Page 1 ?CE?Civil Engineering: Gate 2007 Paper 1 GATE: 2007 CE: CIVIL ENGINEERING Q.1 â€“ Q.20 Carry One Mark Each Q.1 The minimum and the maximum eigen values of the matrix 1 1 3 1 5 1 3 1 1 ? ? ? ? ? ? ? ? ? ? are -2 and 6, respectively. What is the other eigen value? (A) 5 (B) 3 (C) 1 (D) -1 Q.2 The degree of the differential equation 2 3 2 2 d x x dt + = 0 is (A) 0 (B) 1 (C) 2 (D) 3 Q.3 The solution for the differential equation 2 dy x y dx = with condition that y = 1 at x=0 is (A) 3 1 3 2 2 3 ( )ln( ) 4 ( )ln( ) ( ) 3 2 x x x x y e B y C y d y e = = + = = Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN Q.6 The stiffness coefficient k ij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. Q.7 For an isotropic material, the relationship between the Youngâ€™s modulus (E), shear modulus (G) and Poissonâ€™s ratio (µ) is given by ( ) ( ) ( ) ( ) 2(1 ) 2(1 ) (1 2 ) 2(1 ) E G E E A G B E C G D G µ µ µ µ = = = = + + + - Page 2 ?CE?Civil Engineering: Gate 2007 Paper 1 GATE: 2007 CE: CIVIL ENGINEERING Q.1 â€“ Q.20 Carry One Mark Each Q.1 The minimum and the maximum eigen values of the matrix 1 1 3 1 5 1 3 1 1 ? ? ? ? ? ? ? ? ? ? are -2 and 6, respectively. What is the other eigen value? (A) 5 (B) 3 (C) 1 (D) -1 Q.2 The degree of the differential equation 2 3 2 2 d x x dt + = 0 is (A) 0 (B) 1 (C) 2 (D) 3 Q.3 The solution for the differential equation 2 dy x y dx = with condition that y = 1 at x=0 is (A) 3 1 3 2 2 3 ( )ln( ) 4 ( )ln( ) ( ) 3 2 x x x x y e B y C y d y e = = + = = Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN Q.6 The stiffness coefficient k ij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. Q.7 For an isotropic material, the relationship between the Youngâ€™s modulus (E), shear modulus (G) and Poissonâ€™s ratio (µ) is given by ( ) ( ) ( ) ( ) 2(1 ) 2(1 ) (1 2 ) 2(1 ) E G E E A G B E C G D G µ µ µ µ = = = = + + + - ?CE?Civil Engineering: Gate 2007 Paper 2 Q.8 A clay soil sample is tested in triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m 2 . What will be the pore water pressure at a deviator stress of 40kN/m 2 ? (A) 0kN /m 2 (B) 20kN/m 2 (C) 40kN/m 2 (D) 60kN/m 2 Q.9 The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows. Penetration of sampler Number of blows 0-150mm 6 150-300mm 8 300-450mm 10 The observed N value is (A) 8 (B) 14 (C) 18 (D) 24 Q.10 The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain load intensity is 100 kN / m 2 below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (A) 25 (B) 100 (C) 200 (D) 400 Q.11 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate? (A) M 1 (B) M 2 (C) M 3 (D) S 1 Q.12 The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be (A) 10 days (B) 15days (C) 20days (D) 25days Q.13 As per the Laceyâ€™s method for design of alluvial channels, identity the true statement from the following (A) Wetted perimeter increases with an increase in design discharge (B) Hydraulic radius increases with an increase in silt factor. (C) Wetted perimeter decreases with an increase in design discharge. (D) Wetted perimeter increases with an increase in silt factor. Q.14 At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. Both the points are at the same elevation. The Page 3 ?CE?Civil Engineering: Gate 2007 Paper 1 GATE: 2007 CE: CIVIL ENGINEERING Q.1 â€“ Q.20 Carry One Mark Each Q.1 The minimum and the maximum eigen values of the matrix 1 1 3 1 5 1 3 1 1 ? ? ? ? ? ? ? ? ? ? are -2 and 6, respectively. What is the other eigen value? (A) 5 (B) 3 (C) 1 (D) -1 Q.2 The degree of the differential equation 2 3 2 2 d x x dt + = 0 is (A) 0 (B) 1 (C) 2 (D) 3 Q.3 The solution for the