Page 1 GATE ME - 2003 Q.1 - Q.30 Carry One Mark Each 1. 2 0 sin x x Lt x ? is equal to (a) 0 (b) 8 (c) 1 (d) -1 2. The accuracy of Simpson’s rule quadrature for a step size h is (a) O ( ) 2 h (b) O ( ) h 3 (c) O ( ) 4 h (d) O ( ) 5 h 3. For the matrix 4 1 1 4 ? ? ? ? ? ? the eigen vaues are (a) 3 and -3 (b) -3 and -5 (c) 3 and 5 (d) 5 and 0 4. The second moment of a circular area about the diameter is given by (D is the diameter). (a) 4 4 D p (b) 4 16 D p (c) 4 32 D p (d) 4 64 D p 5. A concentrated load of P acts on a simply supported beam of span L at a distance 3 L from the left support. The bending moment at the point of application of the load is given by (a) 3 PL (b) 2 3 PL (c) 9 PL (d) 2 9 PL 6. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct? (a) Both rods elongate by the same amount (b) Mild steel rod elongates more than the cast iron rod (c) Cast iron rod elongates more than the mild steel rod (d) As the stresses are equal strains are also equal in both the rods Page 2 GATE ME - 2003 Q.1 - Q.30 Carry One Mark Each 1. 2 0 sin x x Lt x ? is equal to (a) 0 (b) 8 (c) 1 (d) -1 2. The accuracy of Simpson’s rule quadrature for a step size h is (a) O ( ) 2 h (b) O ( ) h 3 (c) O ( ) 4 h (d) O ( ) 5 h 3. For the matrix 4 1 1 4 ? ? ? ? ? ? the eigen vaues are (a) 3 and -3 (b) -3 and -5 (c) 3 and 5 (d) 5 and 0 4. The second moment of a circular area about the diameter is given by (D is the diameter). (a) 4 4 D p (b) 4 16 D p (c) 4 32 D p (d) 4 64 D p 5. A concentrated load of P acts on a simply supported beam of span L at a distance 3 L from the left support. The bending moment at the point of application of the load is given by (a) 3 PL (b) 2 3 PL (c) 9 PL (d) 2 9 PL 6. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct? (a) Both rods elongate by the same amount (b) Mild steel rod elongates more than the cast iron rod (c) Cast iron rod elongates more than the mild steel rod (d) As the stresses are equal strains are also equal in both the rods GATE ME - 2003 7. Two beams, one having square cross section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then (a) maximum bending stress developed in both the beams is the same (b) the circular beam experiences more bending stress that the square one (c) the square beam experiences more bending stress than the circular one (d) as the material is same both the beams will experience same deformation 8. The mechanism used in a shaping machine is (a) a closed 4-bar chain having 4 revolute pairs (b) a closed 6-bar chain having 6 revolute pairs (c) a closed 4-bar chain having 2 revolute and 2 sliding pairs (d) an inversion of the single slider-crank chain 9. The lengths of the links of a 4-bar linkage with revolute pairs only are p,q,r and s units. Given that p < q < r < s. which of these links should be the fixed one, for obtaining a ‘double crank’ mechanism? (a) link of length p (b) link of length q (c) link of length r (d) link of length s 10. Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K 1 , K 2 , K 3 are the torsional stiffness of the respective shafts. The natural frequency of torsional oscillation of the disc is given by (a) 1 2 3 K K K J + + (b) ( ) 1 2 2 3 3 1 1 2 K K K K K K J K K + + + (c) ( ) 1 2 3 1 2 2 3 3 1 K K K J K K K K K K + + (d) ( ) 1 2 2 3 3 1 2 3 K K K K K K J K K + + + K 1 K 2 K 3 K 3 Fixed end Fixed end Page 3 GATE ME - 2003 Q.1 - Q.30 Carry One Mark Each 1. 2 0 sin x x Lt x ? is equal to (a) 0 (b) 8 (c) 1 (d) -1 2. The accuracy of Simpson’s rule quadrature for a step size h is (a) O ( ) 2 h (b) O ( ) h 3 (c) O ( ) 4 h (d) O ( ) 5 h 3. For the matrix 4 1 1 4 ? ? ? ? ? ? the eigen vaues are (a) 3 and -3 (b) -3 and -5 (c) 3 and 5 (d) 5 and 0 4. The second moment of a circular area about the diameter is given by (D is the diameter). (a) 4 4 D p (b) 4 16 D p (c) 4 32 D p (d) 4 64 D p 5. A concentrated load of P acts on a simply supported beam of span L at a distance 3 L from the left support. The bending moment at the point of application of the load is given by (a) 3 PL (b) 2 3 PL (c) 9 PL (d) 2 9 PL 6. