Page 1 ?IN ?Gate - 2009 1 IN: INSTRUMENTATION ENGINEERING Q.1 to Q.20 Carry 1 Mark Each 1 If z = x+jy, where x and y are real. The value of jz e is (A) 1 (B) 2 2 x y e ? (C) y e (D) y e ? 2 The value of sin z dz, z ? Ñ where the contour of integration is a simple closed curve around the origin, is (A) 0 (B) 2 j ? (C) ? (D) ? ? 1 2 j ? 3 Let P=0 be a 3x3 real matrix. There exist linearly independent vectors x and y such that Px=0 and Py=0. The dimension of the range space of P is (A) 0 (B) 1 (C) 2 (D) 3 4 A sphere of unit of radius is centered at the origin. The unit normal at a point(x,y,z) on the surface of the sphere is the vector (A) (x,y,z) (B) 1 1 1 , , 3 3 3 ? ? ? ? ? ? (C) x y z , , 3 3 3 ? ? ? ? ? ? (D) x y z , , 2 2 2 ? ? ? ? ? ? 5 An LVDT is supplied with a sinusoidal voltage of amplitude 5V and frequency 1kHz. The output is connected to an ac voltmeter. The reading of the voltmeter is 1V for a displacement of 1mm from the null position. When the displacement is 1mm in the opposite direction from the null position, the reading of the voltmeter is (A) -1V (B) -0.2V (C) 1V (D) 5V 6 The circuit shown in the figure is (A) an all-pass filter (B) a bandpass filter (C) a highpass filter (D) a lowpass filter R R R C i v o v ? ? Page 2 ?IN ?Gate - 2009 1 IN: INSTRUMENTATION ENGINEERING Q.1 to Q.20 Carry 1 Mark Each 1 If z = x+jy, where x and y are real. The value of jz e is (A) 1 (B) 2 2 x y e ? (C) y e (D) y e ? 2 The value of sin z dz, z ? Ñ where the contour of integration is a simple closed curve around the origin, is (A) 0 (B) 2 j ? (C) ? (D) ? ? 1 2 j ? 3 Let P=0 be a 3x3 real matrix. There exist linearly independent vectors x and y such that Px=0 and Py=0. The dimension of the range space of P is (A) 0 (B) 1 (C) 2 (D) 3 4 A sphere of unit of radius is centered at the origin. The unit normal at a point(x,y,z) on the surface of the sphere is the vector (A) (x,y,z) (B) 1 1 1 , , 3 3 3 ? ? ? ? ? ? (C) x y z , , 3 3 3 ? ? ? ? ? ? (D) x y z , , 2 2 2 ? ? ? ? ? ? 5 An LVDT is supplied with a sinusoidal voltage of amplitude 5V and frequency 1kHz. The output is connected to an ac voltmeter. The reading of the voltmeter is 1V for a displacement of 1mm from the null position. When the displacement is 1mm in the opposite direction from the null position, the reading of the voltmeter is (A) -1V (B) -0.2V (C) 1V (D) 5V 6 The circuit shown in the figure is (A) an all-pass filter (B) a bandpass filter (C) a highpass filter (D) a lowpass filter R R R C i v o v ? ? ?IN ?Gate - 2009 2 7 The diodes in the circuit shown are ideal. A voltage of 0V represents logic 0 and +5V represents logic 1. The logic function Z realized by the circuit for logic inputs X and Y is (A) Z=X+Y (B) Z=XY (C) Z X Y ? ? (D) Z=XY 8 The minimal sum-of-products expression for the logic function f represented by the given Karnaugh map is PQ RS 00 01 11 10 00 0 1 0 0 01 0 1 1 1 11 1 1 1 0 10 0 0 1 0 (A) QS PRS PQR PRS PQR ? ? ? ? (B) QS PRS PQR PRS PQR ? ? ? ? (C) PRS PQR PRS PQR ? ? ? (D) PRS PQR PRS PQR ? ? ? 9 In the figure shown, the initial state of Q is 0. The output is observed after the application of each clock pulse. The output sequence at Q is (A) 0000… (B) 1010… (C) 1111… (D) 1000… X Y Z 5V ? CLK J K Q Q CLOCK Page 3 ?IN ?Gate - 2009 1 IN: INSTRUMENTATION ENGINEERING Q.1 to Q.20 Carry 1 Mark Each 1 If z = x+jy, where x and y are real. The value of jz e is (A) 1 (B) 2 2 x y e ? (C) y e (D) y e ? 