GATE-CE-2005 - Time Allowed:3 Hours GATE 2005 Maximum Marks...

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Unformatted text preview: Time Allowed :3 Hours GATE - 2005 Maximum Marks : 150 Q.1—Q.3t} Carry One Mark Each. —————____________ 1. nsid ' Co er the matrices XH .3], \{[‘1 .3} and pt2 ,3}_ The order of (P(XTY)" [’TJT will be (a) (2 >< 2) (it) (3 x 3) (c) (4x3)_ (12‘) (3x4) Consider a“ non-homogeneous system of linear equations representing mathematically an over— determined system. Such a system will be (a) consistent having a unique solution (1)) consistent having many solutions (cj' inconsistent having a unique solution ((0 inconsistent having no solution Whjch one of the following is NOT true for complex number Z, and 22 ? 'z 22' ur_l= 1 2 (“2: 22. Izzt (bJElZI'FZZlElZIl'l'lZQl ((1‘- lzl_22lslzll_lz2l (d); lZI+Zzl2+lzi*zzl2=zl‘ztl21'2l22l2 Which one of the following statement is NOT true? (a) The measure of skewness is dependent upon the amount of dispersion (b) In a symmetric distribution, the values of mean, mode and median are the same (:3) In a positively skewed distribution: mean > median 3» mode (d) In a negatively skewed distribution: mode > mean > median IS : 1343 — 1980 limits the minimum characteristic strength of prestressed concrete for post tensioncd works and pretension work as (a) 25 MPa, 30 MPa respectively (b) 25 MPa, 35 MPa respectively (c) 30 Ml’a, 35 MPa respecttvly (d) 30 MPa,4U MPa respectively The permisSible stress in axial tension sFl in steel member on the net effective area of the section shall not exceed the following value ((3, is the yield stress) (a) 0.30s, (b) 0.75ry (a) user}, (a) 0.5m}, 7. 10. 11. 12. The partial factor of IS : 4536—2000 is (rt) 1.50 (b) 1.15 (c) 0.8? (d) 0.446 The symmetry of stress tensor at a point in the body under equilibrium is obtained from (a) conservation of mass (in) force equilibrium equations (c) moment equilibrium equations safety for concrete as per . (5!) conservation of energy Theéomp'o'nents of strain tensor at a point in the pl __3 strain case can be obtained by measuring lon— gitudinal strain in following directions (it) along any two arbitrary directions (b) .along any three arbitrary directions (c) along two mutually orthogonal directions (d) along any arbitrary direction Considering beam as axially rigid, the degree of freedom of a plane frame shown below is (a) 9 (b) 8 (c) 7 I (d) 5 a For a linear elastic frame, if stiffness matrix is doubled, the existing stiffness matrix, the deflec- tion of the resulting frame will be (it) twice the existing value (b) hafftheexistingvaiue (c) the same as existing value (if) indeterminate value A clayey soil has a maximum dry density of 16 l<1\l/m3 and optimum moisture content of 12%. A contractor during the construction of core of an; earth dam obtained the dry density 15.2 kN/rn and watercontent 11%. This constmctijn isaccept- able because (it) the density is less than the maximum dry den- sity and water content is on dry side of Opll- mum (b) the compaction density is very low and water content is less than 12% I (c) the compaction is done on the dry Side of the optimum (d) both the dry density and water content of the compacted soil are within the destrable hunts _t.,.,.. f | I I3. [toot time method is used to determine 19, {.1} T, time factor {it} cw coefficient ufconsolidatiori {1:} er... coefficient at compressibility (d) mm coefficient of ~-'olume compressibility 1-4. Ncgattvr-nsitinfrictioni1in soil is considered when the pile is constructed through a (a) fill material (ti) dense coarse sand fr) over comolidated stiff clay (if) dense fine sand 15. There are two footings resting on the ground sur- I face. One footing is square of dimension ’3’. The’ ' other is strip footing of width ’3‘. Both of them are subjected to a loading intensity of q. The pressure intensity at any depth below the base of the foot- ing along the centertine would be 20. (it) equal in both footings” (b) large for square looting and small