differential equation 2 dy x y dx = with condition that y = 1 at x=0 is (A) 3 1 3 2 2 3 ( )ln( ) 4 ( )ln( ) ( ) 3 2 x x x x y e B y C y d y e = = + = = Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN Q.6 The stiffness coefficient k ij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. Q.7 For an isotropic material, the relationship between the Youngâ€™s modulus (E), shear modulus (G) and Poissonâ€™s ratio (µ) is given by ( ) ( ) ( ) ( ) 2(1 ) 2(1 ) (1 2 ) 2(1 ) E G E E A G B E C G D G µ µ µ µ = = = = + + + - ?CE?Civil Engineering: Gate 2007 Paper 2 Q.8 A clay soil sample is tested in triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m 2 . What will be the pore water pressure at a deviator stress of 40kN/m 2 ? (A) 0kN /m 2 (B) 20kN/m 2 (C) 40kN/m 2 (D) 60kN/m 2 Q.9 The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows. Penetration of sampler Number of blows 0-150mm 6 150-300mm 8 300-450mm 10 The observed N value is (A) 8 (B) 14 (C) 18 (D) 24 Q.10 The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain load intensity is 100 kN / m 2 below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (A) 25 (B) 100 (C) 200 (D) 400 Q.11 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate? (A) M 1 (B) M 2 (C) M 3 (D) S 1 Q.12 The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be (A) 10 days (B) 15days (C) 20days (D) 25days Q.13 As per the Laceyâ€™s method for design of alluvial channels, identity the true statement from the following (A) Wetted perimeter increases with an increase in design discharge (B) Hydraulic radius increases with an increase in silt factor. (C) Wetted perimeter decreases with an increase in design discharge. (D) Wetted perimeter increases with an increase in silt factor. Q.14 At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. Both the points are at the same elevation. The ?CE?Civil Engineering: Gate 2007 Paper 3 fluid density is ?. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P 1 and P 2 at points 1 and 2 is (A) 0.5?V 2 (B) 1.5?V 2 (C) 2?V 2 (D) 3?V 2 Q.15 The presence of hardness in excess of permissible limit causes (A) Cardio Vascular problems (B) Skin discolouration (C) Calcium deficiency (D) Increased laundry expenses Q.16 The dispersion of pollutants in atmosphere is maximum when (A) environmental lapse rate is greater than adiabatic lapse rate. (B) environmental lapse rate is less than adiabatic lapse rate. (C) environmental lapse rate is equal to adiabatic lapse rate. (D) maximum mixing depth is equal to zero. Q.17 The alkalinity and the hardness of a water sample are 250mg/L and 350 mg/L as CaCo 3 , respectively. The water has (A) 350 mg/L carbonate hardness and zero non-carbonate hardness. (B) 250mg/L carbonate hardness and zero non-carbonate hardness. (C) 250mg/L carbonate hardness and 350 mg/L non-carbonate hardness. (D) 250mg/L carbonate hardness and 100 mg/L non-carbonate hardness. Q.18 The consistency and flow resistance of bitumen can be determined from the following. (A) Ductility test (B) Penetration test (C) Softening point Test (D) Viscosity test Q.19 If a two-lane national highway and a two-lane state highway intersect at right right angles, the number of potential conflict points at the intersection, assuming that both the roads are two-way is (A) 11 (B) 17 (C) 24 (D) 32 Q.20 In signal design as per Indian Roads Congress specifications, if the sum of the ratios of normal flows to saturation flow of two directional traffic flow is 0.50 and the total lost time per cycle is 10 seconds, the optimum cycle length in seconds is (A) 100 (B) 80 (C) 60 (D) 40 Q.21 to Q.75 carry two marks