2 The value of sin z dz, z ? Ñ where the contour of integration is a simple closed curve around the origin, is (A) 0 (B) 2 j ? (C) ? (D) ? ? 1 2 j ? 3 Let P=0 be a 3x3 real matrix. There exist linearly independent vectors x and y such that Px=0 and Py=0. The dimension of the range space of P is (A) 0 (B) 1 (C) 2 (D) 3 4 A sphere of unit of radius is centered at the origin. The unit normal at a point(x,y,z) on the surface of the sphere is the vector (A) (x,y,z) (B) 1 1 1 , , 3 3 3 ? ? ? ? ? ? (C) x y z , , 3 3 3 ? ? ? ? ? ? (D) x y z , , 2 2 2 ? ? ? ? ? ? 5 An LVDT is supplied with a sinusoidal voltage of amplitude 5V and frequency 1kHz. The output is connected to an ac voltmeter. The reading of the voltmeter is 1V for a displacement of 1mm from the null position. When the displacement is 1mm in the opposite direction from the null position, the reading of the voltmeter is (A) -1V (B) -0.2V (C) 1V (D) 5V 6 The circuit shown in the figure is (A) an all-pass filter (B) a bandpass filter (C) a highpass filter (D) a lowpass filter R R R C i v o v ? ? ?IN ?Gate - 2009 2 7 The diodes in the circuit shown are ideal. A voltage of 0V represents logic 0 and +5V represents logic 1. The logic function Z realized by the circuit for logic inputs X and Y is (A) Z=X+Y (B) Z=XY (C) Z X Y ? ? (D) Z=XY 8 The minimal sum-of-products expression for the logic function f represented by the given Karnaugh map is PQ RS 00 01 11 10 00 0 1 0 0 01 0 1 1 1 11 1 1 1 0 10 0 0 1 0 (A) QS PRS PQR PRS PQR ? ? ? ? (B) QS PRS PQR PRS PQR ? ? ? ? (C) PRS PQR PRS PQR ? ? ? (D) PRS PQR PRS PQR ? ? ? 9 In the figure shown, the initial state of Q is 0. The output is observed after the application of each clock pulse. The output sequence at Q is (A) 0000… (B) 1010… (C) 1111… (D) 1000… X Y Z 5V ? CLK J K Q Q CLOCK ?IN ?Gate - 2009 3 10 The binary representation of the decimal number 1.375 is (A) 1.111 (B) 1.010 (C) 1.011 (D) 1.001 11 Consider a system consisting of a microprocessor, memory, and peripheral devices connected by a common bus. During DMA data transfer, the microprocessor (A) only reads from the bus (B) only writes to the bus (C) both reads from and writes to the bus (D) neither reads from nor writes to the bus 12 The fundamental period of x(t) 2sin2 t 3sin3 t ? ? ? ? , with t expressed in seconds, is (A) 1s (B) 0.67s (C) 2s (D) 3s 13 A linear time-invariant causal system has a frequency response given in polar form as 1 2 1 tan . 1 ? ? ? ? ? ? For input x(t) = sin t, the output is (A) 1 cos t 2 (B) 1 cos t 4 2 ? ? ? ? ? ? ? ? (C) 1 sin t 2 (D) 1 sin t 4 2 ? ? ? ? ? ? ? ? 14 A 50% duty cycle square wave with zero mean is used as a baseband signal in an ideal frequency modulator with a sinusoidal carrier of frequency ? c . The modulated signal is given as an input to an ideal phase demodulator (a circuit that produces an output proportional to the difference in phase of the modulated signal from that of the carrier). The output of the circuit is (A) a square wave (B) a train of impulses with alternating signs (C) a triangular wave (D) a sinusoidal wave 15 The figure shows a periodic waveform to be displayed on a CRO. A trigger setting which ensures a stationary display is (A) level: 0.2V, slope: -ve (B) level: 0.5V, slope: -ve (C) level: -0.2V, slope: +ve (D) level: 1.8V, slope: -ve 2.5 ? 