Page 1 GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 1/13 Q. 1 – Q. 25 carry one mark each. Q.1 Let ???? be an ???? × ???? matrix with rank ???? (0 < ???? < ???? ). Then ???????? = 0 has ???? independent solutions, where ???? is (A) r (B) n (C) ???? - ???? (D) ???? + ???? Q.2 The value of ? 1 ???? 2 ???????? , where the contour is the unit circle traversed clockwise, is (A) -2 ???????? (B) 0 (C) 2 ???????? (D) 4 ???????? Q.3 The double integral ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 is equivalent to (A) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 (B) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (C) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (D) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 Q.4 The magnitude of the directional derivative of the function ???? ( ???? , ???? ) = ???? 2 + 3 ???? 2 in a direction normal to the circle ???? 2 + ???? 2 = 2, at the point (1,1), is (A) 4 v2 (B) 5 v2 (C) 7 v2 (D) 9 v2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 p 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 V C (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) ± 45 o (B) ± 60 o (C) ± 90 o (D) ± 180 o Page 2 GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 1/13 Q. 1 – Q. 25 carry one mark each. Q.1 Let ???? be an ???? × ???? matrix with rank ???? (0 < ???? < ???? ). Then ???????? = 0 has ???? independent solutions, where ???? is (A) r (B) n (C) ???? - ???? (D) ???? + ???? Q.2 The value of ? 1 ???? 2 ???????? , where the contour is the unit circle traversed clockwise, is (A) -2 ???????? (B) 0 (C) 2 ???????? (D) 4 ???????? Q.3 The double integral ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 is equivalent to (A) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 (B) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (C) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (D) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 Q.4 The magnitude of the directional derivative of the function ???? ( ???? , ???? ) = ???? 2 + 3 ???? 2 in a direction normal to the circle ???? 2 + ???? 2 = 2, at the point (1,1), is (A) 4 v2 (B) 5 v2 (C) 7 v2 (D) 9 v2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 p 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 V C (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) ± 45 o (B) ± 60 o (C) ± 90 o (D) ± 180 o GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 2/13 Q.8 A p-type semiconductor strain gauge has a nominal resistance of 1000 O and a gauge factor of +200 at 25 °C. The resistance of the strain gauge in ohms when subjected to a strain of +10 -4 m/m at the same temperature is __________ O. Q.9 Liquid flow rate is measured using (A) a Pirani gauge (B) a pyrometer (C) an orifice plate (D) a Bourdon tube Q.10 The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by (A) NV i sin ?t (B) - NV i sin ?t (C) 1 N V i sin ?t (D) - 1 N V i sin ?t Q.11 A load resistor R L is connected to a battery of voltage E with internal resistance R i through a resistance R S as shown in the figure. For fixed values of R L and R i , the value of R S ( = 0) for maximum power transfer to R L is (A) 0 (B) R L - R i (C) R L (D) R L + R i Q.12 Consider the logic circuit with input signal TEST shown in the figure. All gates in the figure shown have identical non-zero delay. The signal TEST which was at logic LOW is switched to logic HIGH and maintained at logic HIGH. The output (A) stays HIGH throughout (B) stays LOW throughout (C) pulses from LOW to HIGH to LOW (D) pulses from HIGH to LOW to HIGH Page 3 GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 1/13 Q. 1 – Q. 25 carry one mark each. Q.1 Let ???? be an ???? × ???? matrix with rank ???? (0 < ???? < ???? ). Then ???????? = 0 has ???? independent solutions, where ???? is (A) r (B) n (C) ???? - ???? (D) ???? + ???? Q.2 The value of ? 1 ???? 