Page 1 GATE ME - 1996 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 , i i where 1 i = - , is given by (a) 0 (b) 2 e p - (c) 2 p (d) 1 1.2 The expression curl ( ) grad , where f f is a scalar function, is (a) equal to 2 f ? (b) equal to div (grad f) (c) a scalar of zero magnitude (d) a vector of zero magnitude 1.3 The one dimensional heat conviction partial differential equation 2 2 , T T t x ? ? = ? ? is (a) parabolic (b) hyperbolic (c) elliptic (d) mixed 1.4 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to (a) diagonal matrix (b) lower triangular matrix (c) upper triangular matrix (d) singular matrix 1.5 If the two principal strains at a point are 1000 × 10 -6 and –600 × 10 -6 , then the maximum shear strain is (a) 6 800 10 - × (b) 6 500 10 - × (c) 6 1600 10 - × (d) 6 200 10 - × 1.6 If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is (a) 0.50 (b) 0.75 (c) 0.25 (d) 0.87 1.7 In thick film hydrodynamic journal bearings, the coefficient of friction (a) increases with increase in load (b) is independent of load (c) decreases with increase in load (d) may increase or decrease with increase in load Page 2 GATE ME - 1996 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 , i i where 1 i = - , is given by (a) 0 (b) 2 e p - (c) 2 p (d) 1 1.2 The expression curl ( ) grad , where f f is a scalar function, is (a) equal to 2 f ? (b) equal to div (grad f) (c) a scalar of zero magnitude (d) a vector of zero magnitude 1.3 The one dimensional heat conviction partial differential equation 2 2 , T T t x ? ? = ? ? is (a) parabolic (b) hyperbolic (c) elliptic (d) mixed 1.4 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to (a) diagonal matrix (b) lower triangular matrix (c) upper triangular matrix (d) singular matrix 1.5 If the two principal strains at a point are 1000 × 10 -6 and –600 × 10 -6 , then the maximum shear strain is (a) 6 800 10 - × (b) 6 500 10 - × (c) 6 1600 10 - × (d) 6 200 10 - × 1.6 If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is (a) 0.50 (b) 0.75 (c) 0.25 (d) 0.87 1.7 In thick film hydrodynamic journal bearings, the coefficient of friction (a) increases with increase in load (b) is independent of load (c) decreases with increase in load (d) may increase or decrease with increase in load GATE ME - 1996 1.8 A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact (a) the velocity of ball A is 1 2 2 gh (b) the velocity of ball A is zero (c) the velocity of both ball is 1 2 2 gh (d) None of the above 1.9 The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to (a) shear force and bending moment (b) axial force (c) torsion (d) torsion and bending moment 1.10 A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque T. If the coefficient of kinetic friction is µ, the friction force from the ground on the wheel is: (a) µ mg (b) T r (c) zero (d) None of the above 1.11 In spur gears, the circle on which the involute is generated is called the (a) pitch circle (b) clearance circle (c) base circle (d) addendum circle 1.12 The specific heats of an ideal gas depend on its (a) temperature (b) pressure (c) volume (d) molecular weight and structure 1.13 For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is (a) p dv ? (b) v dp ? (c) T ds ? (d) s dT ? 1.14 A cycle consisting of two reversible isothermal processes and two reversible isobaric processes is known as (a) Atkinson cycle (b) Stirling cycle (c) Brayton cycle (d) Ericsson cycle 1.15 In flow through a pipe, the transition from laminar to turbulent flow does not depend on (a) velocity of the fluid (b) density of the fluid (c) diameter of the pipe (d) length of the pipe Page 3 GATE ME - 1996 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 , i i where 1 i = - , is given by (a) 0 (b) 2 e p - (c) 2 p (d) 1 1.2 The expression curl ( ) grad , where f f is a scalar function, is (a) equal to 2 f ? (b) equal to div (grad f) (c) a scalar of zero magnitude (d) a vector of zero magnitude 1.3 The one dimensional heat conviction partial differential equation 2 2 , T T t x ? ? = ? ? is (a) parabolic (b) hyperbolic (c) elliptic (d) mixed 1.4 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to (a) diagonal matrix (b) lower triangular matrix (c) upper triangular matrix (d) singular matrix 1.5 If the two principal strains at a point are 1000 × 10 -6 and –600 × 10 -6 , then the maximum shear strain is (a) 6 800 10 - × (b) 6 500 10 - × (c) 6 1600 10 - × (d) 6 200 10 - × 1.6 If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is (a) 0.50 (b) 0.75 (c) 0.25 (d) 0.87 1.7 In thick film hydrodynamic journal bearings, the coefficient of friction (a) increases with increase in load (b) is independent of load (c) decreases with increase in load (d) may increase or decrease with increase in load GATE ME - 1996 1.8 A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact (a) the velocity of ball A is 1 2 2 gh (b) the velocity of ball A is zero (c) the velocity of both ball is 1 2 2 gh (d) None of the above 1.9 The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to (a) shear force and bending moment (b) axial force (c) torsion (d) torsion and bending moment 1.10 A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque T. If the coefficient of kinetic friction is µ, the friction force from the ground on the wheel is: (a) µ mg (b) T r (c) zero (d) None of the above 1.11 In spur gears, the circle on which the involute is generated is called the (a) pitch circle (b) clearance circle (c) base circle (d) addendum circle 1.12 The specific heats of an ideal gas depend on its (a) temperature (b) pressure (c) volume (d) molecular weight and structure 1.13 For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is (a) p dv ? (b) v dp ? (c) T ds ? (d) s dT ? 1.14 A cycle consisting of two reversible isothermal processes and two reversible isobaric processes is known as (a) Atkinson cycle (b) Stirling cycle (c) Brayton cycle (d) Ericsson cycle 1.15 In flow through a pipe, the transition from laminar to turbulent flow does not depend on (a) velocity of the fluid (b) density of the fluid (c) diameter of the pipe (d) length of the pipe GATE ME - 1996 1.16 For a given heat flow and for the same thickness, the temperature drop across the material will be maximum for (a) copper (b) steel (c) glass-wool (d) refractory brick 1.17 When wet steam flows through a throttle valve and remains wet at exit (a) its temperature and quality increases (b) its temperature decreases but quality increases (c) its temperature increases but quality decreases (d) its temperature and quality decreases 1.18 The dimenation of surface tension is (a) 1 ML - (b) 2 1 LT - (c) 1 1 ML T - (d) 2 MT - 1.19. The rake angle in a drill (a) increases from centre to periphery (b) decreases from centre to perihery (c) remains constant (d) is irrelevant to the drilling operation 1.20. Light impurities in the molten metal are prevented from reaching the mould cavity by providing a (a) strainer (b) button well (c) skim bob (d) all of the above 1.21. Preheating before welding is done to (a) make the steel softer (b) burn away oil, grease, etc., from the plate surface (c) prevent cold cracks (d) prevent plate distortion 1.22. The fit on a hole-shaft system is specified as 117-s6. The type of fit is (a) clearance fit (b) running fit (sliding fit) (c) push fit (transition fit) (d) force fit (interference fit) 1.23. The iron-carbon diagram an the TTT curves are determined under (a) equilibrium and non-equilibrium conditions respectively (b) non-equilibrium and equilibrium conditions respectively (c) equilibrium conditions for both (d) non-equilibrium conditions for both Page 4 GATE ME - 1996 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 , i i where 1 i = - , is given by (a) 0 (b) 2 e p - (c) 2 p (d) 1 1.2 The expression curl ( ) grad , where f f is a scalar function, is (a) equal to 2 f ? (b) equal to div (grad f) (c) a scalar of zero magnitude (d) a vector of zero magnitude 1.3 The one dimensional heat conviction partial differential equation 2 2 , T T t x ? ? = ? ? is (a) parabolic (b) hyperbolic (c) elliptic (d) mixed 1.4 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to (a) diagonal matrix (b) lower triangular matrix (c) upper triangular matrix (d) singular matrix 1.5 If the two principal strains at a