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

• 1
• exp[- a 4 ]
• ¥
• Zero

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

• 1.13 m
• 2m
• 1.45 m
• 1.04 m

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