1.5 ? 0.5 ? 0.5 1.5 2.5 0 t Page 4 ?IN ?Gate - 2009 1 IN: INSTRUMENTATION ENGINEERING Q.1 to Q.20 Carry 1 Mark Each 1 If z = x+jy, where x and y are real. The value of jz e is (A) 1 (B) 2 2 x y e ? (C) y e (D) y e ? 2 The value of sin z dz, z ? Ñ where the contour of integration is a simple closed curve around the origin, is (A) 0 (B) 2 j ? (C) ? (D) ? ? 1 2 j ? 3 Let P=0 be a 3x3 real matrix. There exist linearly independent vectors x and y such that Px=0 and Py=0. The dimension of the range space of P is (A) 0 (B) 1 (C) 2 (D) 3 4 A sphere of unit of radius is centered at the origin. The unit normal at a point(x,y,z) on the surface of the sphere is the vector (A) (x,y,z) (B) 1 1 1 , , 3 3 3 ? ? ? ? ? ? (C) x y z , , 3 3 3 ? ? ? ? ? ? (D) x y z , , 2 2 2 ? ? ? ? ? ? 5 An LVDT is supplied with a sinusoidal voltage of amplitude 5V and frequency 1kHz. The output is connected to an ac voltmeter. The reading of the voltmeter is 1V for a displacement of 1mm from the null position. When the displacement is 1mm in the opposite direction from the null position, the reading of the voltmeter is (A) -1V (B) -0.2V (C) 1V (D) 5V 6 The circuit shown in the figure is (A) an all-pass filter (B) a bandpass filter (C) a highpass filter (D) a lowpass filter R R R C i v o v ? ? ?IN ?Gate - 2009 2 7 The diodes in the circuit shown are ideal. A voltage of 0V represents logic 0 and +5V represents logic 1. The logic function Z realized by the circuit for logic inputs X and Y is (A) Z=X+Y (B) Z=XY (C) Z X Y ? ? (D) Z=XY 8 The minimal sum-of-products expression for the logic function f represented by the given Karnaugh map is PQ RS 00 01 11 10 00 0 1 0 0 01 0 1 1 1 11 1 1 1 0 10 0 0 1 0 (A) QS PRS PQR PRS PQR ? ? ? ? (B) QS PRS PQR PRS PQR ? ? ? ? (C) PRS PQR PRS PQR ? ? ? (D) PRS PQR PRS PQR ? ? ? 9 In the figure shown, the initial state of Q is 0. The output is observed after the application of each clock pulse. The output sequence at Q is (A) 0000… (B) 1010… (C) 1111… (D) 1000… X Y Z 5V ? CLK J K Q Q CLOCK ?IN ?Gate - 2009 3 10 The binary representation of the decimal number 1.375 is (A) 1.111 (B) 1.010 (C) 1.011 (D) 1.001 11 Consider a system consisting of a microprocessor, memory, and peripheral devices connected by a common bus. During DMA data transfer, the microprocessor (A) only reads from the bus (B) only writes to the bus (C) both reads from and writes to the bus (D) neither reads from nor writes to the bus 12 The fundamental period of x(t) 2sin2 t 3sin3 t ? ? ? ? , with t expressed in seconds, is (A) 1s (B) 0.67s (C) 2s (D) 3s 13 A linear time-invariant causal system has a frequency response given in polar form as 1 2 1 tan . 1 ? ? ? ? ? ? For input x(t) = sin t, the output is (A) 1 cos t 2 (B) 1 cos t 4 2 ? ? ? ? ? ? ? ? (C) 1 sin t 2 (D) 1 sin t 4 2 ? ? ? ? ? ? ? ? 