1 The value of the following improper integral is

• ¼
• 0
• -¼
• 1

• The directional derivative of the following function at (1,2) in the direction of (4i+3j) is:

2.

• 4/5
• 4
• 2/5
• 1

3 The Laplace Transform of the following function is

(A) for all s>0

(B) for all s < p

(c) for all s>0

(d) for all s >0

4 The limit of the following sequence as n ® ¥ is:

• 0
• 1
• ¥
• - ¥

­

5 A steel beam (with a constant El, and span L) is fixed at both ends and carries a uniformly distributed load (w kN/m), which is gradually increased till the beam reaches the stage of plastic collapse (refer to the following figure). Assuming 'B' to be at mid-span, which of the following is true,

• Hinges are formed at A, B and C together
• Hinges are formed at B and then at A and C together
• Hinges are formed at A and C together and then at B
• Hinges are formed at A and C only

6 As per the provisions of IS 456-2000, in the limit state method for. design of beams, the limiting value of the depth of neutral axis in a reinforced concrete beam of effective depth 'd’ given as: .

• 0.53d
• 0.48d
• 0.46d
• any of the, above depending on the different grades of steel

7 ISA 100 x 100 x 10 mm (Cross sectional area = 1908 mm 2) serves as tensile member. This angle is welded to a gusset plate along A and B appropriately as shown. Assuming the yield strength of the steel to be 260 N/ mm2 the tensile strength of this member can be taken to be approximately,

(A) 500 kN

(B) 300 kN

(C) 225 kN

(D) 375 kN

8 ISA 100 x 100 x 10 mm (Cross sectional area = 1908 mm 2) is welded along A and B (Refer to figure for question 2.7), such that the lengths of the weld along A and B are 1 1 and 1 2, respectively. Which of the following is a possibly acceptable combination of 1 1 and 1 2.

(A) 1 1 = 60 mm and 1 2 = 150 mm

(B) 1 1= 150 mm and 1 2 = 60 mm

(C) 1 1 = 150 mm and 1 2 = 150 mm

(D) Any of the above, depending on the size of the weld.

9 In the propped cantilever beam carrying a uniformly distributed load of w N/m, shown in the following Figure, the reaction at the support B is

(A)

(B)

(C)

(D)

10 An infinite slope is to be constructed in a soil. The effective stress strength parameters of the soil are c’=O and f '= 30°. The saturated unit weight of the slope is 20 kN/m 3 and the unit weight of water is 10 kN/m 3. Assuming that seepage is occurring parallel to the slope, the maximum slope angle for a factor of safety of 1.5 would be:

(A) 10.89°

(B) 11.30°

• 12.48°
• 14.73'°

11 If the effective stress strength parameters of a soil are c'=10 kPa and 0'=30°, the shear strength on a plane within the saturated soil mass at a point where the total normal stress is 300 kPa and pore water pressure is 150 kPa will be:

• 90.5 kPa
• 96.6 kPa
• 101.5 kPa
• 1O5.5.kPa

12 The time for a clay layer to achieve 85% consolidation is 10 years. If the layer was half as thick, 10 times more permeable and 4 times more compressible then the time that would be required to achieve the same degree of consolidation is:

• 1 year
• 5 years
• 12 years
• 16 years

13 In a triaxial test carried out on a cohesion less soil sample with a cell pressure of

20 kPa, the observed value of applied stress at the point of failure was 40 kPa. The angle of internal friction of the soil is:

• 10°
• 15°
• 25°
• 30°