Page 1 GATE ME - 2000 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 If Z = f(x,y), dz is equal to (a) f f dx dy x y ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (b) f f dx dy y x ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (c) f f dx dy x y ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (d) f f dx dy y x ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? 1.2 ( ) ( ) 2 1 1 1 x x Lt x ? - - is: (a) 8 (b) 0 (c) 2 (d) 1 1.3 The solution of the differential equation 2 2 0 d y dy y dx dx + + = is (a) x x Ae Be - + (b) ( ) x e Ax B + (c) 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (d) 2 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.4 The three characteristic roots of the following matrix A 1 2 3 0 2 3 0 0 2 A ? ? ? ? = ? ? ? ? ? ? are (a) 1, 2, 3 (b) 1, 2, 2 (c) 1, 0, 0 (d) 0, 2, 3 1.5 Availability of a system at any given state is (a) a property of the system (b) the maximum work obtainable as the system goes to dead state (c) the total energy of the system (d) the maximum useful work obtainable as the system goes to dead state Page 2 GATE ME - 2000 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 If Z = f(x,y), dz is equal to (a) f f dx dy x y ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (b) f f dx dy y x ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (c) f f dx dy x y ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (d) f f dx dy y x ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? 1.2 ( ) ( ) 2 1 1 1 x x Lt x ? - - is: (a) 8 (b) 0 (c) 2 (d) 1 1.3 The solution of the differential equation 2 2 0 d y dy y dx dx + + = is (a) x x Ae Be - + (b) ( ) x e Ax B + (c) 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (d) 2 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.4 The three characteristic roots of the following matrix A 1 2 3 0 2 3 0 0 2 A ? ? ? ? = ? ? ? ? ? ? are (a) 1, 2, 3 (b) 1, 2, 2 (c) 1, 0, 0 (d) 0, 2, 3 1.5 Availability of a system at any given state is (a) a property of the system (b) the maximum work obtainable as the system goes to dead state (c) the total energy of the system (d) the maximum useful work obtainable as the system goes to dead state GATE ME - 2000 1.6 A steam turbine receives steam steadily at 10 bars with an enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to (a) 0 kJ (b) 50 kJ (c) 150 kJ (d) 250 kJ 1.7 In a vapour compression refrigeration system, liquid to suction heat exchanger is used to (a) keep the COP constant (b) prevent the liquid refrigerant from entering the compressor (c) subcool the liquid refrigerant leaving the condensor (d) subcool the vapour refrigerant from the evaporator 1.8 A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is covered with an insulation having a thermal conductivity of 1 W/mK. If the convective heat transfer coefficient between the surface of insulation and the surrounding air is 8 W/m 2 K, the critical radius of insulation is (a) 10 cm (b) 11 cm (c) 12.5 cm (d) 15 cm 1.9 Which of the following is a pressure compounded turbine? (a) Parsons (b) Curtis (c) Rateau (d) all the three 1.10 When the speed of a centrifugal pump is doubled, the power required to drive the pump will (a) increase 8 times (b) increase 4 times (c) double (d) remain the same 1.11 Global warming is caused by (a) ozone (b) carbon dioxide (c) nitrogen (d) carbon monoxide 1.12 Navier Strokes equation represents the conservation of (a) energy (b) mass (c) pressure (d) momentum 1.13 In a bi-axial stress problem, the stresses in x and y directions are 200 x MPa s = and 100 . y MPa s = the maximum principal stress in MPa, is (a) 50 (b) 100 (c) 150 (d) 200 Page 3 GATE ME - 2000 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 If Z = f(x,y), dz is equal to (a) f f dx dy x y ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (b) f f dx dy y x ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (c) f f dx dy x y ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (d) f f dx dy y x ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? 