point are 1000 × 10 -6 and –600 × 10 -6 , then the maximum shear strain is (a) 6 800 10 - × (b) 6 500 10 - × (c) 6 1600 10 - × (d) 6 200 10 - × 1.6 If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is (a) 0.50 (b) 0.75 (c) 0.25 (d) 0.87 1.7 In thick film hydrodynamic journal bearings, the coefficient of friction (a) increases with increase in load (b) is independent of load (c) decreases with increase in load (d) may increase or decrease with increase in load GATE ME - 1996 1.8 A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact (a) the velocity of ball A is 1 2 2 gh (b) the velocity of ball A is zero (c) the velocity of both ball is 1 2 2 gh (d) None of the above 1.9 The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to (a) shear force and bending moment (b) axial force (c) torsion (d) torsion and bending moment 1.10 A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque T. If the coefficient of kinetic friction is µ, the friction force from the ground on the wheel is: (a) µ mg (b) T r (c) zero (d) None of the above 1.11 In spur gears, the circle on which the involute is generated is called the (a) pitch circle (b) clearance circle (c) base circle (d) addendum circle 1.12 The specific heats of an ideal gas depend on its (a) temperature (b) pressure (c) volume (d) molecular weight and structure 1.13 For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is (a) p dv ? (b) v dp ? (c) T ds ? (d) s dT ? 1.14 A cycle consisting of two reversible isothermal processes and two reversible isobaric processes is known as (a) Atkinson cycle (b) Stirling cycle (c) Brayton cycle (d) Ericsson cycle 1.15 In flow through a pipe, the transition from laminar to turbulent flow does not depend on (a) velocity of the fluid (b) density of the fluid (c) diameter of the pipe (d) length of the pipe GATE ME - 1996 1.16 For a given heat flow and for the same thickness, the temperature drop across the material will be maximum for (a) copper (b) steel (c) glass-wool (d) refractory brick 1.17 When wet steam flows through a throttle valve and remains wet at exit (a) its temperature and quality increases (b) its temperature decreases but quality increases (c) its temperature increases but quality decreases (d) its temperature and quality decreases 1.18 The dimenation of surface tension is (a) 1 ML - (b) 2 1 LT - (c) 1 1 ML T - (d) 2 MT - 1.19. The rake angle in a drill (a) increases from centre to periphery (b) decreases from centre to perihery (c) remains constant (d) is irrelevant to the drilling operation 1.20. Light impurities in the molten metal are prevented from reaching the mould cavity by providing a (a) strainer (b) button well (c) skim bob (d) all of the above 1.21. Preheating before welding is done to (a) make the steel softer (b) burn away oil, grease, etc., from the plate surface (c) prevent cold cracks (d) prevent plate distortion 1.22. The fit on a hole-shaft system is specified as 117-s6. The type of fit is (a) clearance fit (b) running fit (sliding fit) (c) push fit (transition fit) (d) force fit (interference fit) 1.23. The iron-carbon diagram an the TTT curves are determined under (a) equilibrium and non-equilibrium conditions respectively (b) non-equilibrium and equilibrium conditions respectively (c) equilibrium conditions for both (d) non-equilibrium conditions for both GATE ME - 1996 1.24. If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that (a) right hand side of the primal constraint can be altered without affecting the optimum solution (b) changing the right hand side of the primal constraint will disturb the optimum solution (c) the objective function is unbounded (d) the problem is degenerate 1.25 The individual human variability in time studies to determine the production standards is taken care of by (a) personal allowances (b) work allowances (c) rating factor (d) None of the above 2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 2.1 The eigen values of 1 1 1 1 1 1 1 1 1 ? ? ? ? ? ? ? ? ? ? are: (a) 0,0,0 (b) 0,0,1 (c) 0,0,3 (d) 1,1,1 2.2. A ball falls from a height of 1m, hits the ground and rebounds with half its velocity just before