14 A 50% duty cycle square wave with zero mean is used as a baseband signal in an ideal frequency modulator with a sinusoidal carrier of frequency ? c . The modulated signal is given as an input to an ideal phase demodulator (a circuit that produces an output proportional to the difference in phase of the modulated signal from that of the carrier). The output of the circuit is (A) a square wave (B) a train of impulses with alternating signs (C) a triangular wave (D) a sinusoidal wave 15 The figure shows a periodic waveform to be displayed on a CRO. A trigger setting which ensures a stationary display is (A) level: 0.2V, slope: -ve (B) level: 0.5V, slope: -ve (C) level: -0.2V, slope: +ve (D) level: 1.8V, slope: -ve 2.5 ? 1.5 ? 0.5 ? 0.5 1.5 2.5 0 t ?IN ?Gate - 2009 4 16 The input impedance of CRO is equivalent to a 1M ? resistance in parallel with a 45pF capacitance. It is used with a compensated 10-to-1 attenuation probe. The effective input capacitance at the probe tip is (A) 4.5pF (B) 5pF (C) 45pF (D) 450pF 17 A galvanometer with internal resistance 100 ? and full-scale current 1mA is used to realize a dc voltmeter with a full scale range of 1V. The full scale range of this voltmeter can be extended to 10V by connecting an external resistance of value (A) 9k ? (B) 9.9k ? (C) 10k ? (D) 11k ? 18 A plant with a transfer function 2 s(s 3) ? is controlled by a PI controller with K p =1 and K i =0 in a unity feedback configuration. The lowest value of K i that ensures zero steady state error for a step change in the reference input is (A) 0 (B) 1/3 (C) 1/2 (D) 1 19 A mass spectrometer is to be used to resolve peaks corresponding to CO + and N 2 + . The atomic masses are 12 16 C 12.0000, O 15.9949, and ? ? 14 N 14.0031 amu. ? The resolving power of the mass spectrometer should be atleast (A) 250 (B) 350 (C) 2500 (D) 3500 20 Assuming complete dissociation, the pH of a 1mM solution of H 2 SO 4 is closest to (A) 3 (B) 2.7 (C) 2.4 (D) 2.1 Q.21 to Q.60 carry 2 Marks each 21 The eigen values of a (2x2) matrix X are -2 and -3. The eigenvalues of matrix (X+I) -1 (X+5I) are (A) -3,-4 (B) -1,-2 (C) -1,-3 (D) -2,-4 22 The matrix 0 0 1 P 1 0 0 0 1 0 ? ? ? ? ? ? ? ? ? ? ? rotates a vector about the axis 1 1 1 ? ? ? ? ? ? ? ? ? ? by an angle of (A) 30º (B) 60º (C) 90º (D) 120º 23 A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a person getting a positive report is 0.01, the probability that a person tested gets an incorrect report is (A) 0.0027 (B) 0.0173 (C) 0.1497 (D) 0.2100 24 One of the roots of the equation x 3 =j, where j is positive square root of -1, is (A) j (B) 3 1 j 2 2 ? (C) 3 1 j 2 2 ? (D) 3 1 j 2 2 ? ? Page 5 ?IN ?Gate - 2009 1 IN: INSTRUMENTATION ENGINEERING Q.1 to Q.20 Carry 1 Mark Each 1 If z = x+jy, where x and y are real. The value of jz e is (A) 1 (B) 2 2 x y e ? (C) y e (D) y e ? 2 The value of sin z dz, z ? Ñ where the contour of integration is a simple closed curve around the origin, is (A) 0 (B) 2 j ? (C) ? (D) ? ? 1 2 j ? 3 Let P=0 be a 3x3 real matrix. There exist linearly independent vectors x and y such that Px=0 and Py=0. The dimension of the range space of P is (A) 0 (B) 1 (C) 2 (D) 3 4 A sphere of unit of radius is centered at the origin. The unit normal at a point(x,y,z) on the surface of the sphere is the vector (A) (x,y,z) (B) 1 1 1 , , 3 3 3 ? ? ? ? ? ? (C) x y z , , 3 3 3 ? ? ? ? ? ? (D) x y z , , 2 2 2 ? ? ? ? ? ? 