for strip footing (c) large for strip footing and small for square - footing ' (d) more for strip footing at shallow depth (5 B) and more for square footing at large depth (> 15} 16. An inert tracer is injected continuously from a point in an unsteady flow field. The locus of loca- tions of all the tracer particles at an instance of time represents. (til Streamline (t‘) Stepmtube (b) Pathline (d) Streakline 17. A horizontal bed channel is followed by a steep bed channel as shown in the figure. The gradu- ally—varied profiles over the horizontal and steep beds are 1? Humour-Merl (q) 1-12 and 51 respectively (b) Hg and ‘51 respectively (e) Hg and 82 respectively (d) H3 and 51 respectively 18. The reading of differential manometer of a Venturimeter, placed at 45: to the horizontal is 11 cm. [f the Ventruimeter is turned to horizontal posrtion, the manometer reading will be JE (d) 1] VIE cm (I?) zero (b) (C) l 1 cm 21. 22. The intensityr of rainfall and time interval Ola typi— cal storm are Time interval (minutes) Intensity of rainfall I (mm/minute) 0 ~ 10 0.7 I w — 20 - t..L_ 20 - 30 2.2 30 — 40' 1.5 40 — 50 1.2 so — 60 1.3 so — 70 0.9 m: 80 0.4 The maxim urn intensity of rainfall for 20 minutes duration of the storm is (a) 1.5 min/minute (b) 1.85 Him/minute (c) 2.2 mm/minute (d) 3.? mm/minute When the outflow from a storage reservoir is un— controlled as in a freely operatingspillway, the peak of outflow hydrograph occurs at ' (a) the point of inter—section of the inflow and outflow hydrographs (b) a'point, after the inter-section of the inflow and on tflow hydrographs (c) the tail of inflow hydrographs (d) a point, before the inter—section of the inflow and outflow hydrographs On which of the canal systems, R.G. Kennedy, executive engineer in the Punjab Irrigation Department made his observations for proposing his theory on stable channels? (it) Krishna Western Delta canals (b) Lower‘Bari Doab canals - (c) Lower Chenab canals (d) Upper Bari Doab canals Which one of die following equations reprsents the downstream profile of Ogee spillway with vertical upstream lace? {(x, y} are the coordinates of the point on the downstream profile with origin at the crest of the spillway and H‘1 is the design head} y I 1.35 —=—0.5_ (“3 Hr .\' 23. 24. 25. 26. 2?. In aerotiic environment. nitrosommas comr [9} NH 1 to N02 (it) N02" to NO;' (c) NH; Io N10 (at) NO:w to t—lt'xtC)J Total Kielclnhl nitrogen is a measure of ert (a) total organicnitrogen (b) total organic and ammonia nitrogen (r) lotalammonia nitrogen (at) total inorganic and ammonia nitrogen TCU is equivalent to the colour produced by {a} I mg/Ltif chlorplatinate ion (is) I I'l‘tg/LOI platinum ion (c) tmg/L Platinum in form ofchlorplatinate ion (d) ] mg/Lof organo—chloxplatinate ion Bulking sludge refers to having (a) WM q 0.3m (b) 0.37:: 4 WM < (la/d (c) F/M = zero (d) F/M > [LG/d Pradhan Mantri Gram Sadak _Yojna (PMGSY). launched in the year 2000, aims to provide rural connectivity with all—weather roads. I t is proposed - to connect the habitations in plain areas of 29. population more than 500 persons by the year in) 2005 (b) 2007 (c) 2010 (d) 2012 Group i contains some properties of Bitumen. Group it gives a list of Laboratory Tests conducted on Bi lumen to determine the properties. Match the property with the correSpond'mg test Group I 1". Resistance to flow Q. Ability to deform tinder load R. Safety Group [I l.'Ductility test 2. Penetration test 3. Flash and Fire point test (a) P—2,Q—l,R—3 .(btP-ZtQ—E'IR" (c) P—l,Q—2,R—3 td)P~3.Q~LR-2 The length of Summit Curve on a two lane two ' way highway depends upon (:1) allowable rate of change of centrifugal acceleration (it) coefficient of lateral friction (5') required Stopping Sight Distance (fl! required Overtaking Sight Distance 30. 3'1. 32. 33. Bituminous concrete is .1 mm: romprtsing of ta} line aggregate, lilier and bitumen (it) Fine aggregate and bitumen .. (t'J coarse aggregate, tine aggregate, iillcr and bi— tu men (rt) coarse aggregate. tiller and bitumen Q.31-Q.8fl Carry Two Marks Each ——_____________ Consider the system of equations Amy-try: vi: '= In; x t. where, l is a sca in r. Let (IL, .