Gate physics sample papers - 2010

                  ⎡2 ⎤
              sin ⎢ x ⎥
                  ⎣ 3 ⎦ is
1. The lim
                  x
         x →0
   (A) 2                                          (C) 1            (D) 1
                             (B) 1
           3                                            4                2
2. Two coins are simultaneously tossed. The probability of two heads simultaneously
   appearing is
   (A) 1                     (B) 1                (C) 1            (D) 1
           8                       6                    4                2
3. The order and degree of the differential equation
                     3
    d3 y       ⎛ dy ⎞     2
         +4 ⎜       ⎟ + y = 0 are respectively
       3
               ⎝ dx ⎠
    dx
   (A) 3 and 2               (B) 2 and 3          (C) 3 and 3      (D) 3 and 1
4. Two people weighing W each are sitting on a plank of length L floating on water
   at L from either end. Neglecting the weight of the plank, the bending moment
         4
   at the centre of the plank is
         WL                       WL                   WL
   (A)                       (B)                  (C)              (D) zero
          8                       16                   32
5. For the truss shown in the figure, the force in the member QR is
                                    Q
                                                R
                                                     L
                                    T
                                                S
                                           L
                                               P
                             (B) P
   (A) Zero                                       (C) P            (D) 2 P
                                     2
6. The major and minor principal stresses at a point are 3MPa and -3MPa
   respectively. The maximum shear stress at the point is
   (A) Zero                  (B) 3MPa             (C) 6MPa         (D) 9MPa
7.  The number of independent elastic constants for a linear elastic isotropic and
    homogeneous material is
    (A) 4                   (B) 3                  (C) 2                 (D) 1
8.  The effective length of a column of length L fixed against rotation and translation
    at one end and free at the other end is
    (A) 0.5 L               (B) 0.7 L              (C) 1.414 L           (D) 2L
9.  As per India standard code of practice for pre stressed concrete (IS:1343-1980)
    the minimum grades of concrete to be used for post-tensioned and pre-tensioned
    structural elements are respectively
    (A) M20 for both        (B) M40 and M30        (C) M15 and M20       (D) M30 and M40
10. A solid circular shaft of diameter d and length L is fixed at one end and free at
    the other end. A torque t is applied at the free end. The shear modulus of the
    material is G. The angle of twist at three free ends is
          16TL                  32TL                    64TL                 128TL
    (A)                     (B)                    (C)                   (D)
          π d4G                 π d4G                    π d4G                π d4G
11. In a compaction test, G, w, S and e represent the specific gravity, water content,
    degree of saturation and void ratio of the soil sample, respectively. If γw
    represents the unit weight of water and γw represents the dry unit weight of the
    soil, the equation for zero air voids line is
              Gγ w                   Gγ w                     Gγ w                Gw
                                                                         (D) γ d
    (A) γ d                 (B) γ d                (C) γ d
                                                                                 1 + Se
             1 + Se                 1 + Gw                  e + γ wS
12. A fine grained soil has liquid limit of 60 and plastic limit of 20. As per the
    plasticity chart, according to IS classification, the soil is represented by the letter
    symbols
    (A) CL                  (B) CI                 (C) CH                (D) CL-ML
13. Quick sand condition occurs when
    (A) The void ratio of the soil becomes 1.0
    (B) The upward seepage pressure in soil becomes zero
    (C) The upward seepage pressure in soil becomes equal to the saturated unit
         weight of the soil
    (D) The upward seepage pressure in soil becomes equal to the submerged unit
         weight of the soil
14. The e-log p curve shown in the figure is representative of
    (A) Normally consolidated clay
                                                                            (B) Over consolidated clay
                                                                            (C) Under consolidated clay
                                                                            (D) Normally consolidated clayey sand
                                                                            Void ratio, e
                                                                                                                                         log p
                                                                            If σh , σv , σh , and σv represent the total horizontal stress, total vertical stress,
15.