5 An LVDT is supplied with a sinusoidal voltage of amplitude 5V and frequency 1kHz. The output is connected to an ac voltmeter. The reading of the voltmeter is 1V for a displacement of 1mm from the null position. When the displacement is 1mm in the opposite direction from the null position, the reading of the voltmeter is (A) -1V (B) -0.2V (C) 1V (D) 5V 6 The circuit shown in the figure is (A) an all-pass filter (B) a bandpass filter (C) a highpass filter (D) a lowpass filter R R R C i v o v ? ? ?IN ?Gate - 2009 2 7 The diodes in the circuit shown are ideal. A voltage of 0V represents logic 0 and +5V represents logic 1. The logic function Z realized by the circuit for logic inputs X and Y is (A) Z=X+Y (B) Z=XY (C) Z X Y ? ? (D) Z=XY 8 The minimal sum-of-products expression for the logic function f represented by the given Karnaugh map is PQ RS 00 01 11 10 00 0 1 0 0 01 0 1 1 1 11 1 1 1 0 10 0 0 1 0 (A) QS PRS PQR PRS PQR ? ? ? ? (B) QS PRS PQR PRS PQR ? ? ? ? (C) PRS PQR PRS PQR ? ? ? (D) PRS PQR PRS PQR ? ? ? 9 In the figure shown, the initial state of Q is 0. The output is observed after the application of each clock pulse. The output sequence at Q is (A) 0000… (B) 1010… (C) 1111… (D) 1000… X Y Z 5V ? CLK J K Q Q CLOCK ?IN ?Gate - 2009 3 10 The binary representation of the decimal number 1.375 is (A) 1.111 (B) 1.010 (C) 1.011 (D) 1.001 11 Consider a system consisting of a microprocessor, memory, and peripheral devices connected by a common bus. During DMA data transfer, the microprocessor (A) only reads from the bus (B) only writes to the bus (C) both reads from and writes to the bus (D) neither reads from nor writes to the bus 12 The fundamental period of x(t) 2sin2 t 3sin3 t ? ? ? ? , with t expressed in seconds, is (A) 1s (B) 0.67s (C) 2s (D) 3s 13 A linear time-invariant causal system has a frequency response given in polar form as 1 2 1 tan . 1 ? ? ? ? ? ? For input x(t) = sin t, the output is (A) 1 cos t 2 (B) 1 cos t 4 2 ? ? ? ? ? ? ? ? (C) 1 sin t 2 (D) 1 sin t 4 2 ? ? ? ? ? ? ? ? 14 A 50% duty cycle square wave with zero mean is used as a baseband signal in an ideal frequency modulator with a sinusoidal carrier of frequency ? c . The modulated signal is given as an input to an ideal phase demodulator (a circuit that produces an output proportional to the difference in phase of the modulated signal from that of the carrier). The output of the circuit is (A) a square wave (B) a train of impulses with alternating signs (C) a triangular wave (D) a sinusoidal wave 15 The figure shows a periodic waveform to be displayed on a CRO. A trigger setting which ensures a stationary display is (A) level: 0.2V, slope: -ve (B) level: 0.5V, slope: -ve (C) level: -0.2V, slope: +ve (D) level: 1.8V, slope: -ve 2.5 ? 1.5 ? 0.5 ? 0.5 1.5 2.5 0 t ?IN ?Gate - 2009 4 16 The input impedance of CRO is equivalent to a 1M ? resistance in parallel with a 45pF capacitance. It is used with a compensated 10-to-1 attenuation probe. The effective input capacitance at the probe tip is (A) 4.5pF (B) 5pF (C) 45pF (D) 450pF 17 A galvanometer with internal resistance 100 ? and full-scale current 1mA is used to realize a dc voltmeter with a full scale range of 1V. The full scale range of this voltmeter can be extended to 10V by connecting an external resistance of value (A) 9k ? (B) 9.9k ? (C) 10k ? (D) 11k ? 