GATE ME 2007 | GATE ME Year Wise Previous Years Questions

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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. Oil flows through a $$200mm$$ diameter horizontal cast iron pipe (friction factor, $$f=0.0225$$) of length $$500m.$$ The 18. Consider steady laminar incompressible axi-symmetric fully developed viscous flow through a straight circular pipe of co 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$$ and short ci 52. Which of the following is a solid state welding process. 53. Match the correct combination for following metal working processes. 54. In open die forging, a disc of diameter $$200mm$$ height $$60mm$$ is compressed without any barreling effect. The final 55. The thickness of metallic sheet is reduced from an initial value of $$16mm$$ to a final value of $$10mm$$ in one single 56. A $$200$$ $$mm$$ long down sprue has an area of cross section of $$650$$ $$m{m^2}$$ where the pouring basin meets the do 57. Volume of a cube of a side $$''l''$$ and volume of sphere of radius $$' r '$$ are equal. Both the cube and the sphere ar 58. A stepped steel shaft shown below is subjected to $$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. 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 79. The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential compon

GATE ME 2007

MCQ (Single Correct Answer)

-0.3

The inlet angle of runner blades of a Francis turbine is $${90^0}.$$ The blades are so shaped that the tangential component of velocity at blade outlet is zero. The flow velocity remains constant throughout the blade passage and is equal to half of the blade velocity at runner inlet. The blade efficiency of the runner is

$${25^0}.$$

$${50^0}.$$

$${80^0}.$$

$${89^0}.$$

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