Gate physics Sample Papers - 2008

                                         dy
   Given y  x2  2x  10, the value of          is equal to
1.
                                         dx x 1
   (A) 0                   (B) 4                     (C) 12               (D) 13
          sin x
   lim          is
2.
            x
    x 0
                                                                          (D) 
   (A) Indeterminate       (B) 0                     (C) 1
3. The power supplied by the dc voltage source in the circuit shown below is
                   3
                    6
                              1
          3V 
   (A) 0W                  (B) 1.0W                  (C) 2.5W             (D) 3.0W
4. The current I supplied by the dc voltage source in the circuit shown below is
                I
                      1
                                   1A
            
         1V
   (A) 0A                  (B) 0.5A                  (C) 1A               (D) 2A
5. For signal conditioning of a piezoelectric type transducer we require
   (A) a charge amplifier                            (B) a differential amplifier
   (C) an instrumentation amplifier                  (D) a transconductance amplifier
6. A linear variable differential transformer (LVDT) is
   (A) a displacement transducer
   (B) an impedance matching transformer
   (C) a differential temperature sensor
   (D) an auto transformer
7.  The temperature being sensed by a negative temperature coefficient (NTC) type
    thermistor is linearly increasing. Its resistance will
    (A) linearly increase with temperature
    (B) exponentially increase with temperature
    (C) linearly decrease with temperature
    (D) exponentially decrease with temperature
8.  For a single stage BJT common base amplifier
    (A) current gain as well as voltage gain can be greater than unity
    (B) current gain can be greater than unity but voltage gain is always less than
         unity
    (C) voltage gain can be greater than unity but current gain is always less than
         unity
    (D) current gain as well as voltage gain is always less than unity
    In the circuit shown below, the ideality factor  of the diode is unity and the
9.
    voltage drop across it is 0.7V. The dynamic resistance of the diode at room
    temperature is approximately
                                1.7V 
                                                      1k
    (A) 15                 (B) 25                (C) 50             (D) 700 
10. An ideal op-amp has the characteristics of an ideal
    (A) voltage controlled voltage source          (B) voltage controlled current source
    (C) current controlled voltage source          (D) current controlled current source
11. The inverters in the ring oscillator circuit shown below are identical. If the output
    waveform has a frequency of 10 MHz, the propagation delay pf each inverter is
                                        output
                            (B) 10 ns              (C) 20 ns           (D) 50 ns
    (A) 5 ns
12. A 2K�8 bit RAM is interfaced to an 8-bit microprocessor. If the address of the first
    memory location in the RAM is 0800H, the address of the last memory location
    will be
    (A) 1000H               (B) 0FFFH              (C) 2848H           (D) 47FFH
                                                                         5 
                                                                       f    n
                                                                         6 
    The fundamental period of the discrete-time signal x n  e
13.                                                                              is
                                                                 
          6                       12
    (A)                      (B)                    (C) 6                       (D) 12
         5                        5
14. Which one of the following discrete-time systems is time invariant?
    (A) y n  nx n       (B) y n  x 3n     (C) y n  x n          (D) y n  x n  3
                                                                                     
                                                             
                       
    If a current of  6 2 sin 100t   6 2 cos 300t    A is passed through a true
15.
                                                             4
                       