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct? (a) Both rods elongate by the same amount (b) Mild steel rod elongates more than the cast iron rod (c) Cast iron rod elongates more than the mild steel rod (d) As the stresses are equal strains are also equal in both the rods GATE ME - 2003 7. Two beams, one having square cross section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then (a) maximum bending stress developed in both the beams is the same (b) the circular beam experiences more bending stress that the square one (c) the square beam experiences more bending stress than the circular one (d) as the material is same both the beams will experience same deformation 8. The mechanism used in a shaping machine is (a) a closed 4-bar chain having 4 revolute pairs (b) a closed 6-bar chain having 6 revolute pairs (c) a closed 4-bar chain having 2 revolute and 2 sliding pairs (d) an inversion of the single slider-crank chain 9. The lengths of the links of a 4-bar linkage with revolute pairs only are p,q,r and s units. Given that p < q < r < s. which of these links should be the fixed one, for obtaining a ‘double crank’ mechanism? (a) link of length p (b) link of length q (c) link of length r (d) link of length s 10. Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K 1 , K 2 , K 3 are the torsional stiffness of the respective shafts. The natural frequency of torsional oscillation of the disc is given by (a) 1 2 3 K K K J + + (b) ( ) 1 2 2 3 3 1 1 2 K K K K K K J K K + + + (c) ( ) 1 2 3 1 2 2 3 3 1 K K K J K K K K K K + + (d) ( ) 1 2 2 3 3 1 2 3 K K K K K K J K K + + + K 1 K 2 K 3 K 3 Fixed end Fixed end GATE ME - 2003 11. Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be (a) 120 MPa (b) 60 MPa (c) 30 MPa (d) 15 MPa 12. A wire rope is designated as 6 × 19 standard hoisting. The numbers 6 × 9 represent (a) diameter in millimeter × length in meter (b) diameter in centimeter × length in meter (c) number of strands × number of wires in each strand (d) number of wires in each strand × number of strands 13. A cylindrical body of cross-sectional area A, height H and density , s ? is immersed to a depth h in a liquid of density ?, and tied to the bottom with a string. The tension in the string is (a) ?ghA (b) ( ) s ghA ? ? - (c) ( ) s ghA ? ? - (d) ( ) s h H gA ? ? - 14. A 2 kW, 40 litre water heater is switched on for 20 minutes. The heat capacity P C for water is 4.2 kJ/kg K. Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is (a) 2.7 (b) 4.0 (c) 14.3 (d) 25.25 15. An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000W, respectively. The COP for the heat pump is (a) 7.5 (b) 6.5 (c) 4.0 (d) 3.0 16. A plate having 10 cm 2 area each side is hanging in the middle of a room of 100 m 2 total surface area. The plate temperature and emissivity are respectively 800 K and 0.6. the temperature and emissivity values for the surfaces of the room are 300K and 0.3 respectively. Boltzmann’s constant s=5.67×10 -8 W/m 2 K 4 . The total heat loss from the two surfaces of the plate is (a) 13.66 W (b) 27.32 W (c) 27.87 W (d) 13.66 W 17. For air with a relative humidity of 80% (a) the dry bulb temperature is less than the wet bulb temperature (b) the dew point temperature is less than wet bulb temperature (c) the dew point and wet bulb temperatures are equal (d) the dry bulb and dew point temperatures are equal Page 4 GATE ME - 2003 Q.1 - Q.30 Carry One Mark Each 1. 2 0 sin x x Lt x ? is equal to (a) 0 (b) 8 (c) 1 (d) -1 2. The accuracy of Simpson’s rule quadrature for a step size h is (a) O ( ) 2 h (b) O ( ) h 3 (c) O ( ) 4 h (d) O ( ) 5 h 3. For the matrix 4 1 1 4 ? ? ? ? ? ? the eigen vaues are (a) 3 and -3 (b) -3 and -5 (c) 3 and 5 (d) 5 and 0 4. The second moment of a circular area about the diameter is given by (D is the diameter). (a) 4 4 D p (b) 4 16 D p (c) 4 32 D p (d) 4 64 D p 5. A concentrated load of P acts on a simply supported beam of span L at a distance 3 L from the left support. The bending moment at the point of application of the load is given by (a) 3 PL (b) 2 3 PL (c) 9 PL (d) 2 9 PL 6. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct? (a) Both rods elongate by the same amount (b) Mild steel rod elongates more than the cast iron rod (c) Cast iron rod elongates more than the mild steel rod (d) As the stresses are equal strains are also equal in both the rods GATE ME - 2003 7. Two beams, one having square cross section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then (a) maximum bending stress developed in both the beams is the same (b) the circular beam experiences more bending stress that the square one (c) the square beam experiences more bending stress than the circular one (d) as the material is same both the beams will experience same deformation 8. The mechanism used in a shaping machine is (a) a closed 4-bar chain having 4 revolute pairs (b) a closed 6-bar chain having 6 revolute pairs (c) a closed 4-bar chain having 2 revolute and 2 sliding pairs (d) an inversion of the single slider-crank chain 9. The lengths of the links of a 4-bar linkage with revolute pairs only are p,q,r and s units. Given that p < q < r < s. which of these links should be the fixed one, for obtaining a ‘double crank’ mechanism? (a) link of length p (b) link of length q (c) link of length r (d) link of length s 10. Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K 1 , K 2 , K 3 are the torsional stiffness of the respective shafts. The natural frequency of torsional oscillation of the disc is given by (a) 1 2 3 K K K J + + (b) ( ) 1 2 2 3 3 1 1 2 K K K K K K J K K + + + (c) ( ) 1 2 3 1 2 2 3 3 1 K K K J K K K K K K + + (d) ( ) 1 2 2 3 3 1 2 3 K K K K K K J K K + + + K 1 K 2 K 3 K 3 Fixed end Fixed end GATE ME - 2003 11. Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be (a) 120 MPa (b) 60 MPa (c) 30 MPa (d) 15 MPa 12. A wire rope is designated as 6 × 19 standard hoisting. The numbers 6 × 9 represent (a) diameter in millimeter × length in meter (b) diameter in centimeter × length in meter (c) number of strands × number of wires in each strand (d) number of wires in each strand × number of strands 13. A cylindrical body of cross-sectional area A, height H and density , s ? is immersed to a depth h in a liquid of density ?, and tied to the bottom with a string. The tension in the string is (a) ?ghA (b) ( ) s ghA ? ? - (c) ( ) s ghA ? ? - (d) ( ) s h H gA ? ? - 14. A 2 kW, 40 litre water heater is switched on for 20 minutes. The heat capacity P C for water is 4.2 kJ/kg K. Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is (a) 2.7 (b) 4.0 (c) 14.3 (d) 25.25 15. An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000W, respectively. The COP for the heat pump is (a) 7.5 (b) 6.5 (c) 4.0 (d) 3.0 16. A plate having 10 cm 2 area each side is hanging in the middle of a room of 100 m 2 total surface area. The plate temperature and emissivity are respectively 800 K and 0.6. the temperature and emissivity values for the surfaces of the room are 300K and 0.3 respectively. Boltzmann’s constant s=5.67×10 -8 W/m 2 K 4 . The total heat loss from the two surfaces of the plate is (a) 13.66 W (b) 27.32 W (c) 27.87 W (d) 13.66 W 17. For air with a relative humidity of 80% (a) the dry bulb temperature is less than the wet bulb temperature (b) the dew point temperature is less than wet bulb temperature (c) the dew point and wet bulb temperatures are equal (d) the dry bulb and dew point temperatures are equal GATE ME - 2003 18. For a spark ignition engine, the equivalence ratio (f) of mixture entering the combustion chamber has values. (a) f < 1 for idling and f > 1 for peak power conditions. (b) f > 1 for both idling and peak power conditions. (c) f > 1 for idling and f < 1 for peak power conditions. (d) f < 1 for both idling and peak power conditions. 19. A diesel engine is usually more efficient than a spark ignition engine because (a) diesel being a heavier hydrocarbon, releases more heat per kg than gasoline (b) the air standard efficiency of diesel cycle is higher than the Otto cycle, at a fixed compression ratio (c) the compression ratio of a diesel engine is higher than that of an SI engine (d) self ignition temperature of diesel is higher than that of gasoline 20. In a Rankine cycle, regeneration results in higher efficiency because (a) pressure inside the boiler increases (b) heat is added before steam enters the low pressure turbine (c) average temperature of heat addition in the boiler increases (d) total work delivered by the turbine increases 21. Considering the variation of static pressure and absolute velocity in an impulse stream turbine, across one row of moving blades (a) both pressure and velocity decrease (b) pressure