    effective horizontal stress and effective vertical stress on a soil element,
    respectively, the coefficient of earth pressure at rest is given by
         σh                      σh                    σv                   σv
    (A)                     (B)                   (C)                   (D)
                                σ 'v                                        σ 'h
         σv                                             σh
16. A mild-sloped channel is followed by a steep-sloped channel. The profiles of
    gradually varied flow in the channel are
    (A) M3 , S2             (B) M3 , S3           (C) M2 , S1           (D) M2 , S2
17. The flow in a rectangular channel is subcritical. If width of the channel is reduced
    at a certain section, the water surface under no-choke condition will
    (A) Drop at a downstream section              (B) Rise at a downstream section
    (C) Rise at an downstream section             (D) Not undergo any change
18. The correct match of Group-I with Group-II is
        Group-II                                       Group-II
    P.  Evapotranspiration                        1.   Penman method
    Q. Infiltration                               2.   Snyder's method
    R.  Synthetic unit hydrograph                 3.   Muskingum method
    S.  Channel Routing                           4.   Horton's method
    (A) P-1, Q-3, R-4, S-2                        (B) P-1, Q-4, R-2, S-3
                                                  (D) P-4, Q-2, R-1, S-3
    (C) P-3, Q-4, R-1, S-2
19. Group-I gives a list of devices and Group-II gives the list of uses
    P.  Pitot tube                               1. Measuring pressure in a pipe
    Q. Manometer                                 2. Measuring velocity of flow in a pipe
    R.  Venturimeter                             3. Measuring air and gas velocity
    S.  Anemometer                               4. Measuring discharge in a pipe20. A coastal city produces municipal solid waste (MSW) with high moisture content,
    high organic materials, low calorific value and low inorganic materials. The most
    effective and sustainable option for MSW management in that city is
    (A) Composting          (B) Dumping in sea     (C) Incineration    (D) Landfill
21. According to the Noise Pollution (Regulation and control) Rules, 2000, of the
    Ministry of Environment and Forests, India, the day time and night time noise
    level limits in ambient air for residential areas expressed in dB(A) Leg are
    (A) 50 and 40           (B) 55 and 45          (C) 65 and 55       (D) 75 and 70
22. An air parcel having 40oC temperature moves from ground level to 500m
    elevation in dry air following the "adiabatic lapse rate". The resulting temperature
    of air parcel at 500m elevation will be
    (A) 35oC                (B) 38oC               (C) 41oC            (D) 44oC
23. Aggregate impact value indicates the following property of aggregates
    (A) Durability          (B) Toughness          (C) Hardness        (D) Strength
24. As per IRC: 67-2001, a traffic sign indicating the Speed Limit on a road should be
    of
    (A) Circular Shape with White Background and Red Border
    (B) Triangular Shape with White Background and Red Border
    (C) Triangular Shape with Red Background and White Border
    (D) Circular Shape with Red Background ad White Border
25. The local mean time at a place located in longitude 90o 40'E when the standard
    time is 6 hours and 30 minutes and the standard meridian is 82o 30'E is
    (A) 5 hours, 2 minutes and 40 seconds
    (B) 5 hours, 57 minutes and 20 seconds
    (C) 6 hours, and 30 minutes
    (D) 7 hours, 02 minutes and 40 seconds
                                                                d2 y dy
26. The solution to the ordinary differential equation                +    − 6y = 0 is
                                                                dx2 dx
    (A) y = c1e3x + c2 e−2x                               (B) y = c1e3x + c2e2x
    (C) y = c1e−3x + c2e2x                                (D) y = c1e−3x + c2e−2x
                                       ⎡3 + 2i   i ⎤
27. The inverse of the matrix ⎢                     ⎥ is
                                       ⎣ − i 3 − 2i⎦
           1 ⎡3 + 2i       −i ⎤                                 1 ⎡3 − 2i     −i ⎤
                                                          (B)
    (A)
                                                               12 ⎢ i              ⎥
          12 ⎢ i               ⎥
                                                                            3 + 2i⎦
                         3 − 2i⎦                                    ⎣
               ⎣
           1 ⎡3 + 2i       −i ⎤                                 1 ⎡3 − 2i     −i ⎤
                                                          (D)
    (C)        ⎢               ⎥                                    ⎢              ⎥
          14 ⎣ i                                               14 ⎣ i
                         3 − 2i⎦                                            3 + 2i⎦
28. The table below gives values of a function F(x) obtained for values of x at
    intervals of 0.25.
