GATE 2000
CE : Civil Engineering
SECTION A (75 Marks)
1. This question consists of 27 (Twenty Seven)
multiple-choice type sub-questions each carrying one mark. The answers
to the multiple choice questions MUST be written only in the boxes
corresponding to the question number by writing A, B, C or D in the
answer book. (27 x 1 = 27)
1.1. If A, B, C are square matrices of the same order,
(ABC) -l is equal to
- C -l A -1 B -1
- C -l B -1 A -1
- A -1 B -1 C -l
- A -1 C -l B -1
1.2. The following integral lim a � �
(a) Diverges (b) Converges to
(c) Converges to
(d) Converges to 0
1.3. A function with a period 2 is shown below
The Fourier series for this function is given by
(a)
 .
(b)
(c)
(d)
1.4. Consider the following two statements:
I. The maximum number of linearly independent column
vectors of a matrix A is called the rank of A.
II. If A is an n x n square matrix, it will be
nonsingular if rank A = n. With reference to the above statements, which
of the following applies?
(a) Both the statements are false. (b) Both the
statements are true.
(c) I is true but II is false. (d) I is false but II
is true.
1.5. The dimensions for the flexural rigidity of a
beam element in mass (M), length (L) and time (T) is given by
(c) ML -lT -2 (d) ML -l T 2�
1.6. A two span beam with an internal hinge is shown
below.
The conjugate beam corresponding to this beam is
1.7. Pick the incorrect statement from the following
four statements:
- On the plane which carries maximum normal stress,
the shear stress is zero.
- Principal planes are mutually orthogonal.
- On the plane which carries maximum shear stress,
the normal stress is zero.
- The principal stress axes and principal strain
axes coincide for an isotropic material.
1.8. A frame ABCD is supported by a roller at A and is
on a hinge at C as shown below:
The reaction at the roller end A is given by
(a) P (b) 2 P
(c) P/2 (d) Zero.
1.9. The following two statements are made with
reference to a simply supported under-reinforced RCC beam:
I. Failure takes place by crushing of concrete before
the steel has yielded.
II. The neutral axis moves up as the load is
increased.
With reference to the above statements, which of the
following applies?
- Both the statements are false.
- I is true but II is false.
- Both the statements are true.
- I is false but II is true.
1.10. The stress-strain diagram for two materials A
and B is shown below:
The following statements are made based on this
diagram:
(I) Material A is more brittle than material B.
(II) The ultimate strength of material B is more than
that of A.
With reference to the above statements, which of the
following applies?
- Both the statements are false. (b) Both the
statements are true.
(c) I is true but II is false. (d) I is false but II
is true.
1.11. Four column of the same material and having
identical geometric properties
are supported in different ways as shown below:
It is required to order these four beams in the
increasing order of their respective first buckling loads. The correct
order is given by
(a) I, II, III, IV (b) III, IV, I, II
(c) II, I, IV, III (d) I, II, IV, III
1.12. A soil sample has a void ratio of 0.5 and its
porosity will be close to
1.13. A borrow pit soil has a dry density of 17 kN/m
3. How many cubic meters of this soil will be required to construct an
embankment of 100 m 3 volume with a dry density of 16 kN/m 3.
(a) 94 m 3 (b) 106 m 3
(c) 100 m 3 (d) 90 m 3
1.14. The group efficiency of a pile group
(a) will be always less than 100%.
(b) will be always greater than 100%
(c) may be less than 100% or more than 100%.
(d) will be more than 100% for pile groups in cohesion
less soils and less than 100% for those in cohesive soils.
1.15. The two criteria for the determination of
allowable bearing capacity of a foundation are
(a) tensile failure and compression failure.
(b) tensile failure and settlement.
(c) bond failure and shear failure.
(d) shear failure and settlement.
