Gate MCQ Quiz Hub

1. The annual precipitation data of a city is normally distributed with mean and standard deviation as 1000 mm and 200 mm, respectively. The probability that the annual precipitation will be more than 1200 mm is
< 50%
50%
75%
100%

2. The infinite series 1 + x + x2/2! + x3/3! + x4/4! + ... corresponds to
sec x
ex
cos x
1 + sin2

3. The Poisson's ratio is defined as
|axial stress/lateral stress|
|lateral strain/axial strain|
|lateral stress/axial stress|
|axial strain/lateral strain|

4. The following statements are related to bending of beams: I The slope of the bending moment diagram is equal to the shear force. II The slope of the shear force diagram is equal to the load intensity. III The slope of the curvature is equal to the flexural rotation. IV The second derivative of the deflection is equal to the curvature. The only FALSE statement is
I
II
III
IV

5. If a small concrete cube is submerged deep in still water in such a way that the pressure exerted on all faces of the cube is p, then the maximum shear stress developed inside the cube is
0
p/2
p
2p

6. As per IS 456:2000, in the Limit State Design of a flexural member, the strain in reinforcing bars under tension at ultimate state should not be less than
fy/Es
fy/Es + 0.002
fy/1.15 Es
fy/1.15 Es + 0.002

7. Which one of the following is categorised as a long-term loss of prestress in a prestressed concrete member?
Loss due to elastic shortening
Loss due to friction
Loss due to relaxation of strands
Loss due to anchorage slip

8. The ratio of the theoretical critical buckling load for a column with fixed ends to that of another column with the same dimensions and material, but with pinned ends, is equal to
0.5
1.0
2.0
4.0

9. The effective stress friction angle of a saturated, cohesionless soil is 380. The ratio of shear stress to normal effective stress on the failure plane is A. B. C.D.
0.781
0.616
0.488
0.438

10. Two series of compaction tests were performed in the laboratory on an inorganic clayey soil employing two different levels of compaction energy per unit volume of soil. With regard to the above tests, the following two statements are made. I The optimum moisture content is expected to be more for the tests with higher energy. II The maximum dry density is expected to be more for the tests with higher energy. The CORRECT option evaluating the above statements is
Only I is TRUE
Only II is TRUE
Both I and II are TRUE
Neither I nor II is TRUE

11. As per the Indian Standard soil classification system, a sample of silty clay with liquid limit of 40% and plasticity index of 28% is classified as
CH
CI
CL
CL-ML

12. An embankment is to be constructed with a granular soil (bulk unit weight = 20 kN/m3) on a saturated clayey silt deposit (undrained shear strength = 25 kPa). Assuming undrained general shear failure and bearing capacity factor of 5.7, the maximum height (in m) of the embankment at the point of failure is
7.1
5.0
4.5
2.5

13. A trapezoidal channel is 10.0 m wide at the base and has a side slope of 4 horizontal to 3 vertical. The bed slope is 0.002. The channel is lined with smooth concrete (Manning's n = 0.012). The hydraulic radius (in m) for a depth of flow of 3.0 m is
20.0
3.5
3.0
2.1

14. A rectangular open channel of width 5.0 m is carrying a discharge of 100 m3/s. The Froude number of the flow is 0.8. The depth of flow (in m) in the channel is
4
5
16
20

15. The ratio of actual evapo-transpiration to potential evapo-transpiration is in the range
0.0 to 0.4
0.6 to 0.9
0.0 to 1.0
1.0 to 2.0

16. A sample of domestic sewage is digested with silver sulphate, sulphuric acid, potassium dichromate and mercuric sulphate in chemical oxygen demand (COD) test. The digested sample is then titrated with standard ferrous ammonium sulphate (FAS) to determine the un-reacted amount of
mercuric sulphate
potassium dichromate
silver sulphate
sulphuric acid

17. Assertion [a]: At a manhole, the crown of the outgoing sewer should not be higher than the crown of the incoming sewer. Reason [r]: Transition from a larger diameter incoming sewer to a smaller diameter outgoing sewer at a manhole should not be made. The CORRECT option evaluating the above statements is :
Both [a] and [r] are true and [r] is the correct reason for [a]
Both [a] and [r] are true but [r] is not the correct reason for [a]
Both [a] and [r] are false
[a] is true but [r] is false

18. Road roughness is measured using
Benkelman beam
Bump integrator
Dynamic cone penetrometer
Falling weight deflectometer

19. Which of the following errors can be eliminated by reciprocal measurements in differential leveling? I Error due to earth's curvature II Error due to atmospheric refraction
Both I and II
I only
II only
Neither I nor II

20. . In an experiment, positive and negative values are equally likely to occur. The probability of obtaining at most one negative value in five trials is
1/32
2/32
3/32
6/32

21. A symmetric frame PQR consists of two inclined members PQ and QR, connected at 'Q' with a rigid joint, and hinged at 'P' and 'R'. The horizontal length PR is l. If a weight W is suspended at 'Q', the bending moment at 'Q' is
Wl/2
Wl/4
Wl/8
zero

22. Two soil specimens with identical geometric dimensions were subjected to falling head permeability tests in the laboratory under identical conditions. The fall of water head was measured after an identical time interval. The ratio of initial to final water heads for the test involving the first specimen was 1.25. If the coefficient of permeability of the second specimen is 5-times that of the first, the ratio of initial to final water heads in the test involving the second specimen is
3.05
3.80
4.00
6.25

23. A layer of normally consolidated, saturated silty clay of 1 m thickness is subjected to one dimensional consolidation under a pressure increment of 20 kPa. The properties of the soil are: specific gravity = 2.7, natural moisture content = 45%, compression index = 0.45, and recompression index = 0.05. The initial average effective stress within the layer is 100 kPa. Assuming Terzaghi's theory to be applicable, the primary consolidation settlement (rounded off to the nearest mm) is
2 mm
9 mm
14 mm
16 mm

24. The top width and the depth of flow in a triangular channel were measured as 4 m and 1 m, respectively. The measured velocities on the centre line at the water surface, 0.2 m and 0.8 m below the surface are 0.7 m/s, 0.6 m/s and 0.4 m/s, respectively. Using two-point method of velocity measurement, the discharge (in m3/s) in the channel is
1.4
1.2
1.0
0.8

25. Wheat crop requires 55 cm of water during 120 days of base period. The total rainfall during this period is 100 mm. Assume the irrigation efficiency to be 60%. The area (in ha) of the land which can be irrigated with a canal flow of 0.01 m3/s is
13.82
18.85
23.04
230.40