18 A plant with a transfer function 2 s(s 3) ? is controlled by a PI controller with K p =1 and K i =0 in a unity feedback configuration. The lowest value of K i that ensures zero steady state error for a step change in the reference input is (A) 0 (B) 1/3 (C) 1/2 (D) 1 19 A mass spectrometer is to be used to resolve peaks corresponding to CO + and N 2 + . The atomic masses are 12 16 C 12.0000, O 15.9949, and ? ? 14 N 14.0031 amu. ? The resolving power of the mass spectrometer should be atleast (A) 250 (B) 350 (C) 2500 (D) 3500 20 Assuming complete dissociation, the pH of a 1mM solution of H 2 SO 4 is closest to (A) 3 (B) 2.7 (C) 2.4 (D) 2.1 Q.21 to Q.60 carry 2 Marks each 21 The eigen values of a (2x2) matrix X are -2 and -3. The eigenvalues of matrix (X+I) -1 (X+5I) are (A) -3,-4 (B) -1,-2 (C) -1,-3 (D) -2,-4 22 The matrix 0 0 1 P 1 0 0 0 1 0 ? ? ? ? ? ? ? ? ? ? ? rotates a vector about the axis 1 1 1 ? ? ? ? ? ? ? ? ? ? by an angle of (A) 30º (B) 60º (C) 90º (D) 120º 23 A screening test is carried out to detect a certain disease. It is found that 12% of the positive reports and 15% of the negative reports are incorrect. Assuming that the probability of a person getting a positive report is 0.01, the probability that a person tested gets an incorrect report is (A) 0.0027 (B) 0.0173 (C) 0.1497 (D) 0.2100 24 One of the roots of the equation x 3 =j, where j is positive square root of -1, is (A) j (B) 3 1 j 2 2 ? (C) 3 1 j 2 2 ? (D) 3 1 j 2 2 ? ? ?IN ?Gate - 2009 5 25 The differential equation dx 4 x , dt ? ? ? with x(0)=0, and the constant 0 ? ? , is to be numerically integrated using the forward Euler method with a constant integration time step T. The maximum value of T such that the numerical solution of x converges is (A) / 4 ? (B) /2 ? (C) ? (D) ? ? 26 A quantity x is calculated by using the formula x = (p-q)/r, The measured values are p=9, q =6, r=0.5. Assume that the measurement errors in p, q and r are independent. The absolute maximum error in the measurement of each of the three quantities is ?. The absolute maximum error in the calculated value of x is (A) ? (B) 2 ? (C) 3 ? (D) 16 ? 27 The response of a first order measurement system to a unit step input is 0.5t 1 e ? ? , where t is in seconds. A ramp of 0.1units per second is given as the input to this system. The error in the measured value after transients have died down is (A) 0.02units (B) 0.1units (C) 0.2units (D) 1unit 28 The source network S is connected to the load network L as shown by dashed lines. The power transferred from S to L would be maximum when R L is (A) 0 ? (B) 0.6 ? (C) 0.8 ? (D) 2 ? 29 A stroboscopic system is used for measuring the speed of a rotating shaft. The shaft has one target mark on it. The maximum strobe rate at which synchronism is achieved is r 1 flashes per minute. The next lower flash rate at which synchronism is achieved is r 2 flashes per minute. The speed of the shaft in rpm is (A) 1 2 1 2 r r r r ? (B) 1 2 1 2 r r r r ? (C) 2 2 1 2 r r r ? (D) 2 1 1 2 r r r ? 30 The figure shSows the cross-sectional diagram of an orifice flow meter with an orifice radius R. Point ‘a’ is 30R upstream while points ‘b’ and ‘c’ are 0.8R and 30R downstream from the orifice respectively. The pressures at points a, b and c are P a , P b and P c respectively. Then 2 ? ? ? 10V 3V ? ? Load Network L Source Network S L RRead More

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