Page 1 GATE ME â€“ 2005 Q.1 to Q.30 Carry One Mark Each. 1. Strokes theorem connects (a) a line integral and a surface integral (b) a surface integral and a volume integral (c) a line integral and a volume integral (d) gradient of a function and its surface integral 2. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is (a) 0.0036 (b) 0.1937 (c) 0.2234 (d) 0.3874 3. ( ) 6 7 sin sin a a x x dx - + ? is equal to (a) 6 0 2 sin a xdx ? (b) 7 0 2 sin a xdx ? (c) ( ) 6 7 0 2 sin sin a x x dx + ? (d) zero 4. A is a 3 × 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is (a) 1 (b) 2 (c) 3 (d) 4 5. Changing the order of the integration in the double integral ( ) 8 2 0 4 , x I f x y dydx = ?? leads to ( ) , . q s r p I f x y dxdy = ?? What is q? (a) 4y (b) 16y 2 (c) x (d) 8 6. The time variation of the position of a particle in rectilinear motion is given by 3 2 2 2 . x t t t - + + If ? is the velocity and a the acceleration of the particle in consistent units, the motion started with (a) ?=0, a=0 (b) ?=0, a=2 (c) ?=2 a=0 (d) ?=2 a=2 7. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is (a) zero (b) 2.5 N (c) 5 N (d) 25 N Page 2 GATE ME â€“ 2005 Q.1 to Q.30 Carry One Mark Each. 1. Strokes theorem connects (a) a line integral and a surface integral (b) a surface integral and a volume integral (c) a line integral and a volume integral (d) gradient of a function and its surface integral 2. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is (a) 0.0036 (b) 0.1937 (c) 0.2234 (d) 0.3874 3. ( ) 6 7 sin sin a a x x dx - + ? is equal to (a) 6 0 2 sin a xdx ? (b) 7 0 2 sin a xdx ? (c) ( ) 6 7 0 2 sin sin a x x dx + ? (d) zero 4. A is a 3 × 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is (a) 1 (b) 2 (c) 3 (d) 4 5. Changing the order of the integration in the double integral ( ) 8 2 0 4 , x I f x y dydx = ?? leads to ( ) , . q s r p I f x y dxdy = ?? What is q? (a) 4y (b) 16y 2 (c) x (d) 8 6. The time variation of the position of a particle in rectilinear motion is given by 3 2 2 2 . x t t t - + + If ? is the velocity and a the acceleration of the particle in consistent units, the motion started with (a) ?=0, a=0 (b) ?=0, a=2 (c) ?=2 a=0 (d) ?=2 a=2 7. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is (a) zero (b) 2.5 N (c) 5 N (d) 25 N GATE ME â€“ 2005 8. A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by and , r z s s respectively, then (a) 0, 0 r z s s = = (b) 0, 0 r z s s ? = (c) 0, 0 r z s s = ? (d) 0, 0 r z s s ? ? 9. Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have (a) equal deflections but not equal slopes (b) equal slopes but not equal deflections (c) equal slopes as well as equal deflections (d) neither equal slopes nor equal deflections 10. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is (a) 1 (b) 2 (c) 3 (d) 4 11. There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz respectively. There are mounted on test setups for conducting vibration experiments. If a loud pure not of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration? (a) P (b) Q (c) R (d) S 12. Which one of the following is a criterion in the design of hydrodynamic journal bearings? (a) Sommerfeld number (b) Rating life (c) Specific dynamic capacity (d) Rotation factor 13. The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively, then u x ? ? is equal to (a) x ? ? ? (b) x ? ? - ? (c) y ? ? ? (d) y ? ? - ? 14. In a case of one dimensional heat conduction in a medium with constant properties, T is the temperature at position x, at time t. then T t ? ? is proportional to (a) T x (b) T x ? ? (c) 2 T x t ? ? ? (d) 2 2 T x ? ? P Page 3 GATE ME â€“ 2005 Q.1 to Q.30 Carry One Mark Each. 1. Strokes theorem connects (a) a line integral and a surface integral (b) a surface integral and a volume integral (c) a line integral and a volume integral (d) gradient of a function and its surface integral 2. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is (a) 0.0036 (b) 0.1937 (c) 0.2234 (d) 0.3874 3. ( ) 6 7 sin sin a a x x dx - + ? is equal to (a) 6 0 2 sin a xdx ? (b) 7 0 2 sin a xdx ? (c) ( ) 6 7 0 2 sin sin a x x dx + ? (d) zero 4. A is a 3 × 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is (a) 1 (b) 2 (c) 3 (d) 4 5. Changing the order of the integration in the double integral ( ) 8 2 0 4 , x I f x y dydx = ?? leads to ( ) , . q s r p I f x y dxdy = ?? What is q? (a) 4y (b) 16y 2 (c) x (d) 8 6. The time variation of the position of a particle in rectilinear motion is given by 3 2 2 2 . x t t t - + + If ? is the velocity and a the acceleration of the particle in consistent units, the motion started with (a) ?=0, a=0 (b) ?=0, a=2 (c) ?=2 a=0 (d) ?=2 a=2 7. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is (a) zero (b) 2.5 N (c) 5 N (d) 25 N GATE ME â€“ 2005 8. A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by and , r z s s respectively, then (a) 0, 0 r z s s = = (b) 0, 0 r z s s ? = (c) 0, 0 r z s s = ? (d) 0, 0 r z s s ? ? 9. Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have (a) equal deflections but not equal slopes (b) equal slopes but not equal deflections (c) equal slopes as well as equal deflections (d) neither equal slopes nor equal deflections 10. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is (a) 1 (b) 2 (c) 3 (d) 4 11. There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz respectively. There are mounted on test setups for conducting vibration experiments. If a loud pure not of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration? (a) P (b) Q (c) R (d) S 12. Which one of the following is a criterion in the design of hydrodynamic journal bearings? (a) Sommerfeld number (b) Rating life (c) Specific dynamic capacity (d) Rotation factor 13. The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively, then u x ? ? is equal to (a) x ? ? ? (b) x ? ? - ? (c) y ? ? ? (d) y ? ? - ? 14. In a case of one dimensional heat conduction in a medium with constant properties, T is the temperature at position x, at time t. then T t ? ? is proportional to (a) T x (b) T x ? ? (c) 2 T x t ? ? ? (d) 2 2 T x ? ? P GATE ME â€“ 2005 T 1 E b?(W/m 2 .µm) T 2 T 3 ?(µm ) 15. The following four figures have been drawn to represent a fictitious thermodynamics cycle, on the p-v and T-s planes. According to the first law of thermodynamics, equal areas are enclosed by (a) Figures 1 and 2 (b) Figures 1 and 3 (c) Figures 1 and 4 (d) Figures 2 and 3 16. A p-v diagram has been obtained from a test on a reciprocating compressor. Which of the following represents that diagram? (a) (b) (c) (d) 17. The following figure was generated from experimental data relating spectral black body emissive power to wave length at three temperatures ( ) 1 2 3 1 2 3 , and . T T T T T T > < P v T s P v T s Figure 1 Figure 2 Figure 3 Figure p p out P in v p p out P in v v c p p out P in v v c p p out P in v v c Page 4 GATE ME â€“ 2005 Q.1 to Q.30 Carry One Mark Each. 1. Strokes theorem connects (a) a line integral and a surface integral (b) a surface integral and a volume integral (c) a line integral and a volume integral (d) gradient of a function and its surface integral 2. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is (a) 0.0036 (b) 0.1937 (c) 0.2234 (d) 0.3874 3. ( ) 6 7 sin sin a a x x dx - + ? is equal to (a) 6 0 2 sin a xdx ? (b) 7 0 2 sin a xdx ? (c) ( ) 6 7 0 2 sin sin a x x dx + ? (d) zero 4. A is a 3 × 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is (a) 1 (b) 2 (c) 3 (d) 4 5. Changing the order of the integration in the double integral ( ) 8 2 0 4 , x I f x y dydx = ?? leads to ( ) , . q s r p I f x y dxdy = ?? What is q? (a) 4y (b) 16y 2 (c) x (d) 8 6. The time variation of the position of a particle in rectilinear motion is given by 3 2 2 2 . x t t t - + + If ? is the velocity and a the acceleration of the particle in consistent units, the motion started with (a) ?=0, a=0 (b) ?=0, a=2 (c) ?=2 a=0 (d) ?=2 a=2 7. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is (a) zero (b) 2.5 N (c) 5 N (d) 25 N GATE ME â€“ 2005 8. A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by and , r z s s respectively, then (a) 0, 0 r z s s = = (b) 0, 0 r z s s ? = (c) 0, 0 r z s s = ? (d) 0, 0 r z s s ? ? 9. Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have (a) equal deflections but not equal slopes (b) equal slopes but not equal deflections (c) equal slopes as well as equal deflections (d) neither equal slopes nor equal deflections 10. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is (a) 1 (b) 2 (c) 3 (d) 4 11. There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz respectively. There are mounted on test setups for conducting vibration experiments. If a loud pure not of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration? (a) P (b) Q (c) R (d) S 12. Which one of the following is a criterion in the design of hydrodynamic journal bearings? (a) Sommerfeld number (b) Rating life (c) Specific dynamic capacity (d) Rotation factor 13. The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively, then u x ? ? is equal to (a) x ? ? ? (b) x ? ? - ? (c) y ? ? ? (d) y ? ? - ? 14. In a case of one dimensional heat conduction in a medium with constant properties, T is the temperature at position x, at time t. then T t ? ? is proportional to (a) T x (b) T x ? ? (c) 2 T x t ? ? ? (d) 2 2 T x ? ? P GATE ME â€“ 2005 T 1 E b?(W/m 2 .µm) T 2 T 3 ?(µm ) 15. The following four figures have been drawn to represent a fictitious thermodynamics cycle, on the p-v and T-s planes. According to the first law of thermodynamics, equal areas are enclosed by (a) Figures 1 and 2 (b) Figures 1 and 3 (c) Figures 1 and 4 (d) Figures 2 and 3 16. A p-v diagram has been obtained from a test on a reciprocating compressor. Which of the following represents that diagram? (a) (b) (c) (d) 17. The following figure was generated from experimental data relating spectral black body emissive power to wave length at three temperatures ( ) 1 2 3 1 2 3 , and . T T T T T T > < P v T s P v T s Figure 1 Figure 2 Figure 3 Figure p p out P in v p p out P in v v c p p out P in v v c p p out P in v v c GATE ME â€“ 2005 The conclusion is that the measurements are (a) correct because the maxima in b E ? show that correct trend (b) correct because Planckâ€™s law is satisfied (c) wrong because the Stefan Boltzmann law is not satisfied (d) wrong because Wienâ€™s displacement law is not satisfied 18. For a typical sample of ambient air (at 35°C, 75% relative humidity and standard atmospheric pressure), the amount of moisture in kg per kg of dry air will be approximately (a) 0.002 (b) 0.027 (c) 0.25 (d) 0.75 19. Water at 42° is sprayed into a stream of air at atmospheric pressure, dry bulb temperature of 40°C and a wet bulb temperature of 20°C. The air leaving the spray humidifier is not saturated. Which of the following statements is true? (a) Air gets cooled and humidified (b) Air gets heated and humidified (c) Air gets heated and dehumidified (d) Air gets cooled and dehumidified 20. Match the items of List I (Equipment) with the items of List II (Process) and select the