1.16. If duty (D) is 1428 hectares/cumec and base
period (B) is 120 days for an irrigated
crop, then delta ( D ) in meters is given by
(a) 102.8 (b) 0.73
(c) 1.38 (d) 0.01
1.17. The relation that must hold for the flow to be
irrotational is
(a)
(b)
(c)
(d)
1.18. Cavitation is caused by
(a) high velocity (b) low pressure
(c) high pressure (d) high temperature
1.19. If the pump head is 15m, discharge is 0.464 m
3/s and the motor speed is 1440 rpm at rated condition, the
specific-speed of the pump is about
(a) 4 (b) 26
(c) 38 (d) 1440
1.20. The BOD removal efficiency, in percentage,
during primary treatment, under normal conditions is about
(a) 65% (b) 85%
(c) 30% (d) Zero
1.21. Critical factors for the activated sludge
treatment process are
(a) maximum hourly flow rate.
(b) maximum and minimum flow rate.
(c) maximum hourly flow rate and maximum daily organic
load.
(d) minimum hourly flow rate and minimum daily organic
load.
1.22. Use of coagulants such as alum
(a) results in reduction of pH of the treated water.
(b) results in increase of pH of the treated water.
(c) results in no change in pH of the treated water.
(d) may cause an increase or decrease of pH of the
treated water.
1.23. The disinfection efficiency of chlorine in water
treatment
(a) is not dependent on pH value.
(b) is increase by increased pH value.
(c) remains constant at all pH values.
(d) is reduced by increased pH value.
1.24. The standard plate size in a plate bearing test
for finding modulus of subgrade reaction (k) value is
- 100 cm diameter
- 50 cm diameter
- 75 cm diameter
- 25 cm diameter
1.25. Width of carriageway for a single lane is
recommended to be
(a) 7.5 m (b) 7.0 m
(c) 3.75 m (d) 5.5 m
1.26. Stopping sight distance is the minimum distance
available on a highway which is the
(a) distance of sufficient length to stop the vehicle
without collision.
(b) distance visible to a driver during night driving.
(c) height of the object above the road surface.
(d) distance equal to the height of the driver's eye
above the road surface.
1.27. Bituminous materials are commonly use in highway
construction because of their good
(a) tensile and compression properties.
(b) binding and water proofing properties.
(c) shear strength and tensile properties.
(d) bond and tensile properties.
2. This question consists of24 (Twenty Four)
multiple-choice type sub-questions, each carrying TWO marks. The answers
to the multiple choice questions MUST be written only in the boxes
corresponding to the question numbers writing A, B, C or D in the answer
book. (24 x 2 = 48)
2.1. If f(x, y, z) = (x 2 +y 2 +z 2) -1/2
is equal to
- Zero
- 1
- 2
- - 3 (x 2 + y 2 + z 2) -5/2
2.2. The Taylor expansion of sin x about x = p /6 is
given by
(a)
(b)
(c)
(d)
2.3. Let F(s) =� [f(t)] denote the Laplace transform
of the function f(t). Which of the following statements is correct?
(a) �
�
(b) �
�
(c) �
�
(d) �
�
2.4. The limit of the function f(x) = [1- a 4 / x 4]
as x � � is given by
2.5. The maxima and minima of the function f(x) = 2x 3
- 15x 2 + 36x + 10 occur, respectively, at
(a) X = 3 and X = 2 (b) X = 1 and X = 3
(c) X = 2 and X = 3 (d) X = 3 and X = 4
2.6. The four cross sections shown below are required
to be ordered in the increasing
order of their respective shape factors.
Which of the following order is correct?
(a) III, I, IV, II (b) I, II, III, IV
(c) III, IV, I II (d) III, IV, II, I
2.7. A simply supported beam with an- overhang is
traversed by a unit concentrated moment from the left t>a. the right as
shown below:
The influence line for reaction at B is given by
(d) zero everywhere
2.8. The following two statements are made with
reference to the planar truss shown
below:
I. The truss is statically determinate
II. The truss is kinematically determinate
With reference to the above statements, which of the
following applies?
(a) Both statements are true. (b) Both statements are
false.
(c) II is true but I false. (d) I is true but II is
false.