each Q.21 For what values of a and ß the following simultaneous equations have an infinite number of solutions? x + y + z = 5; x + 3y + 3z = 9; x + 2y + az = ß (A) 2,7 (B) 3,8 (C) 8,3 (D) 7,2 Page 4 ?CE?Civil Engineering: Gate 2007 Paper 1 GATE: 2007 CE: CIVIL ENGINEERING Q.1 â€“ Q.20 Carry One Mark Each Q.1 The minimum and the maximum eigen values of the matrix 1 1 3 1 5 1 3 1 1 ? ? ? ? ? ? ? ? ? ? are -2 and 6, respectively. What is the other eigen value? (A) 5 (B) 3 (C) 1 (D) -1 Q.2 The degree of the differential equation 2 3 2 2 d x x dt + = 0 is (A) 0 (B) 1 (C) 2 (D) 3 Q.3 The solution for the differential equation 2 dy x y dx = with condition that y = 1 at x=0 is (A) 3 1 3 2 2 3 ( )ln( ) 4 ( )ln( ) ( ) 3 2 x x x x y e B y C y d y e = = + = = Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN Q.6 The stiffness coefficient k ij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. Q.7 For an isotropic material, the relationship between the Youngâ€™s modulus (E), shear modulus (G) and Poissonâ€™s ratio (µ) is given by ( ) ( ) ( ) ( ) 2(1 ) 2(1 ) (1 2 ) 2(1 ) E G E E A G B E C G D G µ µ µ µ = = = = + + + - ?CE?Civil Engineering: Gate 2007 Paper 2 Q.8 A clay soil sample is tested in triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m 2 . What will be the pore water pressure at a deviator stress of 40kN/m 2 ? (A) 0kN /m 2 (B) 20kN/m 2 (C) 40kN/m 2 (D) 60kN/m 2 Q.9 The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows. Penetration of sampler Number of blows 0-150mm 6 150-300mm 8 300-450mm 10 The observed N value is (A) 8 (B) 14 (C) 18 (D) 24 Q.10 The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain load intensity is 100 kN / m 2 below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (A) 25 (B) 100 (C) 200 (D) 400 Q.11 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate? (A) M 1 (B) M 2 (C) M 3 (D) S 1 Q.12 The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be (A) 10 days (B) 15days (C) 20days (D) 25days Q.13 As per the Laceyâ€™s method for design of alluvial channels, identity the true statement from the following (A) Wetted perimeter increases with an increase in design discharge (B) Hydraulic radius increases with an increase in silt factor. (C) Wetted perimeter decreases with an increase in design discharge. (D) Wetted perimeter increases with an increase in silt factor. Q.14 At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. Both the points are at the same elevation. The ?CE?Civil Engineering: Gate 2007 Paper 3 fluid density is ?. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P 1 and P 2 at points 1 and 2 is (A) 0.5?V 2 (B) 1.5?V 2 (C) 2?V 2 (D) 3?V 2 Q.15 The presence of hardness in excess of permissible limit causes (A) Cardio Vascular problems (B) Skin discolouration (C) Calcium deficiency (D) Increased laundry expenses Q.16 The dispersion of pollutants in atmosphere is maximum when (A) environmental lapse rate is greater than adiabatic lapse rate. (B) environmental lapse rate is less than adiabatic lapse rate. (C) environmental lapse rate is equal to adiabatic lapse rate. (D) maximum mixing depth is equal to zero. Q.17 The alkalinity and the hardness of a water sample are 250mg/L and 350 mg/L as CaCo 3 , respectively. The water has (A) 350 mg/L carbonate hardness and zero non-carbonate hardness. (B) 250mg/L carbonate hardness and zero non-carbonate hardness. (C) 250mg/L carbonate hardness and 350 mg/L non-carbonate hardness. (D) 250mg/L carbonate hardness and 100 mg/L non-carbonate hardness. Q.18 The consistency and flow resistance of bitumen can be determined from the following. (A) Ductility test (B) Penetration test (C) Softening point Test (D) Viscosity test Q.19 If a two-lane national highway and a two-lane state highway intersect at right right angles, the number of potential conflict points at the intersection, assuming that both the roads are two-way is (A) 11 (B) 17 (C) 24 (D) 32 Q.20 In signal design as per Indian Roads Congress specifications, if the sum of the ratios of normal flows to saturation flow of two directional traffic flow is 0.50 and the total lost time per cycle is 10 seconds, the optimum cycle length in seconds is (A) 100 (B) 80 (C) 60 (D) 40 Q.21 to Q.75 carry two marks each Q.21 For what values of a and ß the following simultaneous equations have an infinite number of solutions? x + y + z = 5; x + 3y + 3z = 9; x + 2y + az = ß (A) 2,7 (B) 3,8 (C) 8,3 (D) 7,2 ?CE?Civil Engineering: Gate 2007 Paper 4 Q.22 A velocity vector is given as 2 2 5 2 3 V xyi y j yz k = + + r r r r . The divergence of this velocity vector at (1,1,1) is (A) 9 (B) 10 (C) 14 (D) 15 Q.23 A body originally at 60 0 C cools down to 40 0 C in 15minutes when kept in air at a temperature of 25 0 C. What will be the temperature of the body at the end of 30minutes? (A) 35.2 0 C (B) 31.5 0 C (C) 28.7 0 C (D) 15 0 C Q.24 The following equation needs to be numerically solved using the Newton- Raphson method. x 3 + 4x â€“ 9 = 0 The iterative equation for this purpose is (k indicates the iteration level) 3 2 1 1 2 2 2 2 1 1 2 2 9 3 4 ( ) ( ) 3 4 2 9 4 3 ( ) 3 4 ( ) 9 2 k k k k k k k k k k k k x x A x B x x x x C x x x D x x + + + + + + = = + + + = - + = + Q.25 Evaluate 0 sint t 8 ? dt ( ) ( ) ( ) ( ) 2 4 3 A B C D p p p p Q.26 Potential function f is given as 2 2 x y f = + . What will be the stream function (? ) with the condition ? = 0 at x = y = 0? (A) 2xy (B) x 2 + y 2 (C) x 2 â€“ y 2 (D) 2x 2 y 2 Q.27 The inverse of the 2 x 2 matrix 1 2 5 7 ? ? ? ? ? ? is 7 2 7 2 1 1 ( ) ( ) 5 1 5 1 3 3 A B - ? ? ? ? ? ? ? ? - ? ? ? ? 7 2 7 2 1 1 ( ) ( ) 5 1 5 1 3 3 C D - - - ? ? ? ? ? ? ? ? - - - ? ? ? ? Q.28 Given that one root of the equation x 3 -10x 2 +31x-30=0 is 5, the other two roots are (A) 2 and 3 (B) 2 and 4 (C) 3 and 4 (D) -2 and -3 Page 5 ?CE?Civil Engineering: Gate 2007 Paper 1 GATE: 2007 CE: CIVIL ENGINEERING Q.1 â€“ Q.20 Carry One Mark Each Q.1 The minimum and the maximum eigen values of the matrix 1 1 3 1 5 1 3 1 1 ? ? ? ? ? ? ? ? ? ? are -2 and 6, respectively. What is the other eigen value? (A) 5 (B) 3 (C) 1 (D) -1 Q.2 The degree of the differential equation 2 3 2 2 d x x dt + = 0 is (A) 0 (B) 1 (C) 2 (D) 3 Q.3 The solution for the differential equation 2 dy x y dx = with condition that y = 1 at x=0 is (A) 3 1 3 2 2 3 ( )ln( ) 4 ( )ln( ) ( ) 3 2 x x x x y e B y C y d y e = = + = = Q.4 An axially loaded bar is subjected to a normal stress of 173 MPa. The shear stress in the bar is (A) 75MPa (B) 86.5MPa (C) 100MPa (D) 122.3MPa Q.5 A steel column, pinned at both ends, has a buckling load of 200kN. If the column is restrained against lateral movement at its mid-height, its buckling load will be (A) 200kN (B) 283kN (C) 400kN (D) 800kN Q.6 The stiffness coefficient k ij indicates (A) force at i due to a unit deformation at j. (B) deformation at j due to a unit force at i. (C) deformation at i due to a unit force at j. (D) force at j due to a unit deformation at i. Q.7 For an isotropic material, the relationship between the Youngâ€™s modulus (E), shear modulus (G) and Poissonâ€™s ratio (µ) is given by ( ) ( ) ( ) ( ) 2(1 ) 2(1 ) (1 2 ) 2(1 ) E G E E A G B E C G D G µ µ µ µ = = = = + + + - ?CE?Civil Engineering: Gate 2007 Paper 2 Q.8 A clay soil sample is tested in