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 CRead More

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