    RMS ammeter, the meter reading will be
                                                    (C) 12A
    (A) 6 2A                       126A                                         (D) 216A
                             (B)
16. If the ac bridge circuit shown below is
    balanced, the element Z can be a
    (A) Pure capacitor                            :
                                                                  Detector
    (B) Pure inductor                                                D
    (C) R-L series combination
    (D) R-L parallel combination                        Z
17. The Bode asymptotic plot of a transfer function is given below. In the frequency
    range shown, the transfer function has
             dB
           20dB / decade
                                 20dB / decade
          0dB / decade
                                        log 
                      1  2
    (A) 3 poles ands 1 zero                         (B) 1 pole and 2 zeros
    (C) 2 poles and 1 zero                          (D) 2 poles and 2 zeros
18. For radioisotope imaging, an Anger camera is fitted with a parallel hole
    collimator. If the thickness of the collimator is increased, the camera
    (A) resolution and sensitivity will increase
    (B) resolution and sensitivity will decrease
    (C) resolution will increase and sensitivity will decrease
    (D) resolution will decrease and sensitivity will increase
19. In the standard 12-lead ECG recording system, the minimum number of
    electrodes required to be attached to a human subject for recording any one of
    the unipolar chest lead signals is
    (A) 1                    (B) 2                       (C) 4                    (D) 5
20. A laser light with a wavelength of 633nm is passed through 1cm length of tissue
    and 2cm length of glass. The refractive indices of tissue ad glass are 1.33 ad 1.5
    respectively. The velocities of laser light in the tissue and in the glass are in the
    ratio of
    (A) 1.33:0.75            (B) 1.33:3.0                (C) 1.33:15              (D) 1.5:1.33
                       Q. No. 21 � 75 Carry Two Marks Each
    The expression e ln x for x  0 is equal to
21.
                                                         (C) x-1                  (D) -x-1
    (A) -x                   (B) x
                                           dy
                                                  1  y2 . Which one of the following can be
22. Consider the differential equation
                                           dx
    a particular solution of this differential equation?
    (A) y  tan  x  3                                 (C) x  tan  y  3
                             (B) y  tan x  3                                    (D) x  tan y  3
    Consider the function y=x2-6x+9. The maximum value of y obtained when x
23.
    varies over the interval 2 to 5 is
    (A) 1                    (B) 3                       (C) 4                    (D) 9
    It is known that two roots of the nonlinear equation x3  6x2  11x  6  0 are 1
24.
    and 3. The third root will be
    (A) j                    (B) - j                     (C) 2                    (D) 4
25. Consider a Gaussian distributed random variable with zero mean and standard
    deviation . The value of its cumulative distribution function at the origin will be
    (A) 0                    (B) 0.5                     (C) 1                    (D) 10
26. A random variable is uniformly distributed over the interval 2 to 10. Its variance
    will be
          16                                                  256
    (A)                      (B) 6                       (C)                      (D) 36
           3                                                     9
    The Fourier transform of x  t   e atu  t  , where u  t  is the unit step function
27.
    (A) Exists for any real value of a
    (B) Does not exist for any real value of a
    (C) Exists if the real value of a is strictly negative
    (D) Exists if the real value of a is strictly positive
28. In the circuit shown below the maximum power that can be transferred to the
    load ZL is
      i  t  10 2 sin 1000t  A
    (A) 250W
    A complete variable Z  x  j 0.1 has its real part x varying in the range
29.
      to   . Which one of the following is the locus (shown in thick lines) of 1/Z in
    the complex plane?
    (A)
                                   Real axis
                                ^ -j10
    (C)
                                                                                   Image axis
                                                                                                      10 
                                                                                                           ZL
                                                                                                    10mH
                                                                                              (B) 500W      (C) 1000W
                                                                                                            (B)
                                                                                                            (D)
                                                                                                                      Image axis
                                                                                                                                   (D) 2000W
                                                                                                                                   Image axis
                                                                                                                                              Image axis
                                                                                                                                   Real axis
                                                                                                                                 ^ -j10
                                      Real axis                                    Real axis
                                 -j10                                         -j10
                                                                    V1
    For the circuit shown below the input resistance R11                     is
30.
                                                                    I1 I2  0
                                                3I2
                                             
                                                   2
                           1          2V3
                  I1                                 I2 
                                             
                 V1                                      V2
                                       2  V3
                                                        
                                             
    (A) 3                            (B) 2               (C) 3             (D) 13 
    In the circuit shown below the average power consumed by the 2  resistor is
31.
                                           1
        10 2 sin 1000t  V    :
                                         1mH
      100 2 sin 3000t  V     :
    (A) 50W                          (B) 1050W             (C) 5000W              (D) 10100W
32. Which one of the following equations is valid for the circuit shown below?
                  1                1
           I1                              I3
                  1              1
           I2                              I6
                                     1
                              I5
    5V                                              1
                                      1            I4
                                             I7
    (A) I3  I5  I6  I7  0                              (B) I3  I5  I6  I7  0
    (C) I3  I5  I6  I7  0                              (D) I3  I5  I6  I7  0
33. For the circuit shown below the steady-state current I is
                                              I
                                                 1
     v  t   5 2e5t cos 1000t  V
                                                        1000 F
                                                1mH
                                                           (B) 5 2 cos 1000t  A
    (A) 0 A
                                    