‘t‘l-l be an {tigers—pair of an eigen value and its corresponding eigen vector for real matrix A. Let [be a (it ’n) unit matrix. Which one of the [oi—- Zowing statement is NOT correct? (a) Fora homogeneousu x nsystemoflinear equa- tions. (A ~ lltx = 0 having a nontriviat solu- tion, the rank of {rt-ll) is less than n. (b) For matrix A“, to being a positive integer, (PL?.I:11) will be the eigen-pair for all i. (c) [EAT=A", then |1i| = 1 foralli (rt) it AT: A, then i i is real for at! i Transformation to linear form by substituting v = y"" of the equation i—i’ +p(r}_y = q(t)_if' ; tr > D will be (it? . {a} E - [1—iin\*=(i —ntq do (1;) E +(] —it)prr=(1 +1”in (c) % +.(l +nipv =(1-rth {it} (it) Fr- + (l + nipv = (t + n)q A rail engine accelerates from its stationary postion for 3 seconds and travels a distance of 230 m. Ac- cording to the Mean Value Theorem, the speed— ometer at a certain time during acceleration must read exactly (rt) 0 km / h (c) 3’5 km/h (it) 3 km (a) 1'26 km/h 38. a 34. The solution of i.gdi+171,r:o: _v {0) = 1, d1" (31' ‘ in; p rr --' — =0 ' . — ' ' ML!) In the rangeflcxc 4 is given by . | (a) if" [cos 4.1- + Z sin 41'] (b) 1"" [cos 4x - isin 4x] (6) ("[cosx — gsin x] . 39. (d) 13"“[cos 4x — isin all] 35. Value of the integral flit-yd}; _ 3(2de , where,c is the square cut from the first quadrant by the line at = 1 and y = 1 will be (Use Green’s theorem to change the Line integral into double integral) (a) g (b) 1 3 5 (F) E (d) g 40. 36. Consider likely applicability of Cauchy's Integral Theorem to evaluate the following integral counter clockwise around the unit circle c. Ifiéseczdz _C 2 being a complex variable. The value of I will be (a) I = 0 :singularities set = ill (b) I = U: singularities set = {1 2”2+1 Tr 11:0, 1, 2 (c) I = 71/2 : singularities set = {turd 11:0, 1, 2, ....... ..} 41. (d) None of ab0ve 37. A concrete beam of rectangular cross section of 200 mm x 400 mm is prestressed with a force 400 RM at eccentricity 100 mm. The maximum compressive stress in the concrete is (a) 12.5N/rnm2 (b) 17.5N/mm2 {c} 5.0 N/rrtm2 (d) 2.5 N/rnrn2 42. Which one of the following is NOT correct for steel sections as per IS : 800—1984? (at) The maximum bending stress in tension or in compression in extreme fibre calculated on the effective section of a bean-- shall not exceed 0.66 iv. (5)) The bea ring stress in any part of a beam when calculated on the net area shall not exceed 0.75 f3. (c) The direct stress in compression on the gross sectional area of axial loaded compression member shall not exceed 0.6 fy. (9‘) None of above. An unstlffened web 1 section is fabricated from a 10 mm thick plate by fillet welding as shown in the figure. If yield stress of steel is 250 MPa, the maximum shear load that section can take is l 300 mm «——20[! mm——- (a) 750 kN (b) 350 kN (c) 33?.5 kN (d) 300 kN A fillet-welded joint of 6mm size is shown in the figure. The welded surfaces meet at 60-90 degree and permissible stress in the fillet weld is 108 MPa. The safe load Lhat can be transmitted by the joint l5 (a) 162.7kN (c) 113.4 kN (b) 151.6 m (a) 109.5 kN A cantilever beam of length 1, width b and depth d is loaded With a concentrated vertical load at the tip. If yielding starts at a load P, the collapsa load shall be (it) 2.0 I’ (c) 1.2 P The flexural strength of M 3|] concrete as per 15 : 456—2000 is (a) 3.33 MPa (5) 21.23 mm (b) 1.5 P (a) P (b) 5.47 MPa (at) 30.0 MPa 43. 44. 45. 