Page 1 GATE ME - 1997 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 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 for 0 and for 0, y x x y x x = < = = then (a) dy dx is discontinuous at x = 0 (b) y is discontinuous at x = 0 (c) y is not defined at x = 0 (d) both y and dy dx are discontinuous at x = 0 1.2 The sum of the infinite series, 1 1 1 1 2 3 4 + + + +Kis (a) p (b) infinity (c) 4 (d) 2 4 p 1.3 For the following set of simultaneous equations: 1.5 0.5 2 4 2 3 9 7 5 10 x y x y z x y z - = + + = + + = (a) the solution is unique (b) infinitely many solutions exist (c) the equations are incompatible (d) finite number of multiple solutions exist 1.4 The order of error is the Simpsonâ€™s rule for numerical integration with a step size h is (a) h (b) 2 h (c) 3 h (d) 4 h 1.5 The temperature field in a body varies according to the equation ( ) 3 , 4 . T x y x xy = + The direction of fastest variation in temperature at the point (1,0) is given by (a) $ 3 8 i j + $ (b) i $ (c) $ 0.6 0.8 i j + $ (d) $ 0.5 0.866 i j + $ Page 2 GATE ME - 1997 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 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 for 0 and for 0, y x x y x x = < = = then (a) dy dx is discontinuous at x = 0 (b) y is discontinuous at x = 0 (c) y is not defined at x = 0 (d) both y and dy dx are discontinuous at x = 0 1.2 The sum of the infinite series, 1 1 1 1 2 3 4 + + + +Kis (a) p (b) infinity (c) 4 (d) 2 4 p 1.3 For the following set of simultaneous equations: 1.5 0.5 2 4 2 3 9 7 5 10 x y x y z x y z - = + + = + + = (a) the solution is unique (b) infinitely many solutions exist (c) the equations are incompatible (d) finite number of multiple solutions exist 1.4 The order of error is the Simpsonâ€™s rule for numerical integration with a step size h is (a) h (b) 2 h (c) 3 h (d) 4 h 1.5 The temperature field in a body varies according to the equation ( ) 3 , 4 . T x y x xy = + The direction of fastest variation in temperature at the point (1,0) is given by (a) $ 3 8 i j + $ (b) i $ (c) $ 0.6 0.8 i j + $ (d) $ 0.5 0.866 i j + $ GATE ME - 1997 1.6 In a radiative heat transfer, a gray surface is one (a) which appears gray to the eye (b) whose emissivity is independent of wavelength (c) which has reflectivity equal to zero (d) which appears equally bright from all directions 1.7 The specific speed of a centrifugal compressor is generally (a) higher than that of an axial compressor (b) less than that of a reciprocating compressor (c) independent of the type of compressor, but depends only on the size of the compressor (d) more than the specific speed of the reciprocating compressor but less that of the axial compressor 1.8 Which among the following is the boiler mounting? (a) Blow off cock (b) Feed pump (c) Economiser (d) Superheater 1.9 For an ideal gas the epression s s T p T T T ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? ? ? ? ? is always equal to (a) zero (b) p C C ? (c) R (d) RT 1.10 A system undergoes a state change from 1 to 2. According the second law of thermodynamics for the process to be feasible, the entropy change, S 2 â€“ S 1 of the system (a) is positive or zero (b) is negative or zero (c) is zero (d) can be positive, negative or zero 1.11 Kaplan turbine is (a) a high head mixed flow turbine (b) a low axial flow turbine (c) an outward flow reaction turbine (d) an impulse inward flow turbine 1.12 The alloying element mainly used to improve the endurance strength of steel materials is (a) Nickel (b) Vanadium (c) Molybdenum (d) Tungston Page 3 GATE ME - 1997 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 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 for 0 and for 0, y x x y x x = < = = then (a) dy dx is discontinuous at x = 0 (b) y is discontinuous at x = 0 (c) y is not defined at x = 0 (d) both y and dy dx are discontinuous at x = 0 1.2 The sum of the infinite series, 1 1 1 1 2 3 4 + + + +Kis (a) p (b) infinity (c) 4 (d) 2 4 p 1.3 For the following set of simultaneous equations: 1.5 0.5 2 4 2 3 9 7 5 10 x y x y z x y z - = + + = + + = (a) the solution is unique (b) infinitely many solutions exist (c) the equations are incompatible (d) finite number of multiple solutions exist 1.4 The order of error