                       
                                                           (D) 5 2 A
    (C) 5 2 cos 1000t   A
                                    4
                       
34. For the circuit shown below the voltage across the capacitor is
                                           j100
      10  j0 V
                                        j100
          10  j 0 V                 100  j0  V           0  j100  V   (D)  0  j100  V
                                  (B)                      (C)
    (A)
35. The speed of a gear having 60 teeth is measured using a proximity sensor. The
    output of the proximity sensor is fed to a counter with a gating time of 1s. The
    counter indicates a value of 120. The speed at which the gear is rotating is
    (A) 60 rpm                                             (C) 600 rpm         (D) 1200 rpm
36. A piezoelectric type accelerometer has a sensitivity of 100mV/g. The transducer
    is subjected to a constant acceleration of 5g. The steady state output of the
    transducer will be
    (A) 0V                                                 (C) 0.5V            (D) 5V
37. A pair of identical thermocouples is employed for measuring the temperature of a
    specimen as shown below. The characteristic is tabulated below. The reference
    junction is at 20C. The meter reads 48 V . The correct temperature of the
    specimen is
            Specimen
                              10
                     
                      :
                                  (B) 120 rpm
                                  (B) 100mV
                        +
                                                      V
                                                     meter
                        -      -      +
                          Reference junction
        Temperature (0C)            0    10     20 30  40    50   60   70    80    90
            Output ( V )          35    45     55 65  75    85   95   105   115   125
    (A) 130 C                     (B) 460 C                (C) 480 C           (D) 500 C
    A strain gauge has a nominal resistance of 600  and a gauge factor of 2.5. The
38.
    strain gauge is connected in a dc bridge with three other resistances of 600 
    each. The bridge is excited by a 4V battery. If the strain gauge is subjected to a
    strain of 100 m / m , the magnitude of the bridge output will be
                                  (B) 250V                (C) 500V           (D) 750V
    (A) 0V
39. The torque in a rotating shaft is measured using strain gauges. The strain gauges
    must be positioned on the shaft such that the axes of the strain gauges are at
    (A) 00 with respect to the axis of the shaft
    (B) 300 with respect to the axis of the shaft
    (C) 450 with respect to the axis of the shaft
    (D) 900 with respect to the axis of the shaft
40. To reduce the effect of fringing in a capacitive type transducer
    (A) the transducer is shielded and the shield is kept at ground potential
    (B) a guard ring is provided ad it is kept at ground potential
    (C) the transducer is shielded and the shied is kept at the same potential as the
        moving plate
    (D) a guard ring is provided and it is kept at the same potential as the moving
        plate
41. A differential amplifier shown below has a differential mode gain of 100 and a
    CMRR of 40dB. If V1  0.55V and V2  0.45V, the output V0 is
              V1
                     
                                     V0
                     
              V2
    (A) 10V                (B) 10.5V               (C) 11V           (D) 15V
42. The op-amp circuit shown below is that of a
                             
         Vin
             1F
                                        v0
                             
                               1k
               1k        1k
    (A) low-pass filter with a maximum gain of 1
    (B) low-pass filter with a maximum, gin of 2
    (C) high-pass filter with a maximum gain of 1
    (D) high-pass filter with a maximum gain of 2
    In the op-amp circuit shown below is that of a vin is gradually increased from -10V
43.
    to +10V. Assuming that the output voltage vout saturates at -10V and +10V,
    vout will change from                 
                             Vin
                                                   v0
                                          
                                            9k
                                 1k
    (A) 10V to +10V when vin  1V                (B) 10V to +10V when vin  1V
    (C) 10V to -10V when vin  1V                (D) 10V to -10V when vin  1V
    For the op-amp circuit shown below v0 is approximately equal to
44.
                  10V
                                     1M
        105          95 
                                      
                       100k
                                                v0
                        100k
                                      