                           x         0         0.25      0.5        0.75     1.0
                           F(x)      1         0.9412    0.8       0.64      0.50
    The value of the integral of the function between the limits 0 to 1 using
    Simpson's rule is
    (A) 0.7854                    (B) 2.3562              (C) 3.1416               (D) 7.5000
29. The partial differential equation that can be formed from
                                          ⎛                    ∂z ⎞
                                                    ∂z
     z = ax + by + ab has the form ⎜ with p =          and q =     ⎟
                                                    ∂x         ∂y ⎠
                                          ⎝
    (A) z=px+qy                   (B) z=px+pq             (C) z=px+qy+pq           (D) z=qy+pq
30. A parabolic cable is held between two supports at the same level. They horizontal
    span between the supports is L. The sag at the mid-span is h. The equation of
                                    x2
    the parabola is y = 4h 2 , where x is the horizontal coordinate and y is the
                                    L
    vertical coordinate with the origin at the centre of the cable. The expression for
    the total length of the cable is
                                                                L /2
          L
                                                                             h3 x2
                      h2 x2
          ∫                                                       ∫
    (A)                                                   (B) 2
               1 + 64        dx                                       1 + 64         dx
                                                                              L4
                        L4                                        0
          0
          L /2                                                  L /2
                        h2 x2                                                h2 x2
            ∫                                                     ∫
                                                          (D) 2
    (C)          1 + 64        dx                                     1 + 64         dx
                          L4                                                  L4
            0                                                     0
31. Given a function
     f ( x, y ) = 4x2 + 6y2 − 8x − 4y + 8
    The optimal value of f(x, y)
    (A) Is a minimum equal to 10/3              (B) Is a maximum equal to 10/3
    (C) Is a minimum equal to 8/3               (D) Is a maximum equal to 8/3
32. A double cover butt riveted joint is used to connect two flat plates of 200mm
    width and 14mm thickness as show in the figure. There are twelve power driven
    rivets of 20mm diameter at a pitch of 50mm in both directions on either side of
    the plate. Two cover plates of 10mm thickness are used. The capacity of the joint
    in tension considering bearing and shear ONLY, with permissible bearing and
    shear stresses as 300MPa respectively is
                      50mm   50mm 50mm
              50mm
              50mm
              50mm
              50mm
    (A) 1083.6kN                (B) 871.32kN    (C) 541.18kN      (D) 433.7kN
33. Two plates, subjected to direct tension, each of 10mm thickness and having
    widths of 100mm and 175mm, respectively are to be fillet welded with an overlap
    of 200mm. Given that the permissible weld stress is 110MPa and the permissible
    stress in steel is 150MPa, then length of the weld required using the maximum
    permissible weld size as per IS: 800-1984 is
                        100mm                               175mm
                                          200mm
    (A) 245.3mm                 (B) 229.2mm     (C) 205.5mm       (D) 194.8mm34. For the simply supported beam of length L, subjected to a uniformly distributed
    moment M kN-m per unit length as shown in the figure, the bending moment (in
    kN-m) at the mid-span of the beam is
                             M kN - m per unit length
                                           L
(A) Zero                  (B) M                    (C) ML            (D) M/L
    A disc of radius r has a hole of radius r
35.                                               cut-out as shown. The centroid of the
                                               2
    remaining disc (shaded portion) at a radial distance from the centre "O" is
                                              r /2
                                              'O'
                                         O
                                   r
                               r                       r                 r
         r
    (A)                   (B)                      (C)               (D)
                               3                       6                 8
         2
36. A three hinged parabolic arch having a span of 20m and a rise of 5m carries a
    point load of 10kN at quarter span from the left end as shown in the figure. The
    resultant reaction at the left support and its inclination with the horizontal are
    respectively
                                   10kN
                                             5m
                                 5m    5m         10m
    (A) 9.01kN and 56.31o                          (B) 9.01kN and 33.69o
    (C) 7.50kN and 56.31o                          (D) 2.50kN and 33.69o
37. The vertical stress at point P1 due to the point load Q on the ground surface as
    shown in figure is s2. According to Boussinesq's equation, the vertical stress at
