Page 1 GATE ME â€“ 2002 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 Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight? (a) 5 36 (b) 5 18 (c) 1 4 (d) 1 3 1.2 Which of the following functions is not differentiable in the domain [-1,1]? (a) f(x)=x 2 (b) f(x)=x-1 (c) f(x)=2 (d) f(x)=maximum(x,-x) 1.3 A regression model is used to express a variable Y as a function of another variable X. this implies that (a) there is a causal relationship between Y and X (b) a value of X may be used to estimate a value of Y (c) values of X exactly determine values of Y (d) there is no causal relationship between Y and X 1.4 The principles of motion economy are mostly used while conducting (a) a method study on an operation (b) a time study on an operation (c) a financial appraisal of an operation (d) a feasibility study of the proposed manufacturing plant 1.5 The standard time of an operation while conducting a time study is (a) mean observed time + allowances (b) normal time + allowances (c) mean observed time × rating factor + allowances (d) normal time × rating factor + allowances 1.6 In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made? (a) (0.16,0.24) (b) (0.12,0.28) (c) (0.08,0.32) (d) none of these Page 2 GATE ME â€“ 2002 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 Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight? (a) 5 36 (b) 5 18 (c) 1 4 (d) 1 3 1.2 Which of the following functions is not differentiable in the domain [-1,1]? (a) f(x)=x 2 (b) f(x)=x-1 (c) f(x)=2 (d) f(x)=maximum(x,-x) 1.3 A regression model is used to express a variable Y as a function of another variable X. this implies that (a) there is a causal relationship between Y and X (b) a value of X may be used to estimate a value of Y (c) values of X exactly determine values of Y (d) there is no causal relationship between Y and X 1.4 The principles of motion economy are mostly used while conducting (a) a method study on an operation (b) a time study on an operation (c) a financial appraisal of an operation (d) a feasibility study of the proposed manufacturing plant 1.5 The standard time of an operation while conducting a time study is (a) mean observed time + allowances (b) normal time + allowances (c) mean observed time × rating factor + allowances (d) normal time × rating factor + allowances 1.6 In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made? (a) (0.16,0.24) (b) (0.12,0.28) (c) (0.08,0.32) (d) none of these GATE ME â€“ 2002 1.7 An item can be purchased for Rs.100. The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is (a) 50 (b) 100 (c) 200 (d) 400 1.8 The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth gear mechanism with 20° pressure angle is (a) 14 (b) 12 (c) 18 (d) 32 1.9 The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is (a) 2 (b) 3 (c) 4 (d) 5 1.10 The Coriolis component of acceleration is present in (a) 4-bar mechanisms with 4 turning pairs (b) shape mechanism (c) slider-crank mechanism (d) Scotch Yoke mechanism 1.11 The total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is a measure of (a) ductility (b) ultimate strength (c) stiffness (d) toughness 1.12 The number of components in a stress tensor defining stress at a point in three dimensions is (a) 3 (b) 4 (c) 6 (d) 9 1.13 A lead-screw with half nuts in a lathe, free to rotate in both directions has (a) V-threads (b) Whitworth threads (c) Buttress threads (d) Acme threads 1.14 the primary purpose of a sprue in a casting mould is to (a) feed the casting at a rate consistent with the rate of solidification (b) act as a reservoir for molten metal (c) feed molten metal from the pouring basin to the gate (d) help feed the casting until all solidification takes place 1.15 Hot rolling of mild steel is carried out (a) at re-crystallization temperature (b) between 100 C to 150 C (c) between re-crystallization temperature (d) above re-crystallization temperature Page 3 GATE ME â€“ 2002 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 Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight? (a) 5 36 (b) 5 18 (c) 1 4 (d) 1 3 1.2 Which of the following functions is not differentiable in the domain [-1,1]? (a) f(x)=x 2 (b) f(x)=x-1 (c) f(x)=2 (d) f(x)=maximum(x,-x) 1.3 A regression model is used to express a