        95 
                      105         1M
    (A) -10V                (B) -5V                (C) +5v              (D) +10V
    In the amplifier circuit shown below, assume VBE  0.7V and the  of the
45
    transistor and the values of C1 and C2 are extremely high. If the amplifier is
                                                            VCC
    designed such that at the quiescent point its VCE           , where VCC is the power
                                                             2
                                                      vout
    supply voltage, its small signal voltage gain          will be
                                                      vin
                      10V
                            RC
               8.8k
                                     vout
                               C2
           vin
                 C1
               1.2k        RE
    (A) 3.75                (B) 4.5                (C) 9                (D) 19
46. The result of (45)10 � (45)16 expressed in 6-bit 2's complement representation is
    (A) 011000             (B) 100111               (C) 101000           (D) 101001
47. The output F of the multiplexer circuit shown below expressed in terms of the
    inputs P, Q and R is
                           R       I0
                                   I1
                           R
                                            4 1        Y       F
                                           MUX
                           R       I2
                           R       I3    S1      S0
                                                 Q
                                         P
                           (B) F  PQ  QR  RP (C) F  P  Q  R       (D) F  P  Q  R
    (A) F  P  Q  R
48. A part of a program written for an 8085 microprocessor is shown below. When
    the program execution reaches LOOP2, the value of register C will be
                 SUB A
                 MOV C, A
        LOOPI: INR A
                 DAA
                 JC   LOOP2
                 INR C
                 JNC LOOPI
        LOOP2: NOP
    (A) 63H                (B) 64H                  (C) 99H              (D) 100H
49. The minimum sum of products form of the Boolean expression
     Y P QR SP QR SP QR SP QR SP QR SP QR S                     is
                                                    (C) Y  P Q QR S    (D) Y  QS  PQR
    (A) Y  P Q  Q S      (B) Y  P Q  Q R S
50. An X-ray tube is operated at 80kV anode voltage. In order to filter the low
    intensity X-rays, a 2.5mm thick aluminium filter is used. It is given that at 80kV
    anode voltage, the mass attenuation coefficients and densities of aluminium are
    0.02m2kg1 and 2699kgm3          respectively     and     for   copper    these      are
    0.075m2kg1 and 8960 kgm3 respectively. If a copper filter is to replace the
    aluminium filter with the same effect, the thickness of the copper filter should be
    (A) 0.2mm              (B) 0.66mm               (C) 1.5mm            (D) 5mm
51. A 5 MHz acoustic pulse travels from a transducer through a 2cm thick fat tissue
    before it encounters ad interface with a liver tissue at normal incidence. The
    amplitude              attenuation         factors       of      fat         and         liver      are
    0.075 Npcm1 / MHz and 0.1Npcm1 / MHz respectively. The amplitude reflectivity
    coefficient of fat-liver interface is 0.1. Taking both attenuation and reflection
    losses into a account, the amplitude loss (in dB) of echo pulse when it returns to
    the transducers is
    (A) 0.74                        (B) -2.6                 (C) -6                   (D) -33
    Consider a discrete-time LTI system with input x n   n   n  1 and impulse
52.                                                                                  
    response h n   n   n  1 . The output of the system will be given by
                                     
    (A)  n   n  2                                    (B)  n   n  1
                                                                           
    (C)  n  1   n  2                                (D)  n   n  1   n  2
                                                                                      
53. Consider a discrete-time system for which the input x[n] and the output y[n] are
                                       1
    related as y n  x n  y n  1 . If y n  0 for n  0 and x n   n , then y n
                                                                                                   
                                  3        
    can be expressed in terms of the unit step u[n] as
                 n                          n
            1                         1
                                                                 3n u n                      n
                                                                                      (D)  3 u n
                 u n             (B)   u n            (C)
    (A)                                                                                       
            3                          3
    If the bandwidth of a low-pass signal g(t) is 3kHz, the bandwidth of g2  t  will be
54.
           3
              kHz                   (B) 3kHz                 (C) 6kHz                 (D) 9kHz
    (A)
           2
    Consider the AM signal s  t   1  m  t   cos 2fc t  . It is given that the bandwidth
55.                                                   
    of the real, low-pass message signal m(t) is 2kHz. If fc  2MHz , the bandwidth of
    the band-pass signal s(t) will be
    (A) 2.004MHz                    (B) 2MHz                 (C) 4kHz                 (D) 2kHz
56. Ten, real, band-pass message signals, each of bandwidth 3kHz, are to be
    frequency division multiplexed over a band-pass channel with bandwidth B kHz.
    If the guard band in between any two adjacent signals should be of 500 Hz width
    and there is no need to provide any guard band at the edges of the band-pass
    channel, the value of B should be at least
    (A) 30                          (B) 34.5                 (C) 35                   (D) 35.5
57. The region of convergence of the z-transform of the discrete-time signal
     x n  2n u n will be
                  