impact. Then after rising it falls and hits the ground and again rebounds with half its velocity just before impact, and so on. The total distance traveled by the ball till it comes to rest on the ground is (a) 2m (b) 5 3 m (c) 5 2 m (d) 5 4 m 2.3. The particular solution for the differential equation 2 2 3 2 5cos d y dy y x dx dx + + = is: (a) 0.5 cos x + 1.5 sin x (b) 1.5 cos x + 0.5 sin x (c) 1.5 sin x (d) 0.5 cos x 2.4. A solid shaft can resist a bending moment of 3.0 kNm and a twisting moment of 4.0 kNm together, then the maximum torque that can be applied is: (a) 7.0 kNm (b) 3.5 kNm (c) 4.5 kNm (d) 5.0 kNm Page 5 GATE ME - 1996 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 – 1.25) of ONE mark each. For each of these sub-questions, four possible alternatives (A, B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 1.1 , i i where 1 i = - , is given by (a) 0 (b) 2 e p - (c) 2 p (d) 1 1.2 The expression curl ( ) grad , where f f is a scalar function, is (a) equal to 2 f ? (b) equal to div (grad f) (c) a scalar of zero magnitude (d) a vector of zero magnitude 1.3 The one dimensional heat conviction partial differential equation 2 2 , T T t x ? ? = ? ? is (a) parabolic (b) hyperbolic (c) elliptic (d) mixed 1.4 In the Gauss elimination method for solving a system of linear algebraic equations, triangularization leads to (a) diagonal matrix (b) lower triangular matrix (c) upper triangular matrix (d) singular matrix 1.5 If the two principal strains at a point are 1000 × 10 -6 and –600 × 10 -6 , then the maximum shear strain is (a) 6 800 10 - × (b) 6 500 10 - × (c) 6 1600 10 - × (d) 6 200 10 - × 1.6 If the ratio of the diameter of rivet hole to the pitch of rivets is 0.25, then the tearing efficiency of the joint is (a) 0.50 (b) 0.75 (c) 0.25 (d) 0.87 1.7 In thick film hydrodynamic journal bearings, the coefficient of friction (a) increases with increase in load (b) is independent of load (c) decreases with increase in load (d) may increase or decrease with increase in load GATE ME - 1996 1.8 A ball A of mass m falls under gravity from a height h and strikes another ball B of mass m which supported at rest on a spring of stiffness k. Assume perfectly elastic impact. Immediately after the impact (a) the velocity of ball A is 1 2 2 gh (b) the velocity of ball A is zero (c) the velocity of both ball is 1 2 2 gh (d) None of the above 1.9 The bolts in a rigid flanged coupling connecting two shafts transmitting power are subjected to (a) shear force and bending moment (b) axial force (c) torsion (d) torsion and bending moment 1.10 A wheel of mass m and radius r is in accelerated rolling motion without slip under a steady axial torque T. If the coefficient of kinetic friction is µ, the friction force from the ground on the wheel is: (a) µ mg (b) T r (c) zero (d) None of the above 1.11 In spur gears, the circle on which the involute is generated is called the (a) pitch circle (b) clearance circle (c) base circle (d) addendum circle 1.12 The specific heats of an ideal gas depend on its (a) temperature (b) pressure (c) volume (d) molecular weight and structure 1.13 For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is (a) p dv ? (b) v dp ? (c) T ds ? (d) s dT ? 1.14 A cycle consisting of two reversible isothermal processes and two reversible isobaric processes is known as (a) Atkinson cycle (b) Stirling cycle (c) Brayton cycle (d) Ericsson cycle 1.15 In flow through a pipe, the transition from laminar to turbulent flow does not depend on (a) velocity of the fluid (b) density of the fluid (c) diameter of the pipe (d) length of the pipe GATE ME - 1996 1.16 For a given heat flow and for the same thickness, the temperature drop across the material will be maximum for (a) copper (b) steel (c) glass-wool (d) refractory brick 1.17 When wet steam flows through a throttle valve and remains wet at exit (a) its temperature and quality increases (b) its temperature decreases but quality increases (c) its temperature increases but quality decreases (d) its temperature and quality decreases 1.18 The dimenation of surface tension is (a) 1 ML - (b) 2 1 LT - (c) 1 1 ML T - (d) 2 