2 ???????? , where the contour is the unit circle traversed clockwise, is (A) -2 ???????? (B) 0 (C) 2 ???????? (D) 4 ???????? Q.3 The double integral ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 is equivalent to (A) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 (B) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (C) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (D) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 Q.4 The magnitude of the directional derivative of the function ???? ( ???? , ???? ) = ???? 2 + 3 ???? 2 in a direction normal to the circle ???? 2 + ???? 2 = 2, at the point (1,1), is (A) 4 v2 (B) 5 v2 (C) 7 v2 (D) 9 v2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 p 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 V C (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) ± 45 o (B) ± 60 o (C) ± 90 o (D) ± 180 o GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 2/13 Q.8 A p-type semiconductor strain gauge has a nominal resistance of 1000 O and a gauge factor of +200 at 25 °C. The resistance of the strain gauge in ohms when subjected to a strain of +10 -4 m/m at the same temperature is __________ O. Q.9 Liquid flow rate is measured using (A) a Pirani gauge (B) a pyrometer (C) an orifice plate (D) a Bourdon tube Q.10 The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by (A) NV i sin ?t (B) - NV i sin ?t (C) 1 N V i sin ?t (D) - 1 N V i sin ?t Q.11 A load resistor R L is connected to a battery of voltage E with internal resistance R i through a resistance R S as shown in the figure. For fixed values of R L and R i , the value of R S ( = 0) for maximum power transfer to R L is (A) 0 (B) R L - R i (C) R L (D) R L + R i Q.12 Consider the logic circuit with input signal TEST shown in the figure. All gates in the figure shown have identical non-zero delay. The signal TEST which was at logic LOW is switched to logic HIGH and maintained at logic HIGH. The output (A) stays HIGH throughout (B) stays LOW throughout (C) pulses from LOW to HIGH to LOW (D) pulses from HIGH to LOW to HIGH GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 3/13 Q.13 The logic evaluated by the circuit at the output is (A) XY ? +YX ? (B) (X+Y ? ? ? ? ? ? )XY (C) XY ? ? ? ? +XY (D) X ? Y+XY ? +X+Y Q.14 In the circuit shown, the switch is momentarily closed and then opened. Assuming the logic gates to have equal non-zero delay, at steady state, the logic states of X and Y are (A) X is latched, Y toggles continuously (B) X and Y are both latched (C) Y is latched, X toggles continuously (D) X and Y both toggle continuously Q.15 The highest frequency present in the signal ???? ( ???? ) is ???? max . The highest frequency present in the signal ???? ( ???? ) = ???? 2 ( ???? ) is (A) 1 2 ???? max (B) ???? max (C) 2 ???? max (D) 4 ???? max Q.16 The filter whose transfer function is of the form G(s) = ???? 2 - ???????? + ???? ???? 2 + ???????? + ???? is (A) a high-pass filter (B) a low-pass filter (C) an all-pass filter (D) a band-reject filter Q.17 Let 3 + 4 ???? be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is (A) 3 - 4 ???? (B) 3 25 + 4 25 ???? (C) 3 25 - 4 25 ???? (D) 1 3 - 1 4 ???? Page 4 GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 1/13 Q. 1 – Q. 25 carry one mark each. Q.1 Let ???? be an ???? × ???? matrix with rank ???? (0 < ???? < ???? ). Then ???????? = 0 has ???? independent solutions, where ???? is (A) r (B) n (C) ???? - ???? (D) ???? + ???? Q.2 The value of ? 1 ???? 2 ???????? , where the contour is the unit circle traversed clockwise, is (A) -2 ???????? (B) 0 (C) 2 ???????? (D) 4 ???????? Q.3 The double integral ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 is equivalent to (A) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 (B) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (C) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (D) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 Q.4 The magnitude of the directional derivative of the function ???? ( ???? , ???? ) = ???? 