variable Y as a function of another variable X. this implies that (a) there is a causal relationship between Y and X (b) a value of X may be used to estimate a value of Y (c) values of X exactly determine values of Y (d) there is no causal relationship between Y and X 1.4 The principles of motion economy are mostly used while conducting (a) a method study on an operation (b) a time study on an operation (c) a financial appraisal of an operation (d) a feasibility study of the proposed manufacturing plant 1.5 The standard time of an operation while conducting a time study is (a) mean observed time + allowances (b) normal time + allowances (c) mean observed time × rating factor + allowances (d) normal time × rating factor + allowances 1.6 In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made? (a) (0.16,0.24) (b) (0.12,0.28) (c) (0.08,0.32) (d) none of these GATE ME â€“ 2002 1.7 An item can be purchased for Rs.100. The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is (a) 50 (b) 100 (c) 200 (d) 400 1.8 The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth gear mechanism with 20° pressure angle is (a) 14 (b) 12 (c) 18 (d) 32 1.9 The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is (a) 2 (b) 3 (c) 4 (d) 5 1.10 The Coriolis component of acceleration is present in (a) 4-bar mechanisms with 4 turning pairs (b) shape mechanism (c) slider-crank mechanism (d) Scotch Yoke mechanism 1.11 The total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is a measure of (a) ductility (b) ultimate strength (c) stiffness (d) toughness 1.12 The number of components in a stress tensor defining stress at a point in three dimensions is (a) 3 (b) 4 (c) 6 (d) 9 1.13 A lead-screw with half nuts in a lathe, free to rotate in both directions has (a) V-threads (b) Whitworth threads (c) Buttress threads (d) Acme threads 1.14 the primary purpose of a sprue in a casting mould is to (a) feed the casting at a rate consistent with the rate of solidification (b) act as a reservoir for molten metal (c) feed molten metal from the pouring basin to the gate (d) help feed the casting until all solidification takes place 1.15 Hot rolling of mild steel is carried out (a) at re-crystallization temperature (b) between 100 C to 150 C (c) between re-crystallization temperature (d) above re-crystallization temperature GATE ME â€“ 2002 1.16 Which of the following arc welding processes does not use consumable electrodes (a) GMAW (b) GTAW (c) Submerged Arc Welding (d) none of these 1.17 Trepanning is performed for (a) finishing a drilled hole (b) producing a large hole without drilling (c) truing a hole for alignment (d) enlarging a drilled hole 1.18 The hardness of a grinding wheel is determined by the (a) hardness of abrasive grains (b) ability of the bond to retain abrasives (c) hardness of the bond (d) ability of the grinding wheel to penetrate the work piece 1.19 A positive value of Joule-Thomson coefficient of a fluid means (a) temperature drops during throttling (b) temperature remains constant during throttling (c) temperature rises during throttling (d) none of these 1.20 If there are m physical quantities and n fundamental dimensions in a particular process, the number of non-dimensional parameters is (a) m+n (b) m×n (c) m-n (d) m/n 1.21 If x is the distance measured from the leading edge of a flat plate, the laminar boundary layer thickness varies as (a) 1 x (b) 4 5 x (c) 2 x (d) 1 2 x 1.22 Flow separation in flow past a solid object is caused by (a) a reduction of pressure to vapour pressure (b) a negative pressure gradient (c) a positive pressure gradient (d) the boundary layer thickness reducing to zero 1.23 A correctly designed convergent-divergent nozzle working at a designed load is (a) always isentropic (b) always choked (c) never choked (d) never isentropic Page 4 GATE ME â€“ 2002 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 Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight? (a) 5 36 (b) 5 18 (c) 1 4 (d) 1 3 1.2 Which of the following functions is not differentiable in the domain [-1,1]? (a) f(x)=x 2 (b) f(x)=x-1 (c) f(x)=2 (d) f(x)=maximum(x,-x) 1.3 A regression model is used to express a variable Y as a function of another variable X. this implies that (a) there is a causal relationship