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GATE 2015 : Instrumentation Engineering

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GATE 2015 INSTRUMENTATION ENGINEERING - IN Q. 1 Q. 25 carry one mark each. Q.1 Let be an where is matrix with rank (A) r Q.2 The value of 0 (B) 0 (C) 0 0 < ). Then (C) independent solutions, + (D) 0 0 ( , ) (C) 2 (D) 4 is equivalent to ( , ) (B) 0 ( , ) (D) 0 ( , ) 0 ( , ) The magnitude of the directional derivative of the function normal to the circle 2 + 2 = 2, at the point (1,1), is (A) 4 2 = 0 has , where the contour is the unit circle traversed clockwise, is 2 The double integral (A) Q.4 1 2 (A) Q.3 (B) n (0 < (B) 5 2 (C) 7 2 ( , )= 2 +3 2 in a direction (D) 9 2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 t) volts. Assuming ideal diode characteristics with zero forward voltage drop and zero reverse current, the average power consumed in watts by the load resistance R L is __________ W . Q.6 The capacitor shown in the figure is initially charged to +10 V. The switch closes at time t = 0. Then the value of VC (t) in volts at time t = 10 ms is__________ V . Q.7 The torque transmitted by a cylindrical shaft is to be measured by using two strain gauges. The angles for mounting the strain gauges relative to the axis of the shaft for maximum sensitivity are (A) 45o IN (B) 60o (C) 90o (D) 180o 1/13

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