1.2 ( ) ( ) 2 1 1 1 x x Lt x ? - - is: (a) 8 (b) 0 (c) 2 (d) 1 1.3 The solution of the differential equation 2 2 0 d y dy y dx dx + + = is (a) x x Ae Be - + (b) ( ) x e Ax B + (c) 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (d) 2 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.4 The three characteristic roots of the following matrix A 1 2 3 0 2 3 0 0 2 A ? ? ? ? = ? ? ? ? ? ? are (a) 1, 2, 3 (b) 1, 2, 2 (c) 1, 0, 0 (d) 0, 2, 3 1.5 Availability of a system at any given state is (a) a property of the system (b) the maximum work obtainable as the system goes to dead state (c) the total energy of the system (d) the maximum useful work obtainable as the system goes to dead state GATE ME - 2000 1.6 A steam turbine receives steam steadily at 10 bars with an enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to (a) 0 kJ (b) 50 kJ (c) 150 kJ (d) 250 kJ 1.7 In a vapour compression refrigeration system, liquid to suction heat exchanger is used to (a) keep the COP constant (b) prevent the liquid refrigerant from entering the compressor (c) subcool the liquid refrigerant leaving the condensor (d) subcool the vapour refrigerant from the evaporator 1.8 A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is covered with an insulation having a thermal conductivity of 1 W/mK. If the convective heat transfer coefficient between the surface of insulation and the surrounding air is 8 W/m 2 K, the critical radius of insulation is (a) 10 cm (b) 11 cm (c) 12.5 cm (d) 15 cm 1.9 Which of the following is a pressure compounded turbine? (a) Parsons (b) Curtis (c) Rateau (d) all the three 1.10 When the speed of a centrifugal pump is doubled, the power required to drive the pump will (a) increase 8 times (b) increase 4 times (c) double (d) remain the same 1.11 Global warming is caused by (a) ozone (b) carbon dioxide (c) nitrogen (d) carbon monoxide 1.12 Navier Strokes equation represents the conservation of (a) energy (b) mass (c) pressure (d) momentum 1.13 In a bi-axial stress problem, the stresses in x and y directions are 200 x MPa s = and 100 . y MPa s = the maximum principal stress in MPa, is (a) 50 (b) 100 (c) 150 (d) 200 GATE ME - 2000 1.14 The ratio of tension on the tight side to that on the slack side in a flat belt drive is: (a) proportional to the product of coefficient of friction and lap angle (b) an exponential function of the product of coefficient of friction and lap angle (c) proportional to the lap angle (d) proportional to the coefficient of friction 1.15 The natural frequency of an undamped vibrating system is 100 rad/s. A damper with a damping factor of 0.8 is introduced into the system. The frequency of vibration of the damped system, in rad/s, is (a) 60 (b) 75 (c) 80 (d) 100 1.16 A steel shaft ‘A’ of diameter ‘d’ and length ‘l’ is subjected to a torque ‘T’. Anohter shaft ‘B’ made of aluminium of the same diameter ‘d’ and length 0.5 l is alsos subjected to the same torque ‘T’. The shear modulus of steel is 2.5 times the shear modulus of aluminium. The shear stress in the steel shaft is 100 MPa. The shear stress in the aluminium shaft, in MPa, is (a) 40 (b) 50 (c) 100 (d) 250 1.17 A 1.5 kW motor is running at 1440 rev/min. It is to be connected to a stirrer running at 36 rev/min. The gearing arrangement suitable for this application is (a) differential gear (b) helical gear (c) spur gear (d) worm gear 1.18 A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is (a) 0.5 (b) 5 (c) 15 (d) 150 1.19. Abrasive material used in grinding wheel selected for grinding ferrous alloys is: (a) silicon carbide (b) diamond (c) aluminium oxide (d) boron carbide 1.20. Cast steel crankshaft surface is hardened by (a) nitriding (b) normalizing (c) carburising (d) induction heating 1.21. Disposable patterns are made of (a) wood (b) rubber (c) metal (d) polystyrene Page 4 GATE ME - 2000 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 If Z = f(x,y), dz is equal to (a) f f dx dy x y ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (b) f f dx dy y x ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (c) f f dx dy x y ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (d) f f dx dy y x ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? 