decreases but velocity increases (c) pressure remains constant, while velocity increases (d) pressure remains constant, while velocity decreases 22. During heat treatment of steel, the hardness of various structures in increasing order is (a) martensite, fine pearlite, coarse pearlite, spherodite (b) fine pearlite, coarse pearlite, spherodite, martensite (c) martensite, coarse pearlite, fine pearlite, spherodite (d) spherodite, coarse pearlite, fine pearlite, martensite 23. Hardness of green sand mould increases with (a) increase in moisture content beyond 6 percent (b) increase in permeability (c) decrease in permeability (d) increase in both moisture content and permeability Page 5 GATE ME - 2003 Q.1 - Q.30 Carry One Mark Each 1. 2 0 sin x x Lt x ? is equal to (a) 0 (b) 8 (c) 1 (d) -1 2. The accuracy of Simpson’s rule quadrature for a step size h is (a) O ( ) 2 h (b) O ( ) h 3 (c) O ( ) 4 h (d) O ( ) 5 h 3. For the matrix 4 1 1 4 ? ? ? ? ? ? the eigen vaues are (a) 3 and -3 (b) -3 and -5 (c) 3 and 5 (d) 5 and 0 4. The second moment of a circular area about the diameter is given by (D is the diameter). (a) 4 4 D p (b) 4 16 D p (c) 4 32 D p (d) 4 64 D p 5. A concentrated load of P acts on a simply supported beam of span L at a distance 3 L from the left support. The bending moment at the point of application of the load is given by (a) 3 PL (b) 2 3 PL (c) 9 PL (d) 2 9 PL 6. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 Gpa. The other rod is made out of cast iron having he modulus of elasticity of 100 Gpa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct? (a) Both rods elongate by the same amount (b) Mild steel rod elongates more than the cast iron rod (c) Cast iron rod elongates more than the mild steel rod (d) As the stresses are equal strains are also equal in both the rods GATE ME - 2003 7. Two beams, one having square cross section and another circular cross-section, are subjected to the same amount of bending moment. If the cross sectional area as well as the material of both the beams are the same then (a) maximum bending stress developed in both the beams is the same (b) the circular beam experiences more bending stress that the square one (c) the square beam experiences more bending stress than the circular one (d) as the material is same both the beams will experience same deformation 8. The mechanism used in a shaping machine is (a) a closed 4-bar chain having 4 revolute pairs (b) a closed 6-bar chain having 6 revolute pairs (c) a closed 4-bar chain having 2 revolute and 2 sliding pairs (d) an inversion of the single slider-crank chain 9. The lengths of the links of a 4-bar linkage with revolute pairs only are p,q,r and s units. Given that p < q < r < s. which of these links should be the fixed one, for obtaining a ‘double crank’ mechanism? (a) link of length p (b) link of length q (c) link of length r (d) link of length s 10. Consider the arrangement shown in the figure below where J is the combined polar mass moment of inertia of the disc and the shafts. K 1 , K 2 , K 3 are the torsional stiffness of the respective shafts. The natural frequency of torsional oscillation of the disc is given by (a) 1 2 3 K K K J + + (b) ( ) 1 2 2 3 3 1 1 2 K K K K K K J K K + + + (c) ( ) 1 2 3 1 2 2 3 3 1 K K K J K K K K K K + + (d) ( ) 1 2 2 3 3 1 2 3 K K K K K K J K K + + + K 1 K 2 K 3 K 3 Fixed end Fixed end GATE ME - 2003 11. Maximum shear stress developed on the surface of a solid circular shaft under pure torsion is 240 MPa. If the shaft diameter is doubled then the maximum shear stress developed corresponding to the same torque will be (a) 120 MPa (b) 60 MPa (c) 30 MPa (d) 15 MPa 12. A wire rope is designated as 6 × 19 standard hoisting. The numbers 6 × 9 represent (a) diameter in millimeter × length in meter (b) diameter in centimeter × length in meter (c) number of strands × number of wires in each strand (d) number of wires in each strand × number of strands 13. A cylindrical body of cross-sectional area A, height H and density , s ? is immersed to a depth h in a liquid of density ?, and tied to the bottom with a string. The tension in the string is (a) ?ghA (b) ( ) s ghA ? ? - (c) ( ) s ghA ? ? - (d) ( ) s h H gA ? ? - 14. A 2 kW, 40 litre water heater