2 + 3 ???? 2 in a direction normal to the circle ???? 2 + ???? 2 = 2, at the point (1,1), is (A) 4 v2 (B) 5 v2 (C) 7 v2 (D) 9 v2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 p 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 V C (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) ± 45 o (B) ± 60 o (C) ± 90 o (D) ± 180 o GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 2/13 Q.8 A p-type semiconductor strain gauge has a nominal resistance of 1000 O and a gauge factor of +200 at 25 °C. The resistance of the strain gauge in ohms when subjected to a strain of +10 -4 m/m at the same temperature is __________ O. Q.9 Liquid flow rate is measured using (A) a Pirani gauge (B) a pyrometer (C) an orifice plate (D) a Bourdon tube Q.10 The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by (A) NV i sin ?t (B) - NV i sin ?t (C) 1 N V i sin ?t (D) - 1 N V i sin ?t Q.11 A load resistor R L is connected to a battery of voltage E with internal resistance R i through a resistance R S as shown in the figure. For fixed values of R L and R i , the value of R S ( = 0) for maximum power transfer to R L is (A) 0 (B) R L - R i (C) R L (D) R L + R i Q.12 Consider the logic circuit with input signal TEST shown in the figure. All gates in the figure shown have identical non-zero delay. The signal TEST which was at logic LOW is switched to logic HIGH and maintained at logic HIGH. The output (A) stays HIGH throughout (B) stays LOW throughout (C) pulses from LOW to HIGH to LOW (D) pulses from HIGH to LOW to HIGH GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 3/13 Q.13 The logic evaluated by the circuit at the output is (A) XY ? +YX ? (B) (X+Y ? ? ? ? ? ? )XY (C) XY ? ? ? ? +XY (D) X ? Y+XY ? +X+Y Q.14 In the circuit shown, the switch is momentarily closed and then opened. Assuming the logic gates to have equal non-zero delay, at steady state, the logic states of X and Y are (A) X is latched, Y toggles continuously (B) X and Y are both latched (C) Y is latched, X toggles continuously (D) X and Y both toggle continuously Q.15 The highest frequency present in the signal ???? ( ???? ) is ???? max . The highest frequency present in the signal ???? ( ???? ) = ???? 2 ( ???? ) is (A) 1 2 ???? max (B) ???? max (C) 2 ???? max (D) 4 ???? max Q.16 The filter whose transfer function is of the form G(s) = ???? 2 - ???????? + ???? ???? 2 + ???????? + ???? is (A) a high-pass filter (B) a low-pass filter (C) an all-pass filter (D) a band-reject filter Q.17 Let 3 + 4 ???? be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is (A) 3 - 4 ???? (B) 3 25 + 4 25 ???? (C) 3 25 - 4 25 ???? (D) 1 3 - 1 4 ???? GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 4/13 Q.18 Consider the ammeter-voltmeter method of determining the value of the resistance R using the circuit shown in the figure. The maximum possible errors of the voltmeter and ammeter are known to be 1 % and 2 % of their readings, respectively. Neglecting the effects of meter resistances, the maximum possible percentage error in the value of R determined from the measurements, is__________%. Q.19 The bridge most suited for measurement of a four-terminal resistance in the range of 0.001 O to 0.1 O is (A) Wien’s bridge (B) Kelvin double bridge (C) Maxwell’s bridge (D) Schering bridge Q.20 A power line is coupled capacitively through various parasitic capacitances to a shielded signal line as shown in the figure. The conductive shield is grounded solidly at one end. Assume that the length of the signal wire extending beyond the shield, and the shield resistance are negligible. The magnitude of the noise voltage coupled to the signal line is (A) directly proportional to C 1G (B) inversely proportional to the power line frequency (C) inversely proportional to C 1S (D) zero Q.21 A mass-spring-damper system with force as input and displacement of the mass as output has a transfer function ???? ( ???? ) = 1/( ???? 