1.2 ( ) ( ) 2 1 1 1 x x Lt x ? - - is: (a) 8 (b) 0 (c) 2 (d) 1 1.3 The solution of the differential equation 2 2 0 d y dy y dx dx + + = is (a) x x Ae Be - + (b) ( ) x e Ax B + (c) 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (d) 2 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.4 The three characteristic roots of the following matrix A 1 2 3 0 2 3 0 0 2 A ? ? ? ? = ? ? ? ? ? ? are (a) 1, 2, 3 (b) 1, 2, 2 (c) 1, 0, 0 (d) 0, 2, 3 1.5 Availability of a system at any given state is (a) a property of the system (b) the maximum work obtainable as the system goes to dead state (c) the total energy of the system (d) the maximum useful work obtainable as the system goes to dead state GATE ME - 2000 1.6 A steam turbine receives steam steadily at 10 bars with an enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to (a) 0 kJ (b) 50 kJ (c) 150 kJ (d) 250 kJ 1.7 In a vapour compression refrigeration system, liquid to suction heat exchanger is used to (a) keep the COP constant (b) prevent the liquid refrigerant from entering the compressor (c) subcool the liquid refrigerant leaving the condensor (d) subcool the vapour refrigerant from the evaporator 1.8 A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is covered with an insulation having a thermal conductivity of 1 W/mK. If the convective heat transfer coefficient between the surface of insulation and the surrounding air is 8 W/m 2 K, the critical radius of insulation is (a) 10 cm (b) 11 cm (c) 12.5 cm (d) 15 cm 1.9 Which of the following is a pressure compounded turbine? (a) Parsons (b) Curtis (c) Rateau (d) all the three 1.10 When the speed of a centrifugal pump is doubled, the power required to drive the pump will (a) increase 8 times (b) increase 4 times (c) double (d) remain the same 1.11 Global warming is caused by (a) ozone (b) carbon dioxide (c) nitrogen (d) carbon monoxide 1.12 Navier Strokes equation represents the conservation of (a) energy (b) mass (c) pressure (d) momentum 1.13 In a bi-axial stress problem, the stresses in x and y directions are 200 x MPa s = and 100 . y MPa s = the maximum principal stress in MPa, is (a) 50 (b) 100 (c) 150 (d) 200 GATE ME - 2000 1.14 The ratio of tension on the tight side to that on the slack side in a flat belt drive is: (a) proportional to the product of coefficient of friction and lap angle (b) an exponential function of the product of coefficient of friction and lap angle (c) proportional to the lap angle (d) proportional to the coefficient of friction 1.15 The natural frequency of an undamped vibrating system is 100 rad/s. A damper with a damping factor of 0.8 is introduced into the system. The frequency of vibration of the damped system, in rad/s, is (a) 60 (b) 75 (c) 80 (d) 100 1.16 A steel shaft ‘A’ of diameter ‘d’ and length ‘l’ is subjected to a torque ‘T’. Anohter shaft ‘B’ made of aluminium of the same diameter ‘d’ and length 0.5 l is alsos subjected to the same torque ‘T’. The shear modulus of steel is 2.5 times the shear modulus of aluminium. The shear stress in the steel shaft is 100 MPa. The shear stress in the aluminium shaft, in MPa, is (a) 40 (b) 50 (c) 100 (d) 250 1.17 A 1.5 kW motor is running at 1440 rev/min. It is to be connected to a stirrer running at 36 rev/min. The gearing arrangement suitable for this application is (a) differential gear (b) helical gear (c) spur gear (d) worm gear 1.18 A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is (a) 0.5 (b) 5 (c) 15 (d) 150 1.19. Abrasive material used in grinding wheel selected for grinding ferrous alloys is: (a) silicon carbide (b) diamond (c) aluminium oxide (d) boron carbide 1.20. Cast steel crankshaft surface is hardened by (a) nitriding (b) normalizing (c) carburising (d) induction heating 1.21. Disposable patterns are made of (a) wood (b) rubber (c) metal (d) polystyrene GATE ME - 2000 1.22. Deep hole drilling of small diameter, say 0.2 mm is done with EDM by selecting the tool material as (a) copper wire (b) tungsten wire (c) brass wire (d) tungsten carbide 1.23. In computer aided drafting practice, an arc is defined by (a) two end points only (b) center and radius (c) radius and one end point (d) two end points and centre 1.24. In a time study exercise, the time observed for an activity was 54 seconds. The operator had a performance rating of 120. A personal time allowance of 10% is given. The standard time for the activity, in seconds, is (a) 54 (b) 60.8 (c) 72 (d) 58.32 1.25 Cellular manufacturing is suitable for (a) a single product in large volumes (b) one-off production of several varieties (c) products with similar features made in batches (d) large variety of products in large volumes. 