is the Simpsonâ€™s rule for numerical integration with a step size h is (a) h (b) 2 h (c) 3 h (d) 4 h 1.5 The temperature field in a body varies according to the equation ( ) 3 , 4 . T x y x xy = + The direction of fastest variation in temperature at the point (1,0) is given by (a) $ 3 8 i j + $ (b) i $ (c) $ 0.6 0.8 i j + $ (d) $ 0.5 0.866 i j + $ GATE ME - 1997 1.6 In a radiative heat transfer, a gray surface is one (a) which appears gray to the eye (b) whose emissivity is independent of wavelength (c) which has reflectivity equal to zero (d) which appears equally bright from all directions 1.7 The specific speed of a centrifugal compressor is generally (a) higher than that of an axial compressor (b) less than that of a reciprocating compressor (c) independent of the type of compressor, but depends only on the size of the compressor (d) more than the specific speed of the reciprocating compressor but less that of the axial compressor 1.8 Which among the following is the boiler mounting? (a) Blow off cock (b) Feed pump (c) Economiser (d) Superheater 1.9 For an ideal gas the epression s s T p T T T ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? ? ? ? ? is always equal to (a) zero (b) p C C ? (c) R (d) RT 1.10 A system undergoes a state change from 1 to 2. According the second law of thermodynamics for the process to be feasible, the entropy change, S 2 â€“ S 1 of the system (a) is positive or zero (b) is negative or zero (c) is zero (d) can be positive, negative or zero 1.11 Kaplan turbine is (a) a high head mixed flow turbine (b) a low axial flow turbine (c) an outward flow reaction turbine (d) an impulse inward flow turbine 1.12 The alloying element mainly used to improve the endurance strength of steel materials is (a) Nickel (b) Vanadium (c) Molybdenum (d) Tungston GATE ME - 1997 1.13 On completion of heat treatment, the resulting structure will have retained Austenite if (a) rate of cooling is greater than the critical cooling rate (b) rate of cooling is less than the critical cooling rate (c) marten site formation starting temperature is above the room temperature (d) marten site formatin finish temperature is below the room temperature 1.14 The efficiency of a power screw is maximum when the lead angle is (a) 2 2 r p - (b) 2 r p - (c) 2 r p (d) p - r Note: where r is the friction angle 1.15 To restore stable operating condition in a hydrodynamic journal bearing, when it encounters higher magnitude loads, (a) oil viscosity is to be decreased (b) oil viscosity is to be increased (c) oil viscosity index is to be increased (d) oil viscosity index is to be decreased 1.16 Total slip will occur in a belt drive when (a) angle of rest is zero (b) angle of creep is zero (c) angle of rest is greater than angle of creep (d) angle of creep is greater than angle of rest 1.17 To make a worm drive reversible, it is necessary to increase (a) centre distance (b) worm diameter factor (c) number of starts (d) reduction ratio 1.18 Helix angle of fast helix drill is normally (a) 35° (b) 60° (c) 90° (d) 5° 1.19. In a point to point control NC machine, the slides are positioned by an integrally mounted stepper motor drive. If the specification of the motor is 1°/pulse, and the pitch of the lead screw is 3.6 mm, what is the expected positioning accuracy? (a) 1 µm (b) 10 µm (c) 50 µm (d) 100 µm 1.20. Selection electrolyte for ECM is as follows: (a) non-passivating electrolyte for stock removal and passivating electrolyte for finish control (b) passivating electrolyte for stock removal and non-passivating electrolyte for finish control (c) selection of electrolyte is dependent on current density (d) electrolyte selection is based on tool-work electrodes Page 4 GATE ME - 1997 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 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 for 0 and for 0, y x x y x x = < = = then (a) dy dx is discontinuous at x = 0 (b) y is discontinuous at x = 0 (c) y is not defined at x = 0 (d) both y and dy dx are discontinuous at x = 0 1.2 The sum of the infinite series, 1 1 1 1 2 3 4 + + + +Kis (a) p (b) infinity (c) 4 (d) 2 4 p 1.3 For the following set of simultaneous equations: 1.5 0.5 2 4 2 3 9 7 5 10 x y x y z x y z - = + + = + + = (a) the solution is unique (b) infinitely many solutions exist (c) the equations are incompatible (d) finite number of multiple solutions exist 1.4 The order of error is the Simpsonâ€™s rule for numerical integration with a step size h is (a) h (b) 2 h (c) 3 h (d) 4 h 1.5 The temperature field in a body varies according to the equation ( ) 3 , 4 . T x y x xy = + The direction of fastest variation in temperature at the point (1,0) is given by (a) $ 3 8 i j + $ (b) i $ (c) $ 0.6 0.8 i j + $ (d) $ 0.5 0.866 i j + $ GATE ME - 1997 1.6 In a radiative heat transfer, a gray surface is one (a) which appears gray to the eye (b) whose emissivity is independent of wavelength (c) which has reflectivity equal to zero (d) which appears equally bright from all directions 1.7 The specific speed of a centrifugal compressor is generally (a) higher than that of an axial compressor (b) less than that of a reciprocating compressor (c) independent of the type of compressor, but depends only on the size of the compressor (d) more than the specific speed of the reciprocating compressor but less that of the axial compressor 1.8 Which among the following is the boiler mounting? (a) Blow off cock (b) Feed pump (c) Economiser (d) Superheater 1.9 For an ideal gas the epression s s T p T T T ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? ? ? ? ? is always equal to (a) zero (b) p C C ? (c) R (d) RT 1.10 A system undergoes a state change from 1 to 2. According the second law of thermodynamics for the process to be feasible, the entropy change, S 2 â€“ S 1 of the system (a) is positive or zero (b) is negative or zero (c) is zero (d) can be positive, negative or zero 1.11 Kaplan turbine is (a) a high head mixed flow turbine (b) a low axial flow turbine (c) an outward flow reaction turbine (d) an impulse inward flow turbine 1.12 The alloying element mainly used to improve the endurance strength of steel materials is (a) Nickel (b) Vanadium (c) Molybdenum (d) Tungston GATE ME - 1997 1.13 On completion of heat treatment, the resulting structure will have retained Austenite if (a) rate of cooling is greater than the critical cooling rate (b) rate of cooling is less than the critical cooling rate (c) marten site formation starting temperature is above the room temperature (d) marten site formatin finish temperature is below the room temperature 1.14 The efficiency of a power screw is maximum when the lead angle is (a) 2 2 r p - (b) 2 r p - (c) 2 r p (d) p - r Note: where r is the friction angle 1.15 To restore stable operating condition in a hydrodynamic journal bearing, when it encounters higher magnitude loads, (a) oil viscosity is to be decreased (b) oil viscosity is to be increased (c) oil viscosity index is to be increased (d) oil viscosity index is to be decreased 1.16 Total slip will occur in a belt drive when (a) angle of rest is zero (b) angle of creep is zero (c) angle of rest is greater than angle of creep (d) angle of creep is greater than angle of rest 1.17 To make a worm drive reversible, it is necessary to increase (a) centre distance (b) worm diameter factor (c) number of starts (d) reduction ratio 1.18 Helix angle of fast helix drill is normally (a) 35° (b) 60° (c) 90° (d) 5° 1.19. In a point to point control NC machine, the slides are positioned by an integrally mounted stepper motor drive. If the specification of the motor is 1°/pulse, and the pitch of the lead screw is 3.6 mm, what is the expected positioning accuracy? (a) 1 µm (b) 10 µm (c) 50 µm (d) 100 µm 1.20. Selection electrolyte for ECM is as follows: (a) non-passivating electrolyte for stock removal and passivating electrolyte for finish control (b) passivating electrolyte for stock removal and non-passivating electrolyte for finish control (c) selection of electrolyte is dependent on current density (d) electrolyte selection is based on tool-work electrodes GATE ME - 1997 1.21. Inter electrode gap in ECG is controlled by (a) controlling the pressure of electrolyte flow (b) controlling the applied static load (c) controlling the size of diamond particle in the wheel (d) controlling the texture of the work piece 1.22. The most commonly used criteria for measuring forecast error is (a) mean absolute