2.9. A cantilever beam of length L and a cross section
with shape factor f supports a concentrated load P as shown below:
The length L p of the plastic zone, when the maximum
bending moment, equals the plastic moment M p, given by
(a)
(b)
(c)
(d)
2.10. For the structure shown below, the vertical
deflection at point A is given by
(a)
(b)
(c)Zero
(d)
2.11. The ultimate bearing capacity of a soil is 300
kN/m 2. The depth of foundation is 1m and unit weight of soil is 20 kN/m
3. Choosing a factor of safety of 2.5, the net safe bearing capacity is
(a) 100 kN/m 2 (c) 80 kN/m 2
(b) 112 kN/m 2 (d) 100.5 kN/m 2
2.12. A deep cut of 1m has to be made in a clay with
unit weight 16 kN/m 3 and a cohesion of 25 kN/m 2. What will be the
factor of safety if one has to have a slope angle of 30�? Stability
number is given to be 0.178 (from Taylor's chart) for a depth factor of
3.
(a) 0.80 (c) 1.25
(b) 1.1 (d) 1.0
2.13. In a drained triaxial compression test, a
saturated specimen of a cohesion less sand fails under a deviatoric
stress of 3 kgf/cm 2 when the cell pressure is 1 kgf/cm 2. The effective
angle of shearing resistance of sand is about
(a) 37� (b) 45�
(c) 53� (d) 20�
2.14. Two footings, one circular and the other square,
are founded on the surface of a purely cohesion less soil. The diameter
of the circular footing is same as that of the side of the square
footing. The ratio of their ultimate bearing capacities is
(a) 3/4 (b) 4/3
(c) 1.0 (d) 1.3
2.15. To have zero active pressure intensity at the
tip of a wall in cohesive soil, one
should apply a uniform surcharge intensity of
(a) 2 c tan a (b) 2 c cot a
(c) - 2 c tan a (d) - 2 c tan a
2.16. Water flows at a depth of 0.1m with a velocity
of 6 m/s in a rectangular channel. The alternate depth is
- 0.30 m
- 0.40 m
- 0.86 m
- 0.81 m
2.17. In an area of 200 hectare, water table drops by
4 m. If the porosity is 0.35 and the
specific retention is 0.15, change in volume of
storage in the aquifer is.
(a) 160 m 3 (b) 1.6 x 106 m
(c) 8 x 106 m 3 (d) 1.6 x 103 m 3
2.18. A tube well having a capacity of 4 m 3/hour
operates for 20 hours each day during
the irrigation season. How much area can be commanded
if the irrigation interval
is 20 days and depth of irrigation is 7 cm ?
(a) 1.71 x 10 4 m 2 (b) 1.14 x 10 4 m 2
(c) 22.9 x 10 4 m 2 (d) 2.29 x 10 4 m 2
2.19. The parameters in Horton's infiltration equation
[f(t) = f c + (f o - f c ) e -kt] are given as, f o = 7.62 cm/hour, f c
= 1.34 cm/hour and k = 4.182/hour. For assumed continuous ponding the
cumulative infiltration at the end of 2 hours is
(a) 2.68 cm (b) 1.50 cm
(c) 1.34 cm (d) 4.18 cm
2.20. Water flows at a rate of 10 m 3/s in a
rectangular channel 3 m wide. The critical depth of flow is
2.21. A circular sewer 2m diameter has to carry a
discharge of 2 m 3/s when flowing nearly full. What is the minimum
required slope to initiate the flow? Assume Manning's n = 0.015.
(a) 0.00023 (b) 0.000036
(c) 0.000091 (d) 0.000014
2.22. The following characteristics pertain to the
sand filters used in water industry.
- Filtration rate is 1 to 4 m 3/(m 2 day).
- Typical duration of operation in one run is 24 to
72 hours.
- Operating cost is low.
Which of the above characteristics pertain to slow
sand filters?
(a) I, II and III (b) I and II
(c) II and III (d) I and III
2.23. The ruling minimum radius of horizontal curve of
a national highway in plain terrain for a ruling design speed of 100
km/hour with e = 0.07 and f = 0.15 is close to
(a) 250 m (b) 360 m
(c) 36 m (d) 300 m
2.24. Design rate of super elevation for horizontal
highway curve of radius 450 m for a mixed traffic condition, having a
speed of 125 km/hour is
(a) 1.0 (b) 0.05
(c) 0.07 (d) 0.1.54
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