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 Laplace transform of the function 2 sin 2t is: (a) ( ) 2 1 2 2 16 s s s ? ? - ? ? ? ? ? ? + ? ? ? ? (b) ( ) 2 16 s s + (c) ( ) 2 1 4 s s s ? ? - ? ? ? ? + (d) ( ) 2 4 s s + 2.2. The maximum value of the directional derivative of the function 2 2 2 2 3 5 x y z f = + + at a point (1,1,-1) is (a) 10 (b) -4 (c) 152 (d) 152 Page 5 GATE ME - 2000 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 If Z = f(x,y), dz is equal to (a) f f dx dy x y ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (b) f f dx dy y x ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? (c) f f dx dy x y ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? (d) f f dx dy y x ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? 1.2 ( ) ( ) 2 1 1 1 x x Lt x ? - - is: (a) 8 (b) 0 (c) 2 (d) 1 1.3 The solution of the differential equation 2 2 0 d y dy y dx dx + + = is (a) x x Ae Be - + (b) ( ) x e Ax B + (c) 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? (d) 2 3 3 cos cos 2 2 x e A x B x - ? ? ? ? ? ? ? ? + ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? 1.4 The three characteristic roots of the following matrix A 1 2 3 0 2 3 0 0 2 A ? ? ? ? = ? ? ? ? ? ? are (a) 1, 2, 3 (b) 1, 2, 2 (c) 1, 0, 0 (d) 0, 2, 3 1.5 Availability of a system at any given state is (a) a property of the system (b) the maximum work obtainable as the system goes to dead state (c) the total energy of the system (d) the maximum useful work obtainable as the system goes to dead state GATE ME - 2000 1.6 A steam turbine receives steam steadily at 10 bars with an enthalpy of 3000 kJ/kg and discharges at 1 bar with an enthalpy of 2700 kJ/kg. The work output is 250 kJ/kg. The changes in kinetic and potential energies are negligible. The heat transfer from the turbine casing to the surroundings is equal to (a) 0 kJ (b) 50 kJ (c) 150 kJ (d) 250 kJ 1.7 In a vapour compression refrigeration system, liquid to suction heat exchanger is used to (a) keep the COP constant (b) prevent the liquid refrigerant from entering the compressor (c) subcool the liquid refrigerant leaving the condensor (d) subcool the vapour refrigerant from the evaporator 1.8 A steel steam pipe 10 cm inner diameter and 11 cm outer diameter is covered with an insulation having a thermal conductivity of 1 W/mK. If the convective heat transfer coefficient between the surface of insulation and the surrounding air is 8 W/m 2 K, the critical radius of insulation is (a) 10 cm (b) 11 cm (c) 12.5 cm (d) 15 cm 1.9 Which of the following is a pressure compounded turbine? (a) Parsons (b) Curtis (c) Rateau (d) all the three 1.10 When the speed of a centrifugal pump is doubled, the power required to drive the pump will (a) increase 8 times (b) increase 4 times (c) double (d) remain the same 1.11 Global warming is caused by (a) ozone (b) carbon dioxide (c) nitrogen (d) carbon monoxide 1.12 Navier Strokes equation represents the conservation of (a) energy (b) mass (c) pressure (d) momentum 1.13 In a bi-axial stress problem, the stresses in x and y directions are 200 x MPa s = and 100 . y MPa s = the maximum principal stress in MPa, is (a) 50 (b) 100 (c) 150 (d) 200 GATE ME - 2000 1.14 The ratio of tension on the tight side to that on the slack side in a flat belt drive is: (a) proportional to the product of coefficient of friction and lap angle (b) an exponential function of the product of coefficient of friction and lap angle (c) proportional to the lap angle (d) proportional to the coefficient of friction 1.15 The