                                                                       1                          1
    (A) z  2                       (B) z  2                (C) z                   (D) z 
                                                                       2                          2
    The step response of a linear invariant system is y  t   5e10tu  t  , where u(t) is
58.
    the unit step function. If the output of the system corresponding to an impulse
    input   t  is h  t  , then h  t  is
    (A) 50e10tu  t                           (B) 5e10t   t 
    (C) 5u  t   50e10t   t                (D) 5  t   50e10tu  t 
59. A 2A full-scale PMMC type dc ammeter has a voltage drop of 100 mV at 2A. The
    meter can be converted into a 10A full-scale dc ammeter by connecting a
    (A) 12.5 m resistor in parallel with the meter
    (B) 12.5 m resistor in series with the meter
    (C) 50.0 m resistor in parallel with the meter
    (D) 50.0 m resistor in series with the meter
    A 31⁄2 digit, 200 mV full scale DVM has an accuracy specification of  0.5% of
60.
    reading plus 5 counts. When the meter reads 100 mV, the voltage being
    measured is
    (A) Any value between 99.5 mV and 100.5 mV
    (B) Any value between 99.0 mV and 101.0 mV
    (C) Exactly 99.5 mV                          (D) Exactly 100 mV
61. A 230 V, 5A, 50 Hz single phase house service energy meter has a meter
    constant of 360 rev/kWhr. The meter takes 50 s for making 51 revolutions of the
    disc when connected to a 10 kW, unity power factor load. The error in the
    reading of the meter is
    (A) 0%                        (B) +0.5%      (C) -2.0%               (D) +2.0%
62. The op-amp based circuit of a half wave rectifier electronic voltmeter shown
    below uses a PMMC ammeter with a full scale deflection (FSD) current of 1 mA
    and a coil resistance of 1k . The value of R that gives FSD for a sinusoidal input
    voltage of 100 mV (RMS) is
                              
            Sinusoidal
                              
                   input
                                                 1k
                                                 PMMC
                                                 ameter
                                               R
    (A) 45                       (B) 67.5      (C) 100                (D) 144.4 
63. The x and y sensitivities of an analog oscilloscope are set as 2 ms/cm and 1V/cm
    respectively. The trigger is set at 0V with negative slope. An input of
                            
    2 cos 100t  300 V is fed to the y input of the oscilloscope. The waveform seen
    on the oscilloscope will be
    (A)                                                    (B)
    (C)                                                    (D)
64. The     open        loop transfer function of a unity feedback                     system     is
                       K  s  2
    G s                                . The root locus plot of the system has
              s  1  j1  s  1  j1
    (A) two breakaway points located at s  0.59 and s  3.41
    (B) one breakaway point located at s  0.59
    (C) one breakaway point located at s  3.41
    (D) one breakaway point located at s  1.41
65. If a first order system and its time response to a unit step input are as shown
    below, the gain K is
                                                              y
                    
                                        K
              r t                                 y t  0.8
                                    1  ST
                                                                                      t
    (A) 0.25                      (B) 0.8                  (C) 1               (D) 4
                                                                           x  0 1         1 
                                                                                        x   u
                                                                                
                                                                                0  3      0  .
66. The state space representation of a system is given by
                                                                           y  1 0 x
                                                                                     
                                  Y s
    The transfer function                 of the system will be
                                  U s
                                                                                    1
                                             1
         1                                                        1
    (A)                           (B)                      (C)                 (D)
                                        s  s  3                                 s2
         s                                                      s3
    A closed loop control system is shown below. The range of the controller gain KC
67.
    which will make the real parts of all the closed loop poles more negative than -1
    is
                                                  1
                    
                             KC              s  s  3       Y  s
             R  s
                      
    (A) KC  4             (B) KC  0                         (C) KC  2        (D) KC  2
68. For the closed loop system shown below to be sable, the value of time delay
     TD (in seconds) should be less than
                                                         1
                                       