MT - 1.19. The rake angle in a drill (a) increases from centre to periphery (b) decreases from centre to perihery (c) remains constant (d) is irrelevant to the drilling operation 1.20. Light impurities in the molten metal are prevented from reaching the mould cavity by providing a (a) strainer (b) button well (c) skim bob (d) all of the above 1.21. Preheating before welding is done to (a) make the steel softer (b) burn away oil, grease, etc., from the plate surface (c) prevent cold cracks (d) prevent plate distortion 1.22. The fit on a hole-shaft system is specified as 117-s6. The type of fit is (a) clearance fit (b) running fit (sliding fit) (c) push fit (transition fit) (d) force fit (interference fit) 1.23. The iron-carbon diagram an the TTT curves are determined under (a) equilibrium and non-equilibrium conditions respectively (b) non-equilibrium and equilibrium conditions respectively (c) equilibrium conditions for both (d) non-equilibrium conditions for both GATE ME - 1996 1.24. If at the optimum in a linear programming problem, a dual variable corresponding to a particular primal constraint is zero, then it means that (a) right hand side of the primal constraint can be altered without affecting the optimum solution (b) changing the right hand side of the primal constraint will disturb the optimum solution (c) the objective function is unbounded (d) the problem is degenerate 1.25 The individual human variability in time studies to determine the production standards is taken care of by (a) personal allowances (b) work allowances (c) rating factor (d) None of the above 2. This question consists of TWENTY-FIVE sub-questions (2.1 – 2.25) of TWO marks each. For each of these sub-questions, four possible alternatives (A,B, C and D) are given, out of which ONLY ONE is correct. Indicate the correct answer by darkening the appropriate bubble against the question number on the left hand side of the Objective Response Sheet (ORS). You may use the answer book provided for any rough work, if needed. 2.1 The eigen values of 1 1 1 1 1 1 1 1 1 ? ? ? ? ? ? ? ? ? ? are: (a) 0,0,0 (b) 0,0,1 (c) 0,0,3 (d) 1,1,1 2.2. A ball falls from a height of 1m, hits the ground and rebounds with half its velocity just before impact. Then after rising it falls and hits the ground and again rebounds with half its velocity just before impact, and so on. The total distance traveled by the ball till it comes to rest on the ground is (a) 2m (b) 5 3 m (c) 5 2 m (d) 5 4 m 2.3. The particular solution for the differential equation 2 2 3 2 5cos d y dy y x dx dx + + = is: (a) 0.5 cos x + 1.5 sin x (b) 1.5 cos x + 0.5 sin x (c) 1.5 sin x (d) 0.5 cos x 2.4. A solid shaft can resist a bending moment of 3.0 kNm and a twisting moment of 4.0 kNm together, then the maximum torque that can be applied is: (a) 7.0 kNm (b) 3.5 kNm (c) 4.5 kNm (d) 5.0 kNm GATE ME - 1996 2.5. A thick cylinder is subjected to an internal pressure of 60 MPa. If the hoop stress on the outer surface is 150 MPa, then the hoop stress on the internal surface is (a) 105 MPa (b) 180 MPa (c) 210 MPa (d) 135 MPa 2.6. AB and CD tow uniform and identical bars of mass 10 kg each, as shown in Fig.2.6. The hinges at A and B are frictionless. The assembly is released from rest and motion occurs in the vertical plane. At the instant that the hinge B passes the point B, the angle between the two bars will be (a) 60 degrees (b) 37.4 degrees (c) 30 degrees (d) 45 degrees 2.7. A rod of length 1 m is sliding in a corner as shown in Fig.2.7. At an instant when the rod makes an angle of 60 degrees with the horizontal plane, the velocity of point A on the rod is 1 m/s. The angular velocity of the rod at this instant. (a) 2 rad/s (b) 1.5 rad/s (c) 0.5 rad/s (d) 0.75 rad/s 2.8. A mass of 1 kg is suspended by means of 3 springs as shown in Fig.2.8. The spring constants 1 2 3 , and K K K are respectively 1 kN/m, 3 kN/m and 2 kN/m. The natural frequency of the system is approximately (a) 46.90 Hz (b) 52.44 Hz (c) 60.55 Hz (d) 77.46 Hz ° B D 30° 90° A B’ 1m C 0.5m 0.5m 60° 1m/s A 1m K 1 K 2 K 3 m=1kgRead More

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