triaxial apparatus in consolidated-drained conditions at a cell pressure of 100 kN/m 2 . What will be the pore water pressure at a deviator stress of 40kN/m 2 ? (A) 0kN /m 2 (B) 20kN/m 2 (C) 40kN/m 2 (D) 60kN/m 2 Q.9 The number of blows observed in a Standard Penetration Test (SPT) for different penetration depths are given as follows. Penetration of sampler Number of blows 0-150mm 6 150-300mm 8 300-450mm 10 The observed N value is (A) 8 (B) 14 (C) 18 (D) 24 Q.10 The vertical stress at some depth below the corner of a 2m x 3m rectangular footing due to a certain load intensity is 100 kN / m 2 below the centre of a 4m x 6m rectangular footing at the same depth and same load intensity? (A) 25 (B) 100 (C) 200 (D) 400 Q.11 There is a free overfall at the end of a long open channel. For a given flow rate, the critical depth is less than the normal depth. What gradually varied flow profile will occur in the channel for this flow rate? (A) M 1 (B) M 2 (C) M 3 (D) S 1 Q.12 The consumptive use of water for a crop during a particular stage of growth is 2.0mm / day. The maximum depth of available water is the root zone is 60mm. Irrigation is required when the amount of available water is 50% of the maximum available water in the root zone. Frequency of irrigation should be (A) 10 days (B) 15days (C) 20days (D) 25days Q.13 As per the Laceyâ€™s method for design of alluvial channels, identity the true statement from the following (A) Wetted perimeter increases with an increase in design discharge (B) Hydraulic radius increases with an increase in silt factor. (C) Wetted perimeter decreases with an increase in design discharge. (D) Wetted perimeter increases with an increase in silt factor. Q.14 At two points 1 and 2 in a pipeline the velocities are V and 2V, respectively. Both the points are at the same elevation. Both the points are at the same elevation. The ?CE?Civil Engineering: Gate 2007 Paper 3 fluid density is ?. The flow can be assumed to be in compressible, inviscid, steady and irrotational. The difference in pressures P 1 and P 2 at points 1 and 2 is (A) 0.5?V 2 (B) 1.5?V 2 (C) 2?V 2 (D) 3?V 2 Q.15 The presence of hardness in excess of permissible limit causes (A) Cardio Vascular problems (B) Skin discolouration (C) Calcium deficiency (D) Increased laundry expenses Q.16 The dispersion of pollutants in atmosphere is maximum when (A) environmental lapse rate is greater than adiabatic lapse rate. (B) environmental lapse rate is less than adiabatic lapse rate. (C) environmental lapse rate is equal to adiabatic lapse rate. (D) maximum mixing depth is equal to zero. Q.17 The alkalinity and the hardness of a water sample are 250mg/L and 350 mg/L as CaCo 3 , respectively. The water has (A) 350 mg/L carbonate hardness and zero non-carbonate hardness. (B) 250mg/L carbonate hardness and zero non-carbonate hardness. (C) 250mg/L carbonate hardness and 350 mg/L non-carbonate hardness. (D) 250mg/L carbonate hardness and 100 mg/L non-carbonate hardness. Q.18 The consistency and flow resistance of bitumen can be determined from the following. (A) Ductility test (B) Penetration test (C) Softening point Test (D) Viscosity test Q.19 If a two-lane national highway and a two-lane state highway intersect at right right angles, the number of potential conflict points at the intersection, assuming that both the roads are two-way is (A) 11 (B) 17 (C) 24 (D) 32 Q.20 In signal design as per Indian Roads Congress specifications, if the sum of the ratios of normal flows to saturation flow of two directional traffic flow is 0.50 and the total lost time per cycle is 10 seconds, the