between Y and X (b) a value of X may be used to estimate a value of Y (c) values of X exactly determine values of Y (d) there is no causal relationship between Y and X 1.4 The principles of motion economy are mostly used while conducting (a) a method study on an operation (b) a time study on an operation (c) a financial appraisal of an operation (d) a feasibility study of the proposed manufacturing plant 1.5 The standard time of an operation while conducting a time study is (a) mean observed time + allowances (b) normal time + allowances (c) mean observed time × rating factor + allowances (d) normal time × rating factor + allowances 1.6 In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made? (a) (0.16,0.24) (b) (0.12,0.28) (c) (0.08,0.32) (d) none of these GATE ME â€“ 2002 1.7 An item can be purchased for Rs.100. The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is (a) 50 (b) 100 (c) 200 (d) 400 1.8 The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth gear mechanism with 20° pressure angle is (a) 14 (b) 12 (c) 18 (d) 32 1.9 The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is (a) 2 (b) 3 (c) 4 (d) 5 1.10 The Coriolis component of acceleration is present in (a) 4-bar mechanisms with 4 turning pairs (b) shape mechanism (c) slider-crank mechanism (d) Scotch Yoke mechanism 1.11 The total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is a measure of (a) ductility (b) ultimate strength (c) stiffness (d) toughness 1.12 The number of components in a stress tensor defining stress at a point in three dimensions is (a) 3 (b) 4 (c) 6 (d) 9 1.13 A lead-screw with half nuts in a lathe, free to rotate in both directions has (a) V-threads (b) Whitworth threads (c) Buttress threads (d) Acme threads 1.14 the primary purpose of a sprue in a casting mould is to (a) feed the casting at a rate consistent with the rate of solidification (b) act as a reservoir for molten metal (c) feed molten metal from the pouring basin to the gate (d) help feed the casting until all solidification takes place 1.15 Hot rolling of mild steel is carried out (a) at re-crystallization temperature (b) between 100 C to 150 C (c) between re-crystallization temperature (d) above re-crystallization temperature GATE ME â€“ 2002 1.16 Which of the following arc welding processes does not use consumable electrodes (a) GMAW (b) GTAW (c) Submerged Arc Welding (d) none of these 1.17 Trepanning is performed for (a) finishing a drilled hole (b) producing a large hole without drilling (c) truing a hole for alignment (d) enlarging a drilled hole 1.18 The hardness of a grinding wheel is determined by the (a) hardness of abrasive grains (b) ability of the bond to retain abrasives (c) hardness of the bond (d) ability of the grinding wheel to penetrate the work piece 1.19 A positive value of Joule-Thomson coefficient of a fluid means (a) temperature drops during throttling (b) temperature remains constant during throttling (c) temperature rises during throttling (d) none of these 1.20 If there are m physical quantities and n fundamental dimensions in a particular process, the number of non-dimensional parameters is (a) m+n (b) m×n (c) m-n (d) m/n 1.21 If x is the distance measured from the leading edge of a flat plate, the laminar boundary layer thickness varies as (a) 1 x (b) 4 5 x (c) 2 x (d) 1 2 x 1.22 Flow separation in flow past a solid object is caused by (a) a reduction of pressure to vapour pressure (b) a negative pressure gradient (c) a positive pressure gradient (d) the boundary layer thickness reducing to zero 1.23 A correctly designed convergent-divergent nozzle working at a designed load is (a) always isentropic (b) always choked (c) never choked (d) never isentropic GATE ME â€“ 2002 1.24 The value of Biot number is very small (less than 0.01) when (a) the convective resistance of the fluid is negligible (b) the conductive resistance of the fluid is negligible (c) the conductive resistance of the solid is negligible (d) none of these 1.25 For the same inlet and outlet temperatures of hot and cold fluids, the Log Mean Temperature Difference (LMTD) is (a) greater for parallel flow heat exchanger than for counter flow heat exchanger. (b) greater for counter flow heat exchanger than for parallel flow heat exchanger. (c) same for both parallel and counter flow heat exchangers. (d) dependent on the properties of the fluids. 