. Two metallic sheets, each of $$2.0$$ $$mm$$ thickness are welded in lap joint configuration by resistance spot welding 51. A $$DC$$ welding machine with a linear power source characteristic provides open circuit voltage of $$80V$$ and short ci 52. Which of the following is a solid state welding process. 53. In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final 54. The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single 55. Match the correct combination for following metal working processes. 56. Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ are equal. Both the cube and the sphere ar 57. A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the do 58. A stepped steel shaft shown below is subjected to $$10$$ N-m torque. If the modulus of rigidity is $$80$$ GPa, the strai 59. A uniformly loaded propped cantilever beam and its free body diagram are shown below. The reactions are 60. A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio 61. A machine frame shown in the figure below is subjected to a horizontal force of $$600$$ $$N$$ parallel to $$Z$$-directio 62. A disc of radius' r 'has a hole of radius 'r/2' cut-out as shown. The centroid of the remaining disc (shaded portion) at 63. In a simply-supported beam loaded as shown below, the maximum bending moment in N-m is 64. A steel rod of length $$L$$ and diameter $$D$$, fixed at both ends, is uniformly heated to a temperature rise of $$\Delt 65. The input link Q2P of a four bar linkage is rotated at $$2$$ rad/s counter clockwise direction as shown below. The angul 66. A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction The ang 67. A quick return mechanism is shown in below. The crank OS is drive at $$2$$ rev/s in counter clockwise direction If the 68. The natural frequency of the system shown below is 69. The equation of motion of a harmonic oscillator is given by $${{{d^2}x} \over {d{t^2}}} + 2\xi {\omega _n}{{dx} \over {d 70. For an under damped harmonic oscillator, resonance 71. The speed of an engine varies from $$210$$ rad/s to $$190$$ rad/s. During cycle the change in kinetic energy is found to 72. Which combination of the following statements is correct? The incorporation of re-heater in a steam power plant. $$P:$$ 73. Which of the following relationships is valid only for reversible process undergone by a closed system of simple compres 74. An irreversible heat engine extracts heat from a high temperature source at a rate of $$100kW$$ and rejects heat to a si 75. A heat transformer is a device that transfers a part of the heat, supplied to it at an intermediate temperature, to a hi 76. Water has a critical specific volume of $$0.003155$$ $${m^3}/kg.$$ A closed and rigid steel tank of volume $$0.025{m^3}$ 77. Match the items in columns $$I$$ and $$II$$. Column $$I$$ $$P:$$ Centrifugal compressor $$Q:$$ Centrifugal pump $$R:$$ P 78. The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential compon 79. A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. T

GATE ME 2007

MCQ (Single Correct Answer)

-0.3

A model of a hydraulic turbine is tested at a head of $$1/{4^{th}}$$ of that under which the full scale turbine works. The diameter of the model is half of that of the full scale turbine. If $$N$$ is the $$RPM$$ of the full scale turbine, then the $$RPM$$ of the model will be

$$N/4$$

$$N/2$$

$$N$$

$$2N$$

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