2 + 24 ???? + 900). A force input F(t) = 10 sin (70t) newtons is applied at time ???? = 0 s. A beam from an optical stroboscope is focused on the mass. In steady state, the strobe frequency in hertz at which the mass appears to be stationary is (A) 5/ ???? (B) 15/ ???? (C) 35/ ???? (D) 50/ ???? Q.22 A system with transfer function G(s) = 1 ???? 2 +1 has zero initial conditions. The percentage overshoot in its step response is _________ %. Page 5 GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 1/13 Q. 1 – Q. 25 carry one mark each. Q.1 Let ???? be an ???? × ???? matrix with rank ???? (0 < ???? < ???? ). Then ???????? = 0 has ???? independent solutions, where ???? is (A) r (B) n (C) ???? - ???? (D) ???? + ???? Q.2 The value of ? 1 ???? 2 ???????? , where the contour is the unit circle traversed clockwise, is (A) -2 ???????? (B) 0 (C) 2 ???????? (D) 4 ???????? Q.3 The double integral ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 is equivalent to (A) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 (B) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (C) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? ???? ???? 0 (D) ? ? ???? ( ???? , ???? ) ???????? ???????? ???? 0 ???? 0 Q.4 The magnitude of the directional derivative of the function ???? ( ???? , ???? ) = ???? 2 + 3 ???? 2 in a direction normal to the circle ???? 2 + ???? 2 = 2, at the point (1,1), is (A) 4 v2 (B) 5 v2 (C) 7 v2 (D) 9 v2 Q.5 The figure shows a half-wave rectifier circuit with input voltage V(t) = 10 sin (100 p 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 V C (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) ± 45 o (B) ± 60 o (C) ± 90 o (D) ± 180 o GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 2/13 Q.8 A p-type semiconductor strain gauge has a nominal resistance of 1000 O and a gauge factor of +200 at 25 °C. The resistance of the strain gauge in ohms when subjected to a strain of +10 -4 m/m at the same temperature is __________ O. Q.9 Liquid flow rate is measured using (A) a Pirani gauge (B) a pyrometer (C) an orifice plate (D) a Bourdon tube Q.10 The output voltage of the ideal transformer with the polarities and dots shown in the figure is given by (A) NV i sin ?t (B) - NV i sin ?t (C) 1 N V i sin ?t (D) - 1 N V i sin ?t Q.11 A load resistor R L is connected to a battery of voltage E with internal resistance R i through a resistance R S as shown in the figure. For fixed values of R L and R i , the value of R S ( = 0) for maximum power transfer to R L is (A) 0 (B) R L - R i (C) R L (D) R L + R i Q.12 Consider the logic circuit with input signal TEST shown in the figure. All gates in the figure shown have identical non-zero delay. The signal TEST which was at logic LOW is switched to logic HIGH and maintained at logic HIGH. The output (A) stays HIGH throughout (B) stays LOW throughout (C) pulses from LOW to HIGH to LOW (D) pulses from HIGH to LOW to HIGH GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 3/13 Q.13 The logic evaluated by the circuit at the output is (A) XY ? +YX ? (B) (X+Y ? ? ? ? ? ? )XY (C) XY ? ? ? ? +XY (D) X ? Y+XY ? +X+Y Q.14 In the circuit shown, the switch is momentarily closed and then opened. Assuming the logic gates to have equal non-zero delay, at steady state, the logic states of X and Y are (A) X is latched, Y toggles continuously (B) X and Y are both latched (C) Y is latched, X toggles continuously (D) X and Y both toggle continuously Q.15 The highest frequency present in the signal ???? ( ???? ) is ???? max . The highest frequency present in the signal ???? ( ???? ) = ???? 2 ( ???? ) is (A) 1 2 ???? max (B) ???? max (C) 2 ???? max (D) 4 ???? max Q.16 The filter whose transfer function is of the form G(s) = ???? 2 - ???????? + ???? ???? 