47. In a random sampling procedure forcube strength of concrete, one sample consists of X number of specimens. These specimens are tested at 28 days and average strength of these X specimens is considered as test result of the sample, provided the individual variation in the strength of 48' specimens is not more than i Y percent of the average strength. The values of X and Y as per 15: 456-2000 are (rt) 4 and 10 respectively (b) 3 and 10 respectively (5) 4- and 15 respectively (0') 3 and 15 respectively A rectangular column section of 250 mm x 400 mm is reinforced with live steel bars of grade Fe 500, each of 20 mm diameter. Concrete mix is M 31]. Axial load on the column section with minimum eccentricity as per IS : 456—2000 using limit state method can be applied upto (:1) 1707.37 (b) 180530 (E) 1806.40 (rt) 1903.? A circular shaft shown in the figure is subjected to torsion T at two points A and B. The torsional ri- gidity of portions CA and SD is (311 and that of portion AB is GJZ. The rotations of shaft at points A and B are E, and 82. The relation 3, is 49' 31:“ at; ’1‘: DE L J L T L __| TL IL (I?) Gli + G]: (b) Gli Tl. TL ('3) E “’l GI. —Gtz [f principal stresses in a two‘dimensional case are -10MPa and 20 MP3. respectively, then maximum shear stress at the point is (a) 10 MP3 (b) 15 MP3 (c) 20 MP2. (d) 30 MPa The bending moment diagram for a beam is given ' below : 5|]. ZflDkNm lI-JIF b l . I I I I I I I l l l . ., I I . 9.5m i “‘3 Theshear forceat sections are“ and bb’ are of the magnitude (a) mu kN,150 kN (c) zero, 50 kN respectively (1:) zero, IUD kN id) 100 kN, 10E! kN For a 25 cm thick cement concrete pavement, analysis of stresses gives the following values Wheel load stress due to corner loading 30 ngcm2 Wheel load stress due to edge loading 32 kg/cm2 Warping streSs at corner region during surruner 9 kg/cm2 Warping stress at corner region during winter 3” kglcrrl2 Warping stress at edge region during summer 8 log/cm2 Warping stress at edge region during winter 6 ltg/cm1 Frictional stress during summer 5 kg/cm2 Frictional stress during winter 4 leg/cm2 The most critical stress value for this pavement is (a) 40 kg/cm2 (1:) 42 leg/cm2 (c) 44 kg/cm2 (a) 45 l-<g/crn2 Match the following : Group 1 P. Slope deflection method Q. Moment distribution mefliod R. Method of three moments S. Castigliano’s second theorem GroupZ 1. Force method 2. Displacement method (rt) P—l,Q—2,R—t,S—2 (b) P—l,Q—1.R-—2,S—2 (c) P-—2,Q—2, R—1,S—1 (d) t’—2,Q—1, R-2,S—1 All members of the frame shown below have the same flexurai rigidity EI and length L. It a moment M is applied at joint B, the rotation of die joint 15 ML (a) Ea ML lb) TIE ML (6) gig; ML (#1) Y—EI‘ 5]. A soil mass contains 40% gravel, 50% sand and 10“!” silt. This soil can be classified as (a) silty sandy gravel having coefficient of uniformity less than 60 (ii) silty gravelly sand having coefficient of uniformity equal to 10 (c) gravelly silty sand having coefficient of uniformity greater than 60 (d) gravetiy silty sand and its coefficient of uniformity cannot be determined. 52. A saturated soil mass has a total density 221<Nlm3 and a water contentof 10%. The bulk density and dry density of this soil are (a) 12 kN/m1 and 20 kN/ m“ respectively (b) 22 kNg‘nr‘ and 20 RN/ rn3 respectively {c} 19.3 kN/mt and 19.3 lcN/m3 respectively (11') 23.2 kl'\l/1'n3 and 19.8 kN / n13 respectively. 53. [n a constant head permearneter with cross section area of 10 cm2, when the flow was taking place under a hydraulic gradient of 0.5, the amount of water collected in 60 seconds is 600 cc. The permeability of the soil is (a) 0.002 em/s (it) 0.02 cm/s (c) 0.2 crri,’s (d) 20 cm/s 54. Assuming that a river bed level does not change and the depth of water in river was 10 m', 15 m and 8 m during the months of February, Iuly and December respectively of a particular year. The average bulk density of the soil is 20 kN/m3. The density of water is 10 kN/m3. The effective stress ata depth of 10 m below the river bed during these months would be {a} 300 kNi’in3 in February, 350 kN/m2 July and 320 l-(N/I'n2 in December (b) 100 kN/rn2 in February, 100 kN/m2 July and 100 kN/m2 in December (c) 200 kN/m‘E in February, 250 kN/mfjuly and 180 l-<l\.l/in’2 in December (:1) 300 kN/m2 in February, 350 kN/rn2 July and 280 kN/ In2 in December ' 55. For a lriaxial shear test conducted on a sand specimen at a confining pressure of 100 kN/rn" under