CE-l. This question consists of TWENTY FIVE sub-questions (1.1 - 1.25) of ONE mark each. For each of these sub-questions four possible answers (A, B, C and D) are given, out of which ONLY ONE is correct. Answer each sub question by darkening the appropriate bubble on the OBJECTIVE RESPONSE SHEET (ORS) using a soft HB pencil. Do not use the ORS for any rough work. . You may use the Answer Book for any rough work, if needed.

1.1 Eigen values of the following matrix are:

(A) 3 and-5 (B) -3 and 5

(C) -3 and-5 (D) 3 and 5

1.2 The value of the following definite integral is:

(A) -2 In2

(B) 2

(C) 0

• The following function has a local minima at which value of x:

(a)

(b)

(c)

(d)

1.4 For the loading given in the figure below; two statements (I and II) are made.

• Member AB carries shear force and bending moment
• Member BC carries axial load and shear force.

Which of the following is true:

• Statement I is true but II is false
• Statement I is false but II is true
• Both statements I and II are true
• Both statements I and II are false

1.5 Read the following two statements

I. Maximum strain in concrete at the outermost compression fibre is taken to be 0.0035 in bending.

II. The maximum compressive strain in concrete in axial compression is taken as 0.002.

Keeping the provisions of IS 456-2000 on limit state design in mind, which of the following is true:

• Statement I is true but II is false
• Statement I is false but II is true
• Both statements I and II are true
• Both statements I and II are false

1.6 As per the provisions of IS 456-2000, the (short term) modulus of elasticity of M25 grade concrete (in N/mm 2) can be assumed to be,

(a) 25000 (B) 28500 (C) 30000 (D) 36000

1.7 The shear modulus (G), modulus of elasticity (E) and the Poisson's ratio (v) of a material are related as,

• G=E/ [2(1+v)]
• E=G / [2(1+v)]
• G=E / [2(1-v)] ­
• G=E / [2(v-1)]

• When designing steel structures, one must ensure that local buckling in webs does not take place. This check may not be very critical when using rolled steel sections because,

• Quality control at the time of manufacture of rolled sections is very good
• Web depths available are small
• Web stiffeners are in-built in rolled sections
• Depth to thickness ratios (of the web) are appropriately adjusted

1.9 An ISMB 500 is used as a beam in a multi-storey construction. From the viewpoint of structural design, it can be considered to be 'laterally restrained' when,

• the tension flange is 'laterally restrained'
• the compression flange is 'laterally restrained'
• the web is adequately stiffened
• the conditions in (A) and (C) are met.

1.10 Data from a sieve analysis conducted on a given sample of soil showed that 67% of the particles passed through 75 micron IS sieve. The liquid limit and plastic limit of the finer fraction was found to be 45 and 33 percents respectively. The group symbol of the given soil as per IS:1498-1970 is:

• SC (B) MI (C) CH (D) MH

1.11 The void ratios at the densest, loosest and the natural states of a sand deposit are 0.2, 0.6 and 0.4, respectively. The relative density of the deposit is:

• 100%
• 75%
• 50%
• 25%

1.12 The following data were obtained from a liquid limit test conducted on a soil sample.

The liquid limit of the soil is:

(A) 63.1%

(B) 62.8%

(C) 61.9%

(D) 60.6%

1.13 The specific gravity and insitu void ratio of a soil deposit are 2.71 and 0.85 respectively. The value of the critical hydraulic gradient is:

• 0.82
• 0.85
• 0.95
• 0.92