2 + ???????? + ???? is (A) a high-pass filter (B) a low-pass filter (C) an all-pass filter (D) a band-reject filter Q.17 Let 3 + 4 ???? be a zero of a fourth order linear-phase FIR filter. The complex number which is NOT a zero of this filter is (A) 3 - 4 ???? (B) 3 25 + 4 25 ???? (C) 3 25 - 4 25 ???? (D) 1 3 - 1 4 ???? GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 4/13 Q.18 Consider the ammeter-voltmeter method of determining the value of the resistance R using the circuit shown in the figure. The maximum possible errors of the voltmeter and ammeter are known to be 1 % and 2 % of their readings, respectively. Neglecting the effects of meter resistances, the maximum possible percentage error in the value of R determined from the measurements, is__________%. Q.19 The bridge most suited for measurement of a four-terminal resistance in the range of 0.001 O to 0.1 O is (A) Wien’s bridge (B) Kelvin double bridge (C) Maxwell’s bridge (D) Schering bridge Q.20 A power line is coupled capacitively through various parasitic capacitances to a shielded signal line as shown in the figure. The conductive shield is grounded solidly at one end. Assume that the length of the signal wire extending beyond the shield, and the shield resistance are negligible. The magnitude of the noise voltage coupled to the signal line is (A) directly proportional to C 1G (B) inversely proportional to the power line frequency (C) inversely proportional to C 1S (D) zero Q.21 A mass-spring-damper system with force as input and displacement of the mass as output has a transfer function ???? ( ???? ) = 1/( ???? 2 + 24 ???? + 900). A force input F(t) = 10 sin (70t) newtons is applied at time ???? = 0 s. A beam from an optical stroboscope is focused on the mass. In steady state, the strobe frequency in hertz at which the mass appears to be stationary is (A) 5/ ???? (B) 15/ ???? (C) 35/ ???? (D) 50/ ???? Q.22 A system with transfer function G(s) = 1 ???? 2 +1 has zero initial conditions. The percentage overshoot in its step response is _________ %. GATE 2015 INSTRUMENTATION ENGINEERING - IN IN 5/13 Q.23 The voltage ( ???? 0 ) developed across a glass electrode for pH measurement is related to the temperature ( ???? ) by the relation (A) ???? 0 ? 1 ???? 2 (B) ???? 0 ? 1 ???? (C) ???? 0 ? ???? (D) ???? 0 ? ???? 2 Q.24 A light detector circuit using an ideal photo-diode is shown in the figure. The sensitivity of the photo-diode is 0.5 µA/µW. With V r = 6 V, the output voltage V o = -1.0 V for 10 µW of incident light. If V r is changed to 3 V, keeping all other parameters the same, the value of V o in volts is __________V. Q.25 An apparatus to capture ECG signals has a filter followed by a data acquisition system. The filter best suited for this application is (A) low pass with cutoff frequency 200 Hz (B) high pass with cutoff frequency 200 Hz (C) band pass with lower and upper cutoff frequencies 100 Hz and 200 Hz for its pass band (D) band reject with lower and upper cutoff frequencies 1 Hz and 200 Hz for its stop band Q. 26 – Q. 55 carry two marks each. Q.26 The probability that a thermistor randomly picked up from a production unit is defective is 0.1. The probability that out of 10 thermistors randomly picked up, 3 are defective is (A) 0.001 (B) 0.057 (C) 0.107 (D) 0.3 Q.27 The probability density function of a random variable ???? is ???? ???? ( ???? ) = ???? - ???? for ???? = 0 and 0 otherwise. The expected value of the function ???? ???? ( ???? ) = ???? 3 ???? /4 is __________ . Q.28 The z-transform of ???? [ ???? ] = ???? | ???? | , 0 < | ???? | < 1, is ???? ( ???? ). The region of convergence of ???? ( ???? ) is (A) | ???? | < | ???? | < 1 | ???? | (B) | ???? | > ???? (C) | ???? | > 1 | ???? | (D) | ???? | < min [| ???? |, 1 | ???? | ] Q.29 The current in amperes through the resistor R in the circuit shown in the figure is __________ A.Read More

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