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EC GATE 2015 - 1

13 pages, 14 questions, 0 questions with responses, 0 total responses,

Sourav Ghosh
Burdwan University (BU), Rajbati, Bardhaman
M.Tech Microwaves

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GATE 2015 SET 1 ELECTRONICS AND COMMUNICATION ENGINEERING - EC Q. 1 Q. 25 carry one mark each. Q.1 Consider a system of linear equations: x 2 y + 3 z = 1 , x 3 y + 4 z = 1 , and 2 x + 4 y 6 z = k . The value of k for which the system has infinitely many solutions is ______. Q.2 2 3 A function f ( x) = 1 x + x is defined in the closed interval [ 1,1] . The value of x , in the open interval ( 1, 1) for which the mean value theorem is satisfied, is (A) 1 2 Q.3 (B) 1 3 (D) 1/2 Suppose and B are two independent events with probabilities ( ) 0 and ( ) 0. Let and be their complements. Which one of the following statements is FALSE? (A) ( ) = ( ) ( ) (C) ( ) = ( ) + ( ) Q.4 (C) 1 3 (B) ( | ) = ( ) (D) = ( ) Let z = x + iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TRUE? (A) The residue of (B) (C) z at z = 1 is 1/2 z 1 2 =0 =1 (D) z (complex conjugate of z ) is an analytical function Q.5 4 1 The value of p such that the vector 2 is an eigenvector of the matrix 3 14 _______. Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ________. EC 1 2 4 2 1 is 10 1/13

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