    point P2 shown in figure will be
                                     Q
                                                z
                                               2
                                                P2
                              z
                                        r
                                        2
                                                         P1
                                             r
          σz
    (A)                    (B) σz                  (C) 2σz              (D) 4σz
          2
38. An open ended steel barrel of 1m height and 1m diameter is filled with saturated
    fine sand having coefficient of permeability of 10−2 m / s . The barrel stands on a
    saturated bed of gravel. The time required for the water level in the barrel to
    drop by 0.75m is
    (A) 58.9s              (B) 75s                 (C) 100s             (D)150s
39. The ultimate load capacity    of a 10m long concrete pile of square cross section
    500mm x 500mm driven          into a homogeneous clay layer having undrained
    cohesion value of 40kPa is    700kN. If the cross section of the pile is reduced to
    250mm x 250mm and the         length of the pile is increased to 20m, the ultimate
    load capacity will be
    (A) 350kN              (B) 632.5kN             (C) 722.5kN          (D) 1400kN
40. For a rectangular channel section, Group I lists geometrical elements and Group
    II gives proportions for hydraulically efficient section.
                       Group I                              Group II
                                                                    ye
             P              Top width                 1
                                                                    2
                                                                    ye
             Q              Perimeter                 2
                                                                   2 ye
             R           Hydraulic Radius             3
                                                                   4 ye
             S           Hydraulic Depth              4
    ye is the follow depth corresponding to hydraulically efficient section. The correct
    match of Group I with Group II is
    (A) P-2, Q-4, R-1, S-3                         (B) P-3,Q-1,R-4,S-2
    37. The vertical stress at point P1 due to the point load Q on the ground surface as
    shown in figure is s2. According to Boussinesq's equation, the vertical stress at
    point P2 shown in figure will be
                                     Q
                                                z
                                               2
                                                P2
                              z
                                        r
                                        2
                                                         P1
                                             r
          σz
    (A)                    (B) σz                  (C) 2σz              (D) 4σz
          2
38. An open ended steel barrel of 1m height and 1m diameter is filled with saturated
    fine sand having coefficient of permeability of 10−2 m / s . The barrel stands on a
    saturated bed of gravel. The time required for the water level in the barrel to
    drop by 0.75m is
    (A) 58.9s              (B) 75s                 (C) 100s             (D)150s
39. The ultimate load capacity    of a 10m long concrete pile of square cross section
    500mm x 500mm driven          into a homogeneous clay layer having undrained
    cohesion value of 40kPa is    700kN. If the cross section of the pile is reduced to
    250mm x 250mm and the         length of the pile is increased to 20m, the ultimate
    load capacity will be
    (A) 350kN              (B) 632.5kN             (C) 722.5kN          (D) 1400kN
40. For a rectangular channel section, Group I lists geometrical elements and Group
    II gives proportions for hydraulically efficient section.
                       Group I                              Group II
                                                                    ye
             P              Top width                 1
                                                                    2
                                                                    ye
             Q              Perimeter                 2
                                                                   2 ye
             R           Hydraulic Radius             3
                                                                   4 ye
             S           Hydraulic Depth              4
    ye is the follow depth corresponding to hydraulically efficient section. The correct
    match of Group I with Group II is
    (A) P-2, Q-4, R-1, S-3                         (B) P-3,Q-1,R-4,S-2
    (C) P-3,Q-4,R-1,S-2                            (D) P-3,Q-4,R-2,S-1
(41. The Froude number of flown in a rectangular channel is 0.8. If the depth of flow
    is 1.5m, the critical depth is
    (A) 1.80m                (B) 1.56m               (C) 1.36m            (D) 1.29m
42. A wall of diameter 20cm fully penetrates a confined aquifer. After a long period of
    pumping at a rate of 2720litres per minute, the observations of drawdown taken
    at 10m and 100m distances from the center of the wall are found to be 3m and
    0.5m respectively. The transmissivity of the aquifer is
    (A) 676m2/day            (B) 576 m2/day          (C) 526 m2/day       (D) 249 m2/day
    If the BOD3 of a wastewater sample is 75mg/L and reaction rate constant k
43.