correct answer using the given codes. List I (Equipment) List (Process) P â€“ Hot Chamber Machine 1 â€“ Cleaning Q â€“ Muller 2 â€“ Core making R â€“ Dielectric Baker 3 â€“ Die casting S â€“ Sand Blaster 4 â€“ Annealing 5 â€“ Sand mixing (a) P â€“ 2 Q â€“ 1 R â€“ 4 S - 5 (b) P â€“ 4 Q â€“ 2 R â€“ 3 S - 5 (c) P â€“ 4 Q â€“ 5 R â€“ 1 S - 2 (d) P â€“ 3 Q â€“ 5 R â€“ 2 S - 1 21. When the temperature of a solid metal increases. (a) strength of the metal decreases but ductility increases (b) both strength and ductility of the metal decrease (c) both strength and ductility of the metal increase (d) strength of the metal increases but ductility decreases Page 5 GATE ME â€“ 2005 Q.1 to Q.30 Carry One Mark Each. 1. Strokes theorem connects (a) a line integral and a surface integral (b) a surface integral and a volume integral (c) a line integral and a volume integral (d) gradient of a function and its surface integral 2. A lot has 10% defective items. Ten items are chosen randomly from this lot. The probability that exactly 2 of the chosen items are defective is (a) 0.0036 (b) 0.1937 (c) 0.2234 (d) 0.3874 3. ( ) 6 7 sin sin a a x x dx - + ? is equal to (a) 6 0 2 sin a xdx ? (b) 7 0 2 sin a xdx ? (c) ( ) 6 7 0 2 sin sin a x x dx + ? (d) zero 4. A is a 3 × 4 real matrix and A x = b is an inconsistent system of equations. The highest possible rank of A is (a) 1 (b) 2 (c) 3 (d) 4 5. Changing the order of the integration in the double integral ( ) 8 2 0 4 , x I f x y dydx = ?? leads to ( ) , . q s r p I f x y dxdy = ?? What is q? (a) 4y (b) 16y 2 (c) x (d) 8 6. The time variation of the position of a particle in rectilinear motion is given by 3 2 2 2 . x t t t - + + If ? is the velocity and a the acceleration of the particle in consistent units, the motion started with (a) ?=0, a=0 (b) ?=0, a=2 (c) ?=2 a=0 (d) ?=2 a=2 7. A simple pendulum of length 5m, with a bob of mass 1 kg, is in simple harmonic motion. As it passes through its mean position, the bob has a speed of 5 m/s. the net force on the bob at the mean position is (a) zero (b) 2.5 N (c) 5 N (d) 25 N GATE ME â€“ 2005 8. A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by and , r z s s respectively, then (a) 0, 0 r z s s = = (b) 0, 0 r z s s ? = (c) 0, 0 r z s s = ? (d) 0, 0 r z s s ? ? 9. Two identical cantilever beams are supported as shown, with their free ends in contact through a rigid roller. After the load P is applied, the free ends will have (a) equal deflections but not equal slopes (b) equal slopes but not equal deflections (c) equal slopes as well as equal deflections (d) neither equal slopes nor equal deflections 10. The number of degrees of freedom of a planar linkage with 8 links and 9 simple revolute joints is (a) 1 (b) 2 (c) 3 (d) 4 11. There are four samples P, Q, R and S, with natural frequencies 64, 96, 128 and 256 Hz respectively. There are mounted on test setups for conducting vibration experiments. If a loud pure not of frequency 144 Hz is produced by some instrument, which of the samples will show the most perceptible induced vibration? (a) P (b) Q (c) R (d) S 12. Which one of the following is a criterion in the design of hydrodynamic journal bearings? (a) Sommerfeld number (b) Rating life (c) Specific dynamic capacity (d) Rotation factor 13. The velocity components in the x and y directions of a two dimensional potential flow are u and v, respectively, then u x ? ? is equal to (a) x ? ? ? (b) x ? ? - ? (c) y ? ? ? (d) y ? ? - ? 14. In a case of one dimensional heat conduction in a medium with constant properties, T is the temperature at position x, at time t. then T t ? ? is proportional to (a) T x (b) T x ? ? (c) 2 T x t ? ? ? (d) 2 2 T x ? ? P GATE ME â€“ 2005 T 1 E b?