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 The following set of equations has 3 2 4 2 2 2 5 x y z x y z x z + + = - + = - + = (a) no solution (b) a unique solution (c) multiple solutions (d) an inconsistency 2.2 The function ( ) 2 3 , 2 2 f x y x xy y = + - has (a) only one stationary point at (0,0) (b) two stationary points at (0,0) and 1 1 , 6 3 ? ? ? ? ? ? (c) two stationary points at (0,0) and (1,-1) (d) no stationary point 2.3 Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D? Page 5 GATE ME â€“ 2002 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 Two dice are thrown. What is the probability that the sum of the numbers on the two dice is eight? (a) 5 36 (b) 5 18 (c) 1 4 (d) 1 3 1.2 Which of the following functions is not differentiable in the domain [-1,1]? (a) f(x)=x 2 (b) f(x)=x-1 (c) f(x)=2 (d) f(x)=maximum(x,-x) 1.3 A regression model is used to express a variable Y as a function of another variable X. this implies that (a) there is a causal relationship between Y and X (b) a value of X may be used to estimate a value of Y (c) values of X exactly determine values of Y (d) there is no causal relationship between Y and X 1.4 The principles of motion economy are mostly used while conducting (a) a method study on an operation (b) a time study on an operation (c) a financial appraisal of an operation (d) a feasibility study of the proposed manufacturing plant 1.5 The standard time of an operation while conducting a time study is (a) mean observed time + allowances (b) normal time + allowances (c) mean observed time × rating factor + allowances (d) normal time × rating factor + allowances 1.6 In carrying out a work sampling study in a machine shop, it was found that a particular lathe was down for 20% of the time. What would be the 95% confidence interval of this estimate if 100 observations were made? (a) (0.16,0.24) (b) (0.12,0.28) (c) (0.08,0.32) (d) none of these GATE ME â€“ 2002 1.7 An item can be purchased for Rs.100. The ordering cost is Rs.200 and the inventory carrying cost is 10% of the item cost per annum. If the annual demand is 4000 units, the economic order quantity (in units) is (a) 50 (b) 100 (c) 200 (d) 400 1.8 The minimum number of teeth on the pinion to operate without interference in standard full height involute teeth gear mechanism with 20° pressure angle is (a) 14 (b) 12 (c) 18 (d) 32 1.9 The minimum number of links in a single degree-of-freedom planar mechanism with both higher and lower kinematic pairs is (a) 2 (b) 3 (c) 4 (d) 5 1.10 The Coriolis component of acceleration is present in (a) 4-bar mechanisms with 4 turning pairs (b) shape mechanism (c) slider-crank mechanism (d) Scotch Yoke mechanism 1.11 The total area under the stress-strain curve of a mild steel specimen tested up to failure under tension is a measure of (a) ductility (b) ultimate strength (c) stiffness (d) toughness 1.12 The number of components in a stress tensor defining stress at a point in three dimensions is (a) 3 (b) 4 (c) 6 (d) 9 1.13 A lead-screw with half nuts in a lathe, free to rotate in both directions has (a) V-threads (b) Whitworth threads (c) Buttress threads (d) Acme threads 1.14 the primary purpose of a sprue in a casting mould is to (a) feed the casting at a rate consistent with the rate of solidification (b) act as a reservoir for molten metal (c) feed molten metal from the pouring basin to the gate (d) help feed the casting until all solidification takes place 1.15 Hot rolling of mild steel is carried out (a) at re-crystallization temperature (b) between 100 C to 150 C (c) between re-crystallization temperature (d) above re-crystallization temperature GATE ME â€“ 2002 1.16 Which of the following arc welding processes does not use consumable electrodes (a) GMAW (b) GTAW (c) Submerged Arc Welding (d) none of these 1.17 Trepanning is performed for (a) finishing a drilled hole (b) producing a large hole without drilling (c) truing a hole for alignment (d) enlarging a drilled hole 1.18 The hardness of a grinding wheel is determined by the (a) hardness of abrasive grains (b) ability of the bond to retain abrasives (c) hardness of the bond (d) ability of the