    (base e) is 0.345 per day, the amount of BOD remaining in the given sample
    after 10days is
    (A) 3.21 mg/L            (B) 3.45 mg/L           (C) 3.69 mg/L        (D)   3.92 mg/L
44. Consider the following statements in the context of geometric design of roads.
    I:   A simple parabolic curve is an acceptable shape for summit curves.
    II: Comfort to passengers is an important consideration in the design of summit
         curves.
    The correct option evaluating the above statements and their relationship is
    (A) I is true, II is false
    (B) I is true, II is true, and II is the correct reason for I
    (C) I is true, II is true, and II is NOT the correct reason for I
    (D) I is false, II is true
45. The design speed for a two-lane road is 80kmph. When a design vehicle with a
    wheelbase of 6.6m is negotiating a horizontal curve on that road, the off-tracking
    is measured as 0.096m. The required widening of carriageway of the two-lane
    road on the curve is approximately
    (A) 0.55m                (B) 0.65m               (C) 0.75m            (D) 0.85m
46. Consider the following statements in the context of cement concrete pavements.
    I.   Warping stresses in cement concrete pavements are caused by the seasonal
         variation in temperature.
    II. Tie bars are generally provided across transverse joints of cement concrete
         pavements
    The correct option evaluating the above statements is
    (A) I: True II: False                            (B) I: False II: True
  47.      A bench mark has been established at the soffit of an ornamental arch at the
         known elevation of 100.0m above sea level. The back sight used to establish
         height of instrument is an inverted staff reading of 2.105m. A forward sight
         reading with normally held staff of 1.105m is taken on a recently constructed
         plinth. The elevation of the plinth is
         (A) 103.210m            (B) 101.000m         (C) 99.000m          (D) 96.790m
                               Common Data Questions: 48 & 49
         Ion concentrations obtained for a groundwater sample (having pH=8.1) are given
         below.
                              Ca2+       Mg2+      Na+                              Cl-
                                                              HCO3-      SO42-
         Ion
         Ion                  100        6         15         250        45         39
         concentration
         (mg/L)
                                                              H=1,       S=32,
         Atomic Weight        Ca=40      Mg=24     Na=23                            Cl=35.5
                                                              C=12,      O=16
                                                              O=16
         Total hardiness (mg/L as CaCO3) present in the above water sample is
48.
         (A) 205                 (B) 250              (C) 275              (D) 308
         Carbonate hardness (mg/L as CaCO3) present in the above water sample is
49.
         (A) 205                 (B) 250              (C) 275              (D) 289
                           Common Data Questions: 50 & 51
The moisture holding capacity of the soil in a 100 hectare farm is 18cm/m. the field is to
be irrigated when 50 percent of the available moisture in the root zone is depleted. The
irrigation water is to be supplied by a pump working for 10hours a day, and water
application efficiency is 75%. Details of crops planned for cultivation are as follows:
                                                              Peak rate of moisture use
               Crop            Root zone depth (m)
                                                                      (mm/day)
                 X                     1.0                               5.0
                 Y                     0.8                               4.0
50.      The capacity of irrigation system required to irrigate crop X in 36 hectares is
         (A) 83litres/sec        (B) 67 liters/sec    (C) 57 liters/sec    (D) 53 liters/sec
  (51.     The area of crop Y that can be irrigated when the available capacity of irrigation
        system is 40 liters / sec is
        (A) 40hectares         (B) 36 hectares        (C) 30 hectares     (D) 27 hectares
                       Linked Answer Questions 52 & 53
A doubly reinforced rectangular concrete beam has a width of 300mm and an effective
depth of 500mm. the beam is reinforced with 2200mm2 of steel in tension and 628mm2
of steel in compression. The effective cover for compression steel is 50mm. Assume that
both tension and compression steel yield. The grades of concrete and steel used are M20
and Fe250 respectively. The stress lock parameters (rounded off to first two decimal
places) for concrete shall be as per IS 456:200.
