1.25 The first algorithm for Linear programming was given by a) Bellman b) Dantzig c) Kulm d) Von Neumann Ans: (b) 2. Write in your answer book at the space provided for Question –2 the correct or the most appropriate answers to ALL. The following twenty five multiple choice sub questions, by writing one or more of the alphabets A, B, C and D which correspond (s) to your choice of the answer (s). Write the alphabets only in the ANSWER column, against the corresponding NUMBER of the sub-question. 2.1 The eigenvalues of the matrix 5333are
IES-GATE ACADEMY GATE-1999-ME Best coaching for IES, GATE, PSU’s in Chennai & Coimbatore 9445017000, 90037370000 | 6 Ans : (a, d) Explanation: 2 2 5 3 A I = 3 3 5 3 9 15 5 3 9 2 24 0 6 4 0 6 4 or 2.2 The static moment of the area of a half circle of unit radius about y –axis. 1xxydx is equal to 4 2 2.3 In a flow field is x, y –plane, the variation of velocity with time t is given by v = (x2+ yt) and v= (x2+ y2) i. The acceleration of the particle in this field, occupying point (1, 1) at time t = 1 will be i
IES-GATE ACADEMY GATE-1999-ME Best coaching for IES, GATE, PSU’s in Chennai & Coimbatore 9445017000, 90037370000| a) 1.414 b) 1.5 c) 2.0 d) none of these Ans: (b) Explaantion: x2 –2 = 0, 0100111.52fxxxfxf(x) = 2x f(x0) = 2x0 = 2(1) = 2. 2.6 Four arbitrary points (x1, y1), (x2, y2), (x3, y3), (x4, y4) are given in the x, y –plane. Using the method of least squares, if, regressing y upon x gives the fitted line y = ax + b; and regressing y upon x gives the fitted line y = ax + b; and regressing x upon y gives the fitted line x = cy + d, then a) the two fitted lines must coincide b) the two fitted lines need not coincide c) it is possible that ac = 0 d) a must be 1Ans: (d) Explanation: y = ax+b……………(i)x = cy+d …………..(ii)From equation (ii), x –d = cy or y = 1dxc……………….(iii) 7 2 2 1 2, 1 1 2 2 0 0 1 5 x u u x x t u y t y u u u u a u v w x y z t i i 2 2 2.4 d y dx + (x 2 + 4x) dy dx + y = x 8 – 8. The above equation is a a) Partial differential equation b) Non-linear differential equation c) Non-homogeneous differential equation d) Ordinary differential equation Ans : (d) 2.5 We wish to solve x2–2 = 0 by Newton Raphson technique. Let the initial guess b x0= 1.0. Subsequent estimate of x (i.e. x1) will be C
IES-GATE ACADEMY GATE-1999-ME Best coaching for IES, GATE, PSU’s in Chennai & Coimbatore 9445017000, 90037370000 | 8
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