deviation (b) mean absolute percentage error (c) mean standard error (d) mean square error 1.23. Setup costs do not include (a) labour cost of setting up machines (b) ordering cost of raw material (c) maintenance cost of the machines (d) cost of processing the work piece 1.24. A dummy activity is used in PERT network to describe (a) precedence relationship (b) necessary time delay (c) resource restriction (d) resource idleness 1.25 The cost of providing service in a queuing system increases with (a) increased mean time in the queue (b) increased arrival rate (c) decreased mean time in the queue (d) decreased arrival rate 2. This question consists of TWENTY-FIVE sub-questions (2.1 â€“ 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 A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is (a) 3 8 (b) 2 15 (c) 15 28 (d) 1 2 2.2. A triangle ABC consists of vertex points A(0,0) B(1,0) and C(0,1). The value of the integral 2xdxdy ?? over the triangle is (a) 1 (b) 1 3 (c) 1 8 (d) 1 9 Page 5 GATE ME - 1997 SECTION - A 1. This question consists of TWENTY-FIVE sub-questions (1.1 â€“ 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 for 0 and for 0, y x x y x x = < = = then (a) dy dx is discontinuous at x = 0 (b) y is discontinuous at x = 0 (c) y is not defined at x = 0 (d) both y and dy dx are discontinuous at x = 0 1.2 The sum of the infinite series, 1 1 1 1 2 3 4 + + + +Kis (a) p (b) infinity (c) 4 (d) 2 4 p 1.3 For the following set of simultaneous equations: 1.5 0.5 2 4 2 3 9 7 5 10 x y x y z x y z - = + + = + + = (a) the solution is unique (b) infinitely many solutions exist (c) the equations are incompatible (d) finite number of multiple solutions exist 1.4 The order of error is the Simpsonâ€™s rule for numerical integration with a step size h is (a) h (b) 2 h (c) 3 h (d) 4 h 1.5 The temperature field in a body varies according to the equation ( ) 3 , 4 . T x y x xy = + The direction of fastest variation in temperature at the point (1,0) is given by (a) $ 3 8 i j + $ (b) i $ (c) $ 0.6 0.8 i j + $ (d) $ 0.5 0.866 i j + $ GATE ME - 1997 1.6 In a radiative heat transfer, a gray surface is one (a) which appears gray to the eye (b) whose emissivity is independent of wavelength (c) which has reflectivity equal to zero (d) which appears equally bright from all directions 1.7 The specific speed of a centrifugal compressor is generally (a) higher than that of an axial compressor (b) less than that of a reciprocating compressor (c) independent of the type of compressor, but depends only on the size of the compressor (d) more than the specific speed of the reciprocating compressor but less that of the axial compressor 1.8 Which among the following is the boiler mounting? (a) Blow off cock (b) Feed pump (c) Economiser (d) Superheater 1.9 For an ideal gas the epression s s T p T T T ? ? ? ? ? ? ? ? ? - ? ? ? ? ? ? ? ? ? ? ? ? ? ? is always equal to (a) zero (b) p C C ? (c) R (d) RT 1.10 A system undergoes a state change from 1 to 2. According the second law of thermodynamics for the process to be feasible, the entropy change, S 2 â€“ S 1 of the system (a) is positive or zero (b) is negative or zero (c) is zero (d) can be positive, negative or zero 1.11 Kaplan turbine is (a) a high head mixed flow turbine (b) a low axial flow turbine (c) an outward flow reaction turbine (d) an impulse inward flow turbine 1.12 The alloying element mainly used to improve the endurance strength of steel materials is (a) Nickel (b) Vanadium (c) Molybdenum (d) Tungston GATE ME - 1997 1.13 On completion of heat treatment, the resulting structure will have retained Austenite if (a) rate of cooling is greater than the critical cooling rate (b) rate of cooling is less than the critical cooling rate (c) marten site formation starting temperature is above the room temperature (d) marten site formatin finish temperature is below the room temperature 1.14 The efficiency of a power screw is maximum when the lead angle is (a) 2 2 r p - (b) 2 r p - (c) 2 r p (d) p - r Note: where r is the friction angle 1.15 To restore stable operating condition in a hydrodynamic journal bearing, when it encounters higher magnitude loads, (a) oil viscosity is to be decreased (b) oil viscosity is to be increased (c) oil viscosity index is to be increased (d) oil viscosity index is to be decreased 1.16 Total slip will occur in a belt drive when (a) angle of rest is zero (b) angle of creep is zero (c) angle of rest is greater than angle of creep (d) angle of creep is greater than angle of rest 1.17 To make a worm drive reversible, it is necessary to increase (a) centre distance (b) worm diameter factor (c) number of starts (d) reduction ratio 1.18 Helix angle of fast helix drill is normally (a) 35° (b) 60° (c) 90° (d) 5° 1.19. In a point to point control NC machine, the slides are positioned by an integrally mounted stepper motor drive. If the specification of the motor is 1°/pulse, and the pitch of the lead screw is 3.6 mm, what is the expected positioning accuracy? (a) 1 µm (b) 10 µm (c) 50 µm (d) 100 µm 1.20. Selection electrolyte for ECM is as follows: (a) non-passivating electrolyte for stock removal and passivating electrolyte for finish control (b) passivating electrolyte for stock removal and non-passivating electrolyte for finish control (c) selection of electrolyte is dependent on current density (d) electrolyte selection is based on tool-work electrodes GATE ME - 1997 1.21. Inter electrode gap in ECG is controlled by (a) controlling the pressure of electrolyte flow (b) controlling the applied static load (c) controlling the size of diamond particle in the wheel (d) controlling the texture of the work piece 1.22. The most commonly used criteria for measuring forecast error is (a) mean absolute deviation (b) mean absolute percentage error (c) mean standard error (d) mean square error 1.23. Setup costs do not include (a) labour cost of setting up machines (b) ordering cost of raw material (c) maintenance cost of the machines (d) cost of processing the work piece 1.24. A dummy activity is used in PERT network to describe (a) precedence relationship (b) necessary time delay (c) resource restriction (d) resource idleness 1.25 The cost of providing service in a queuing system increases with (a) increased mean time in the queue (b) increased arrival rate (c) decreased mean time in the queue (d) decreased arrival rate 2. This question consists of TWENTY-FIVE sub-questions (2.1 â€“ 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 A box contains 5 black balls and 3 red balls. A total of three balls are picked from the box one after another, without replacing them back. The probability of getting two black balls and one red ball is (a) 3 8 (b) 2 15 (c) 15 28 (d) 1 2 2.2. A triangle ABC consists of vertex points A(0,0) B(1,0) and C(0,1). The value of the integral 2xdxdy ?? over the triangle is (a) 1 (b) 1 3 (c) 1 8 (d) 1 9 GATE ME - 1997 2.3. Refer to figure 2.3, the absolute pressure of gas A in the bulb is: (a) 771.2 mm Hg (b) 752.65 mm Hg (c) 767.35 mm Hg (d) 748.8 mm Hg 2.4. The Reynolds number for flow of a certain fluid in a circular tube is specified as 2500. What will be the Reynolds number when the tube diameter is increased by 20% and the fluid velocity is decreased by 40% keeping fluid the same? (a) 1200 (b) 1800 (c) 3600 (d) 200 2.5. In a certain heat exchanger, both the fluids have identical mass flow rate-specific heat product. The hot fluid enters at 76°C and leaves at 47°C and the cold fluid entering at 26°C leaves at 55°C. The effectiveness of the heat exchanger is (a) 0.16 (b) 0.58 (c) 0.72 (d) 1.0 2.6. The following data pertain to a single stage impulse steam turbine: Nozzle angle = 20° Blade velocity = 200 m/s Relative steam velocity at entry = 350 m/s Blade inlet = 30° Blade exit angle = 25° If blade friction is neglected, the work done per kg steam is: (a) 124 kJ (b) 164 kJ (c) 169 kJ (d) 174 kJ 2.7. Consider an actual regenerative Rankine cycle with one open feed water heater. For each kg steam entering the turbine, if m kg steam with a specific enthalpy of 1 h is bled from the turbine, and the specific enthalpy of liquid water entering the heater is 2 h , then 3 h specific enthalpy of saturated liquid leaving the heater is equal to (a) ( ) 1 2 1 mh h h - - (b) ( ) 1 2 1 h m h h - - (c) ( ) 2 2 1 h m h h - - (d) ( ) 2 2 1 mh h h - - A F E ?=13.6g/ml C B D P A 10 cm 5 cm 2 cmRead More

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