                                                                         Y  s
                                R  s                   s
                                         
                                                        esTD
                                                                      
                                    
    (A)                     (B)                                (C)               (D) 
          4                                                            2
                                    3
69. A tissue with a refractive index 1.33 is introduced on one of the light paths of a
    Michelson interferometer operating with a monochromatic coherent light source
    of wavelength 589nm. After the introduction of a tissue sample of thickness t ,
    the fringe pattern is observed to shift by 50 fringes. If the thickness is 2t , the
    fringe pattern will shift by
    (A) 25 fringes          (B) 50 fringes                     (C) 100 fringes   (D) 200 fringes
70. In the process of non-destructive testing of a 10cm diameter cylinder, a cross-
    sectional (trans-axial) image of the cylinder is reconstructed with the help of
    parallel beam computer tomography technique. To realize a spatial resolution of
    1mm in the image, the minimum number of ray sample in each projection set
    and the minimum number of projection sets required are
    (A) 200 and 315 respectively                               (B) 100 and 315 respectively
    (C) 200 and 629 respectively                               (D) 100 and 629 respectively
                        Common Data Questions 71, 72 & 73
    A data acquisition system (DAS) shown below employs                              a   successive
    approximation type 12-bit ADC having a conversion time of 5 s.
                                                              A      B
                                         Filter
                                         Filter
                              Y
                                         Filter
                                         Filter
71. The quantization error of the ADC is
                            (B) 0.012%              (C) 0.024%        (D) 0.048%
    (A) 0%
72. The system is used as a single channel DAS with channel 1 selected as input to
    the ADC which is set in the continuous conversion mode. For avoiding aliasing
    error, the cutoff frequency fc of the filter in channel 1 should be
    (A) fc  100kHz                                  (B) fc  100kHz
    (C) 100kHz  fc  200kHz                         (D) fc  200kHz
73. If the multiplexer is controlled such that the channels are sequenced every 5 s
    as 1, 2, 1, 3, 1, 4, 1, 2, 1, 3, 1, 4, 1......, the input connected to channel 1 will be
    sampled at the rate of
    (A) 25k samples/s                                (B) 50k samples/s
    (C) 100k samples/s                               (D) 200k samples/s
                          Common Data Questions: 74 & 75
    Laser light is generated by energizing helium-neon gas in a chamber. The ground
    and metastable states of helium are 0eV and 20.61eV respectively. The ground,
    higher and metastable energies of neon is 0eV, 18.70eV and 20.66eV
    respectively. The values of speed of light, Planks constant and charge of electron
    are 3  108 m / s, 6.625  1034 Js and 1.6  1019 C respectively
74. In this process, helium molecules
    (A) play no role
    (B) produce laser light
    (C) give energy to neon molecules
    (D) absorb energy from neon molecules
75. Wavelength of laser light generated in this process is
    (A) 61.6nm              (B) 66.4nm               (C) 633.8nm        (D) 650.3nm
        Linked Answer Questions: Q.76 to Q.85 Carry Two Marks Each
               Statement for Linked Answer Questions: 76 & 77
    In the Wheatstone bridge shown below the galvanometer G has a current
    sensitivity of 1 A / mm , a resistance of 2.5k and a scale resolution of 1 mm. Let
    R be the minimum increase in R from its nominal value of            2 k that can be
    detected by this bridge.
                                          3k              6k
                                  
                            15V                 G
                                                          A      
                                        R
                                                                  VAN
                                                           4k
                                                                  
                                                           N
    When R is 2 k  R, VAN is
76.
    (A) 6 V                 (B) 6.0024 V            (C) 6.0038V   (D) 6.005 V
    The value of R is approximately
77.
    (A) 2.8                (B) 3.4                (C) 5.2      (D) 12 
               Statement for Linked Answer Questions 78 & 79
    In the circuit shown below the steady-state is reached with the switch K open.
    Subsequently the switch is closed at time t = 0
                           1         I2
               K                 I
                t0                 I1
                                2
                                               1H
            
            
          5V
                                               10V
                               1F            
    At time t  0 , current I is
78.
           5                                            5
                                                                  (D)  A
    (A)     A                                            A
                            (B) 0A                  (C)
           3                                            3
                     dI2
    At time t  0 ,     is
79.
                      dt
                                   10
                            (B)        A /s
    (A) 5A / s                                     (C) 0A / s    (D) 5A / s
                                    3

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