natural frequency of an undamped vibrating system is 100 rad/s. A damper with a damping factor of 0.8 is introduced into the system. The frequency of vibration of the damped system, in rad/s, is (a) 60 (b) 75 (c) 80 (d) 100 1.16 A steel shaft ‘A’ of diameter ‘d’ and length ‘l’ is subjected to a torque ‘T’. Anohter shaft ‘B’ made of aluminium of the same diameter ‘d’ and length 0.5 l is alsos subjected to the same torque ‘T’. The shear modulus of steel is 2.5 times the shear modulus of aluminium. The shear stress in the steel shaft is 100 MPa. The shear stress in the aluminium shaft, in MPa, is (a) 40 (b) 50 (c) 100 (d) 250 1.17 A 1.5 kW motor is running at 1440 rev/min. It is to be connected to a stirrer running at 36 rev/min. The gearing arrangement suitable for this application is (a) differential gear (b) helical gear (c) spur gear (d) worm gear 1.18 A steel wheel of 600 mm diameter rolls on a horizontal steel rail. It carries a load of 500 N. The coefficient of rolling resistance is 0.3 mm. The force in N, necessary to roll the wheel along the rail is (a) 0.5 (b) 5 (c) 15 (d) 150 1.19. Abrasive material used in grinding wheel selected for grinding ferrous alloys is: (a) silicon carbide (b) diamond (c) aluminium oxide (d) boron carbide 1.20. Cast steel crankshaft surface is hardened by (a) nitriding (b) normalizing (c) carburising (d) induction heating 1.21. Disposable patterns are made of (a) wood (b) rubber (c) metal (d) polystyrene GATE ME - 2000 1.22. Deep hole drilling of small diameter, say 0.2 mm is done with EDM by selecting the tool material as (a) copper wire (b) tungsten wire (c) brass wire (d) tungsten carbide 1.23. In computer aided drafting practice, an arc is defined by (a) two end points only (b) center and radius (c) radius and one end point (d) two end points and centre 1.24. In a time study exercise, the time observed for an activity was 54 seconds. The operator had a performance rating of 120. A personal time allowance of 10% is given. The standard time for the activity, in seconds, is (a) 54 (b) 60.8 (c) 72 (d) 58.32 1.25 Cellular manufacturing is suitable for (a) a single product in large volumes (b) one-off production of several varieties (c) products with similar features made in batches (d) large variety of products in large volumes. 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 Laplace transform of the function 2 sin 2t is: (a) ( ) 2 1 2 2 16 s s s ? ? - ? ? ? ? ? ? + ? ? ? ? (b) ( ) 2 16 s s + (c) ( ) 2 1 4 s s s ? ? - ? ? ? ? + (d) ( ) 2 4 s s + 2.2. The maximum value of the directional derivative of the function 2 2 2 2 3 5 x y z f = + + at a point (1,1,-1) is (a) 10 (b) -4 (c) 152 (d) 152 GATE ME - 2000 2.3. ( ) 2 2 0 0 sin x y dxdy p p + ?? is: (a) 0 (b) p (c) 2 p (d) 2 2.4. In a manufacturing plant, the probability of making a defective bolt is 0.1. The mean and standard deviation of defective bolts in a total of 900 bolts are respectively (a) 90 and 9 (b) 9 and 90 (c) 81 and 9 (d) 9 and 81 2.5. In Fig.2.5 if the pressure of gas in bulb A is 50 cm Hg vacuum and 76 cm Hg, atm p = the height of column H is equal to (a) 26 cm (b) 50 cm (c) 76 cm (d) 126 cm 2.6. For a compressible fluid, sonic velocity is (a) a property of the fluid (b) always given by ( ) 1 2 RT ? , where ?, R and T are respectively the ratio of specific heats, gas constant and temperature in K (c) always given by 1 2 s p ? ? ? ? ? ? ? ? ? where p, ? and s are respectively pressure, density and entropy. (d) always greater than the velocity of fluid at any location. 2.7. When an ideal gas with constant specific heats is throttled adiabatically, with negligible changes in kinetic and potential energies (a) 0, 0 h T ? = ? = (b) 0, 0 h T ? > ? = (c) 0, 0 h s ? > ? > (d) 0, 0 h s ? = ? > where h, T and s represent respectively, enthalpy, temperature and entropy. 2.8. When atmospheric air is heated at constant pressure, its (a) humidity ratio does not change (b) relative humidity increases (c) dew point temperature does not change (d) wet bulb temperature increases P atm H A HgRead More

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