(W/m 2 .µm) T 2 T 3 ?(µm ) 15. The following four figures have been drawn to represent a fictitious thermodynamics cycle, on the p-v and T-s planes. According to the first law of thermodynamics, equal areas are enclosed by (a) Figures 1 and 2 (b) Figures 1 and 3 (c) Figures 1 and 4 (d) Figures 2 and 3 16. A p-v diagram has been obtained from a test on a reciprocating compressor. Which of the following represents that diagram? (a) (b) (c) (d) 17. The following figure was generated from experimental data relating spectral black body emissive power to wave length at three temperatures ( ) 1 2 3 1 2 3 , and . T T T T T T > < P v T s P v T s Figure 1 Figure 2 Figure 3 Figure p p out P in v p p out P in v v c p p out P in v v c p p out P in v v c GATE ME â€“ 2005 The conclusion is that the measurements are (a) correct because the maxima in b E ? show that correct trend (b) correct because Planckâ€™s law is satisfied (c) wrong because the Stefan Boltzmann law is not satisfied (d) wrong because Wienâ€™s displacement law is not satisfied 18. For a typical sample of ambient air (at 35°C, 75% relative humidity and standard atmospheric pressure), the amount of moisture in kg per kg of dry air will be approximately (a) 0.002 (b) 0.027 (c) 0.25 (d) 0.75 19. Water at 42° is sprayed into a stream of air at atmospheric pressure, dry bulb temperature of 40°C and a wet bulb temperature of 20°C. The air leaving the spray humidifier is not saturated. Which of the following statements is true? (a) Air gets cooled and humidified (b) Air gets heated and humidified (c) Air gets heated and dehumidified (d) Air gets cooled and dehumidified 20. Match the items of List I (Equipment) with the items of List II (Process) and select the correct answer using the given codes. List I (Equipment) List (Process) P â€“ Hot Chamber Machine 1 â€“ Cleaning Q â€“ Muller 2 â€“ Core making R â€“ Dielectric Baker 3 â€“ Die casting S â€“ Sand Blaster 4 â€“ Annealing 5 â€“ Sand mixing (a) P â€“ 2 Q â€“ 1 R â€“ 4 S - 5 (b) P â€“ 4 Q â€“ 2 R â€“ 3 S - 5 (c) P â€“ 4 Q â€“ 5 R â€“ 1 S - 2 (d) P â€“ 3 Q â€“ 5 R â€“ 2 S - 1 21. When the temperature of a solid metal increases. (a) strength of the metal decreases but ductility increases (b) both strength and ductility of the metal decrease (c) both strength and ductility of the metal increase (d) strength of the metal increases but ductility decreases GATE ME â€“ 2005 22. The strength of a brazed joint (a) decreases with increase in gap between the two joining surfaces (b) increases with increase in gap between the two joining surfaces (c) decreases up to certain gap between the two joining surfaces beyond which it increases (d) increases up to certain gap between the two joining surfaces beyond which it decreases 23. A zigzag cavity in a block of high strength alloy is to be finish machined. This can be carried out by using (a) electric discharge machining (b) electro-chemical machining (c) laser beam machining (d) abrasive flow machining 24. In order to have interfernce fit, it is essential that the lower limit of the shaft should be (a) greater than the upper limit of the hole (b) lesser than the upper limit of the hole (c) greater than the lower limit of the hole (d) lesser than the lower limit of the hole 25. When 3-2-1 principle in used to support and locate a three dimensional work- piece during machining, the number of degrees of freedom that are restricted is (a) 7 (b) 8 (c) 9 (d) 10 26. The figure below shows a graph, which qualitatively relates cutting speed and cost per piece produced. Total Cost Cost per piece Cutting Speed 1 2 3Read More

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