optimum cycle length in seconds is (A) 100 (B) 80 (C) 60 (D) 40 Q.21 to Q.75 carry two marks each Q.21 For what values of a and ß the following simultaneous equations have an infinite number of solutions? x + y + z = 5; x + 3y + 3z = 9; x + 2y + az = ß (A) 2,7 (B) 3,8 (C) 8,3 (D) 7,2 ?CE?Civil Engineering: Gate 2007 Paper 4 Q.22 A velocity vector is given as 2 2 5 2 3 V xyi y j yz k = + + r r r r . The divergence of this velocity vector at (1,1,1) is (A) 9 (B) 10 (C) 14 (D) 15 Q.23 A body originally at 60 0 C cools down to 40 0 C in 15minutes when kept in air at a temperature of 25 0 C. What will be the temperature of the body at the end of 30minutes? (A) 35.2 0 C (B) 31.5 0 C (C) 28.7 0 C (D) 15 0 C Q.24 The following equation needs to be numerically solved using the Newton- Raphson method. x 3 + 4x â€“ 9 = 0 The iterative equation for this purpose is (k indicates the iteration level) 3 2 1 1 2 2 2 2 1 1 2 2 9 3 4 ( ) ( ) 3 4 2 9 4 3 ( ) 3 4 ( ) 9 2 k k k k k k k k k k k k x x A x B x x x x C x x x D x x + + + + + + = = + + + = - + = + Q.25 Evaluate 0 sint t 8 ? dt ( ) ( ) ( ) ( ) 2 4 3 A B C D p p p p Q.26 Potential function f is given as 2 2 x y f = + . What will be the stream function (? ) with the condition ? = 0 at x = y = 0? (A) 2xy (B) x 2 + y 2 (C) x 2 â€“ y 2 (D) 2x 2 y 2 Q.27 The inverse of the 2 x 2 matrix 1 2 5 7 ? ? ? ? ? ? is 7 2 7 2 1 1 ( ) ( ) 5 1 5 1 3 3 A B - ? ? ? ? ? ? ? ? - ? ? ? ? 7 2 7 2 1 1 ( ) ( ) 5 1 5 1 3 3 C D - - - ? ? ? ? ? ? ? ? - - - ? ? ? ? Q.28 Given that one root of the equation x 3 -10x 2 +31x-30=0 is 5, the other two roots are (A) 2 and 3 (B) 2 and 4 (C) 3 and 4 (D) -2 and -3 ?CE?Civil Engineering: Gate 2007 Paper 5 Q.29 If the standard deviation of the spot speed of vehicles in a highway is 8.8 kmph and the mean speed of the vehicles is 33kmph, the coefficient of variation in speed is (A) 0.1517 (B) 0.1867 (C) 0.2666 (D) 0.3646 Q.30 A metal bar of length 100mm is inserted between two rigid supports and its temperature is increased by 10 0 C. If the coefficient of thermal expansion is 12 x 10 -6 per 0 C and the Youngâ€™s modulus is 2 x 10 5 MPa, the stress in the bar is (A) zero (B) 12MPa (C) 24MPa (D) 2400MPa Q.31 A rigid bar is suspended by three rods made of the same material as shown in the figure. The area and length of the central rod are 3A and L, respectively while that of the two outer rods are 2A and 2L respectively. If a downward force of 50kN is applied to the rigid bar, the forces in the central and each of the outer rods will be (A) 16.67 kN each (B) 30kN and 15kN (C) 30kN and 10kN (D) 21.4kN and 14.3kN Q.32 The maximum and minimum shear stresses in a hollow circular shaft of outer diameter 20mm and thickness 2mm, subjected to a torque of 92.7 N.m will be (A) 59 MPa and 47.2 MPa (B) 10MPa and 80MPa (C) 118 MPa and 160 MPa (D) 200 MPa and 160 MPa Q.33 The shear stress at the neutral axis in a beam of triangular section with a base of 40mm and height of 20mm, subjected to a shear force of 3kN is (A) 3MPa (B) 6MPa (C) 10MPa (D) 20MPa Q.34 U 1 and U 2 are the strain energies stored in a prismatic bar due to axial tensile forces P 1 and P 2 respectively. The strain energy stored in the same bar due to combined action of P 1 and P 2 will be (A) U = U 1 + U 2 (B) U = U 1 U 2 (C) U <U 1 + U 2 (D) U > 1 + U 2 Q.35 The right triangular truss is made of members having equal cross sectional area of 1550 mm 2 and Youngâ€™s modulus of 2 x 10 5 MPa. The horizontal deflection of the joint Q is P Q R 135kN 6m 4.5m (A) 2.47mm (B) 10.25mm (C) 14.1mm (D) 15.68mmRead More

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