Civil Engineering (CE) 2014 (Set 1) GATE Paper without solution (unsolved) GATE Notes | EduRev

GATE : Civil Engineering (CE) 2014 (Set 1) GATE Paper without solution (unsolved) GATE Notes | EduRev

 Page 1


GATE 2015 SET-2 CIVIL -  CE 
CE 1/8
Q. 1 – Q. 25 carry one mark each. 
Q.1 While minimizing the function f(x), necessary and sufficient conditions for a point, x
0
 to be a 
minima are: 
(A) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (B) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f 
(C) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f (D) 0 ) ( " and 0 ) ( '
0 0
? ? x f x f 
 
Q.2 In Newton-Raphson iterative method, the initial guess value (x
ini
) is considered as zero while 
finding the roots of the equation:
3 2
5 . 0 4 6 2 ) ( x x x x f ? ? ? ? ? . The correction, ?x, to be added to 
x
ini
 in the first iteration is ________________.  
 
 
Q.3 
Given, 1 ? ? i , the value of the definite integral, I = 
?
?
?
2
0
sin cos
sin cos
?
dx
x i x
x i x
 is: 
(A) 1 (B) ?1 (C) i  (D) ?i  
 
 
Q.4 
x
x
x
2
1
1 lim ?
?
?
?
?
?
?
? ?
 is equal to 
(A) 
2 ?
e 
(B) e 
(C) 1 (D) 
2
e  
 
Q.5 
Let n j i a
ij
? ? ? , 1 , ] [ A with 3 ? n and j i a
ij
. ? . The rank of A is: 
(A) 0 (B) 1  (C) n ?1 (D) n 
 
Q.6 A horizontal beam ABC is loaded as shown in the figure below. The distance of the point of 
contraflexure from end A (in m) is ____________________.  
 
 
 
 
  
 
 
 
Q.7 For the plane stress situation shown in the figure, the maximum shear stress and the plane on which 
it acts are: 
 
 
 
 
 
 
 
 
(A) –50 MPa, on a plane 45
0
 clockwise w.r.t. x-axis 
(B) –50 MPa, on a plane 45
0
 anti-clockwise w.r.t. x-axis 
(C) 50 MPa, at all orientations 
(D) Zero, at all orientations 
 
?
x
 = 50 MPa 
?
y
 = 50 MPa 
?
y
 = 50 MPa 
?
x
 = 50 MPa 
x 
y 
A 
B 
10 kN 
1 m 
0.75 m 
C 
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