drained conditions. resulted in a devia tor stress (sl—se} at failure of 100 kN/m’l. The angle of shearing resistance of the soil would be (a) 18-43” (b) 19.473 (c) 26.56“ (a) 30° 56. During the subsurface investigations for design of foundations, a standard penetration test was conducted at 4.5 m below the ground surface. The record of number of blows is given below Penetration depth (cm) No. of blows 0—915 3 7.5-15 ‘15—225 225-30 30-315 315415 MOOGNO‘W Assuming the water table at ground level, soil as fine sand and correction factor for overburden as 1.0, the corrected ’N' value for the soil would be (a) 18 (b) 19 (is) 21 (d) 33 5?. For two infinite slopes (one in dry condition and other in submerged condition) in a sand deposit having the angle of shearing resistance 30°, factor of safety was determined as 1.5 (for both slopes)._ The slope angles Would have been (a) 21 .05° for dry slope and 2105" for submerged slope ' (b) 19.41?"J for dry slope and 18.40" for submerged slope - (c) 18.4” for dry slope and 2_1.05° for submerged slope ' (d) 216° for dry slope and 1947" for submerged slope 58. A strip footing (8m wide] is designed for a total settlement of 40mm. The safe bearing capacity (shear) was 150 kN/rnz and safe allowable soil pressure was 100 kN/mz. Due to importance of the structure, now the looting is to be redesigned for total settlement of 25 mm. The new width of _ the footing will be (a) 5111 (c) l 2 m (b) 8 m (a) 12.8 m 59. A 3 m high retaining wall issupporting a saturated sand (saturated due to capillary action) of bulk density is lcN/m:E and angle ofshearing resistance 30“. The change in magnitude of active earth pressure at the base due to rise in ground water table from the base of the footing to the ground surfaceshall (3!" = 1'0 kN/m") {a} increase by 20 kN / m? (b) decrease by 20 kN/ m2 (6) increase by 30 kN/rn:a (a) decrease by30 lai'kl/rn2 60. 61. 62. 63. Critical depth at a section ofa rectangular channel is 1.5 m. The specific energy at that section is (a) 0.75 m (b) 1.0m (c) 1.5 in (ii) 2.25 m A partially open sluice gale discharges water into a rectangular channel. The tail water depth tn the i zfiJfa free hydraulic jump is to be formed at a downstream of the sluice gate after the vena contracta of the jet coming out from the sluice gate, the sluice gate opening should be (coefficient of contraction Cc = 0.9) (a) 0.3m (c) 0.69 rii channel is 3 m and Froude number is (b) 0.4 rn (d) 0.9 m A stream function is given by _v=2x1y+(x+1)y2 The flow rate across a line joining points A(3, 0) and B(0, 2) is (a) 0.4 units (c) 4 units (1:) 1.1 units ((1‘) 5 units C ross-section of an object (having same section normal to the paper) submerged into a fluid consists ofa square of sides 2 rm and triangle as shown in the figure. The object is hinged at point P that is one meter below the fluid free surface. If the object is to be kept in the position as shown in the figure, the value of ’x’ should be ‘ (b) 45 (d) 8 m (at 245 (c) 4m The circulation ’0’ around a circle of radius 2 units for the velocity field :i = 2x + 3y and v = — 23; is (:1) —6R units (11) —12a units (C) ~18?! units ' (ti) —24it units A tank and a deflector are placed on a'frictionless trolley. The tank issues water jet (mass density of water = 1000 kg/m“), which strikes the deflector and. truns by 45°, if the velocity of jet leaving the - deflector is 4 11115 and discharge is 0.1 m3/s, the force recorded by the spring will be 66. 67. 68. .__. .1 t 69. Sp ring finite} (a) 100M (L‘) ZUDN is) 10046 N (d) 200& N Two observation Wells penetrated into a confined aquifer and located 1.5 km apart in the direction of flow, indicate head of 45 in and 20 m. If the coefficient of permeability of the aquifer is 30 rn/day and porosity is 0.25, the time of travel of an inert tracer from one well to another is (a) 416.7 days (in) 500 days (9) 750 days (if) 3000 days A triangular irrigation lined canal carries a discharge ...
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