is switched on for 20 minutes. The heat capacity P C for water is 4.2 kJ/kg K. Assuming all the electrical energy has gone into heating the water, increase of the water temperature in degree centigrade is (a) 2.7 (b) 4.0 (c) 14.3 (d) 25.25 15. An industrial heat pump operates between the temperatures of 27°C and –13°C. The rates of heat addition and heat rejection are 750 W and 1000W, respectively. The COP for the heat pump is (a) 7.5 (b) 6.5 (c) 4.0 (d) 3.0 16. A plate having 10 cm 2 area each side is hanging in the middle of a room of 100 m 2 total surface area. The plate temperature and emissivity are respectively 800 K and 0.6. the temperature and emissivity values for the surfaces of the room are 300K and 0.3 respectively. Boltzmann’s constant s=5.67×10 -8 W/m 2 K 4 . The total heat loss from the two surfaces of the plate is (a) 13.66 W (b) 27.32 W (c) 27.87 W (d) 13.66 W 17. For air with a relative humidity of 80% (a) the dry bulb temperature is less than the wet bulb temperature (b) the dew point temperature is less than wet bulb temperature (c) the dew point and wet bulb temperatures are equal (d) the dry bulb and dew point temperatures are equal GATE ME - 2003 18. For a spark ignition engine, the equivalence ratio (f) of mixture entering the combustion chamber has values. (a) f < 1 for idling and f > 1 for peak power conditions. (b) f > 1 for both idling and peak power conditions. (c) f > 1 for idling and f < 1 for peak power conditions. (d) f < 1 for both idling and peak power conditions. 19. A diesel engine is usually more efficient than a spark ignition engine because (a) diesel being a heavier hydrocarbon, releases more heat per kg than gasoline (b) the air standard efficiency of diesel cycle is higher than the Otto cycle, at a fixed compression ratio (c) the compression ratio of a diesel engine is higher than that of an SI engine (d) self ignition temperature of diesel is higher than that of gasoline 20. In a Rankine cycle, regeneration results in higher efficiency because (a) pressure inside the boiler increases (b) heat is added before steam enters the low pressure turbine (c) average temperature of heat addition in the boiler increases (d) total work delivered by the turbine increases 21. Considering the variation of static pressure and absolute velocity in an impulse stream turbine, across one row of moving blades (a) both pressure and velocity decrease (b) pressure decreases but velocity increases (c) pressure remains constant, while velocity increases (d) pressure remains constant, while velocity decreases 22. During heat treatment of steel, the hardness of various structures in increasing order is (a) martensite, fine pearlite, coarse pearlite, spherodite (b) fine pearlite, coarse pearlite, spherodite, martensite (c) martensite, coarse pearlite, fine pearlite, spherodite (d) spherodite, coarse pearlite, fine pearlite, martensite 23. Hardness of green sand mould increases with (a) increase in moisture content beyond 6 percent (b) increase in permeability (c) decrease in permeability (d) increase in both moisture content and permeability GATE ME - 2003 24. In Oxyacetylene gas welding, temperature at the inner cone of the flame is around (a) 3500°C (b) 3200°C (c) 2900°C (d) 2550°C 25. Cold working of steel is defined as working (a) at its re-crystallization temperature (b) above its re-crystallization temperature (c) below its re-crystallization temperature (d) at two thirds of the melting temperature of the metal 26. Quality screw threads are produced by (a) thread milling (b) thread chasing (c) thread cutting with single point tool (d) thread casting 27. As tool and work are not in contact in EDM process (a) no relative motion occurs between them (b) no water of tool occurs (c) no power is consumed during metal cutting (d) no force between tool and work occurs 28. The dimensional limits on a shaft of 25h7 are (a) 25.000, 25.021 mm (b) 25.000, 24.979 mm (c) 25.000, 25.007 mm (d) 25.000, 24.993 mm 29. When a cylinder is located in a Vee-block, the number of degrees of freedom which area arrested is (a) 2 (b) 4 (c) 7 (d) 8 30. The symbol used for Transport in work-study is (a) ? (b) T (c) (d) ?Read More

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