52.     The depth of neutral axis is
        (A) 205.30mm           (B) 184.56mm           (C) 160.91mm        (D) 145.30mm
53.     The moment of resistance of the section is
        (A) 206.00kN-m         (B) 209.20 kN-m        (C) 236.80 kN-m     (D) 251.90kN-m,
                   Statement for Linked Answer Questions: 54 & 55
        The unconfined compressive strength of a saturated clay sample is 54kPa.
54.      The value of cohesion for the clay is
        (A) zero               (B) 13.5kPa            (C) 27kPa           (D)54kPa
55.     If a square footing of size 4m x 4m is resting on the surface of a deposit of the
        above clay, the ultimate bearing capacity of the footing (as per Terzaghi's
        equation) is
        (A) 1600kPa            (B) 315kPa             (C) 27kPa           (D)54kPh
                          Q. No. 56 – 60 Carry One Mark Each
56.     Which of the following options is closest in meaning to the word Circuitous.
        (A) cyclic             (B) indirect           (C) confusing       (D) crooked
57.     The question below consists of a pair of related words followed by four pairs of
        words. Select the pair that best expresses the relation in the original pair.
        Unemployed: Worker
    58. Choose the most appropriate word from the options given below to complete the
    following sentence:
    If we manage to ____________ our natural resources, we would leave a better
    planet for our children.
    (A) uphold              (B) restrain          (C) cherish          (D) conserve
59. Choose the most appropriate word from the options given below to the complete
    the following sentence:
    His rather casual remarks on politics ___________ his lack of seriousness about
    the subject.
    (A) masked              (B) belied            (C) betrayed         (D)suppressed
60. 25 persons are in a room. 15 of them play hockey, 17 of them play football and
    10 of them play both hockey and football. Then the number of persons playing
    neither hockey nor football is:
    (A) 2                   (B)17                 (C)13                (D) 3
                          Q. No. 61 – 65 Carry Two Marks Each
61. Hari (H), Gita (G), Irfan (I) and Saira (S) are siblings (i.e. brothers and sisters).
    All were born on 1st January. The age difference between any two successive
    siblings (that is born one after another) is less than 3 years. Given the following
    facts:
    i.    Hari's age + Gita's age > Irfan's age + Saira's age
    ii.   The age difference between Gita and Saira is 1 year. However Gita is not the
          oldest and Saira is not the youngest.
    iii. There are no twins.
    In what order were they born (oldest first)?
    (A) HSIG                (B) SGHI              (C) IGSH             (D) IHSG
62. 5 skilled workers can build a wall in 20days: 8 semi-skilled workers can build a
    wall in 25 days; 10 unskilled workers can build a wall in 30days. If a team has 2
    skilled, 6 semi-skilled and 5 unskilled workers, how long will it take to build the
    wall?
    (A) 20                  (B) 18                (C) 16               (D) 15
63. Modern warfare has changed from large scale clashes of armies to suppression of
    civilian populations. Chemical agents that do their work silently appear to be
    suited to such warfare; and regretfully, there exist people in military
    establishments who think that chemical agents are useful tools for their cause.
      Which of the following statements best sums up the meaning of the above
    passage:
    (A) Modern warfare has resulted in civil strife.
    (B) Chemical agents are useful in modern warfare.
    (C) Use of chemical agents in warfare would be undesirable
    (D) People in military establishments like to use chemical agents in war.
64. Given digits 2,2,3,3,4,4,4,4 how many distinct 4 digit numbers greater than 3000
    can be formed?
    (A) 50                 (B) 51                 (C) 52            (D) 54
65. If 137+276=435 how much is 731+672?
    (A) 534                (B) 1403               (C) 1623          (D)1513
  (A) fallow: land                              (B) unaware: sleeper
        (C) wit: jester                               (D) renovated: house
C) I: True II: True                             (D) I: False II: False
C) P-3,Q-4,R-1,S-2                            (D) P-3,Q-4,R-2,S-1