grinding wheel to penetrate the work piece 1.19 A positive value of Joule-Thomson coefficient of a fluid means (a) temperature drops during throttling (b) temperature remains constant during throttling (c) temperature rises during throttling (d) none of these 1.20 If there are m physical quantities and n fundamental dimensions in a particular process, the number of non-dimensional parameters is (a) m+n (b) m×n (c) m-n (d) m/n 1.21 If x is the distance measured from the leading edge of a flat plate, the laminar boundary layer thickness varies as (a) 1 x (b) 4 5 x (c) 2 x (d) 1 2 x 1.22 Flow separation in flow past a solid object is caused by (a) a reduction of pressure to vapour pressure (b) a negative pressure gradient (c) a positive pressure gradient (d) the boundary layer thickness reducing to zero 1.23 A correctly designed convergent-divergent nozzle working at a designed load is (a) always isentropic (b) always choked (c) never choked (d) never isentropic GATE ME â€“ 2002 1.24 The value of Biot number is very small (less than 0.01) when (a) the convective resistance of the fluid is negligible (b) the conductive resistance of the fluid is negligible (c) the conductive resistance of the solid is negligible (d) none of these 1.25 For the same inlet and outlet temperatures of hot and cold fluids, the Log Mean Temperature Difference (LMTD) is (a) greater for parallel flow heat exchanger than for counter flow heat exchanger. (b) greater for counter flow heat exchanger than for parallel flow heat exchanger. (c) same for both parallel and counter flow heat exchangers. (d) dependent on the properties of the fluids. 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 The following set of equations has 3 2 4 2 2 2 5 x y z x y z x z + + = - + = - + = (a) no solution (b) a unique solution (c) multiple solutions (d) an inconsistency 2.2 The function ( ) 2 3 , 2 2 f x y x xy y = + - has (a) only one stationary point at (0,0) (b) two stationary points at (0,0) and 1 1 , 6 3 ? ? ? ? ? ? (c) two stationary points at (0,0) and (1,-1) (d) no stationary point 2.3 Manish has to travel from A to D changing buses at stops B and C enroute. The maximum waiting time at either stop can be 8 minutes each, but any time of waiting up to 8 minutes is equally likely at both places. He can afford up to 13 minutes of total waiting time if he is to arrive at D on time. What is the probability that Manish will arrive late at D? GATE ME â€“ 2002 (a) 8 13 (b) 13 64 (c) 119 128 (d) 9 128 2.4 Arrivals at a telephone booth are considered to be Poisson, with an average time of 10 minutes between successive arrivals. The length of a phone call is distributed exponentially with mean 3 minutes. The probability that an arrival does not have to wait before service is (a) 0.3 (b) 0.5 (c) 0.7 (d) 0.9 2.5 The supply at three sources is 50, 40 and 60 units respectively whilst the demand at the four destinations is 20, 30, 10 and 50 units. In solving this transportation problem (a) a dummy source of capacity 40 units is needed (b) a dummy destination of capacity 40 units is needed (c) no solution exists as the problem is infeasible (d) none solution exists as the problem is degenerate 2.6 A project consists of three parallel paths with mean durations and variances of (10,4), (12,4) and (12,9) respectively. According to the standard PERT assumptions, the distribution of the project duration is (a) Beta with mean 10 and standard deviation 2 (b) Beta with mean 12 and standard deviation 2 (c) Normal with mean 10 and standard deviation 3 (d) Normal with mean 12 and standard deviation 3 2.7 The coupling used to connect two shafts with large angular misalignment is (a) a Flange coupling (b) an Oldhamâ€™s coupling (c) a Flexible bush coupling (d) a Hookeâ€™s joint 2.8 A static load is mounted at the center of a shaft rotating at uniform angular velocity. This shaft will be designed for (a) the maximum compressive stress (static) (b) the maximum tensile (static) (c) the maximum bending moment (static) (d) fatigue loading 2.9 Large speed reductions (greater than 20) in one stage of a gear train are possible through (a) Spur gearing (b) Worm gearing (c) Bevel gearing (d) Helical gearingRead More

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