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# Civil Engineering (CE) 2015 (Set 2) GATE Paper without solution (unsolved) GATE Notes | EduRev

## GATE : Civil Engineering (CE) 2015 (Set 2) 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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