CE GATE 2015 (Test 4)



Tag: ce gate 2015
Q.1
In a pre-stressed concrete beam section shown in the figure, the net loss is 10% and the final prestressing force applied at X is 750 kN. The initial fiber stresses (in N/mm2 ) at the top and bottom of the beam were: 

A. 4.166 and 20.833
B. –4.166 and –20.833
C. 4.166 and –20.833
D. –4.166 and 20.833
Answer : Option D
Explaination / Solution:

Loss = 10% 
Find force = 750 kN  
Initial force = 750/0.9 = 833.33kN
Top & Bottom stress = P/A ± m/z

Top = -4.166 (T) 
Bottom = 20.833 (C) 

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Q.2
Stress path equation for tri-axial test upon application of deviatoric stress is,q = 10√3 + 0.5p..The respective values of cohesion, c (in kPa) and angle of internal friction, φ are:
A. 20 and 20°
B. 20 and 30°
C. 30 and 30°
D. 30 and 20°
Answer : Option B
Explaination / Solution:



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Q.3
In Marshall method of mix design, the coarse aggregate, fine aggregate, fines and bitumen having respective values of specific gravity 2.60, 2.70, 2.65 and 1.01, are mixed in the relative proportions (% by weight) of 55.0, 35.8, 3.7 and 5.5 respectively. The theoretical specific gravity of the mix and the effective specific gravity of the aggregates in the mix respectively are
A. 2.42 and 2.63
B. 2.42 and 2.78
C. 2.42 and 2.93
D. 2.64 and 2.78
Answer : Option A
Explaination / Solution:



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Q.4
In a system two connected rigid bars AC and BC are of identical length, L with pin supports at A and B. The bars are interconnected at C by a frictionless hinge. The rotation of the hinge is restrained by a rotational spring of stiffness, k. The system initially assumes a straight line configuration, ACB. Assuming both the bars as weightless, the rotation at supports, A and B, due to a transverse load, P applied at C is
A. PL/4k
B. PL/2k
C. P/4k
D. Pk/4L
Answer : Option A
Explaination / Solution:


External work done 
= 1/2 × ρ × L.θ..........(1)
Strain energy stored in spring 


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Q.5
A fixed end beam is subjected to a load, W at 1/3rd span from the left support as shown in the figure. The collapse load of the beam is

A. 16.5 MP/L
B. 15.5 MP/L
C. 15.0 MP/L
D. 16.0 MP/L
Answer : Option C
Explaination / Solution:
No Explaination.


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Q.6
Four cards are randomly selected from a pack of 52 cards. If the first two cards are kings, what is the probability that the third card is a king?
A. 4/52
B. 2/50
C. 1/52 × (1/52)
D. 1/52 × (1/52) × (1/50)
Answer : Option B
Explaination / Solution:

There are 4 kings in a pack of 52 cards. If 2 cards are selected and both are kings, remaining cards will be 50 out of which 2 will be kings.

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Q.7
Given i = √-1 the value of the definite integral 
A. 1
B. -1
C. i
D. -i
Answer : Option B
Explaination / Solution:



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Q.8
 Let A = [ αij ], 1≤ i, j ≤ n with n ≥ 3 and aij = i.j . The rank of A is
A. 0
B. 1
C. n-1
D. n
Answer : Option B
Explaination / Solution:



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Q.9
 is equal to
A. e-2
B. e
C. 1
D. e2
Answer : Option D
Explaination / Solution:



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Q.10
 The two Eigen values of the matrix  have a ratio of 3 : 1 for p = 2. What is another value of p for which the Eigen values have the same ratio of 3 : 1?
A. -2
B. 1
C. 7/3
D. 14/3
Answer : Option D
Explaination / Solution:

Let A = 
Given that two eigen values of A are in 3:1 
Ratio for p = 2  
⇒ Characteristic equation λ2 -4λ+3 = 0 (by substituting p=2) 
⇒ λ=1,3 

Eigen values 5, 5/3 are in ratio 3:1
P = 14/3

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