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GATE IN 2025: Instrumentation Engineering

  • Paper code: IN
  • Language: English
  • 65 pages
GATE IN 2025 question paper, GATE 2025, Instrumentation Engineering, page 1 of 65
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Instrumentation Engineering (IN)


General Aptitude
Q.1 – Q.5 Carry ONE mark Each

 Q.1      Despite his initial hesitation, Rehman’s _________ to contribute to the success of
          the project never wavered.

          Select the most appropriate option to complete the above sentence.




 (A)      ambivalence


 (B)      satisfaction


 (C)      resolve


 (D)      revolve




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 Q.2      Bird : Nest :: Bee : _______

          Select the correct option to complete the analogy.




 (A)      Kennel


 (B)      Hammock


 (C)      Hive


 (D)      Lair




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 Q.3      If Pe x = Qe −x for all real values of x, which one of the following statements is
          true?




 (A)      P=Q=0


 (B)      P=Q=1


 (C)      P = 1; Q = −1


 (D)      P
            =0
          Q




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 Q.4      The paper as shown in the figure is folded to make a cube where each square
          corresponds to a particular face of the cube. Which one of the following options
          correctly represents the cube?

          Note: The figures shown are representative.




 (A)




 (B)



 (C)



 (D)




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 Q.5      Let p1 and p2 denote two arbitrary prime numbers. Which one of the following
          statements is correct for all values of p1 and p2 ?




 (A)      p1 + p2 is not a prime number.


 (B)      p1 p2 is not a prime number.


 (C)      p1 + p2 + 1 is a prime number.


 (D)      p1 p2 + 1 is a prime number.




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Q.6 – Q.10 Carry TWO marks Each

 Q.6      Based only on the conversation below, identify the logically correct inference:

          “Even if I had known that you were in the hospital, I would not have gone there to
          see you”, Ramya told Josephine.




 (A)      Ramya knew that Josephine was in the hospital.


 (B)      Ramya did not know that Josephine was in the hospital.


 (C)      Ramya and Josephine were once close friends; but now, they are not.


 (D)      Josephine was in the hospital due to an injury to her leg.




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 Q.7      If IMAGE and FIELD are coded as FHBNJ and EMFJG respectively then, which
          one among the given options is the most appropriate code for BEACH ?




 (A)      CEADP


 (B)      IDBFC


 (C)      JGIBC


 (D)      IBCEC




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 Q.8      Which one of the following options is correct for the given data in the table?



                          Iteration (i)       0        1         2          3


                          Input (I)          20      −4          10        15


                          Output (X)         20       16         26        41


                          Output (Y)         20      −80       −800     −12000


 (A)       X(i) = X(i − 1) + I(i);        Y(i) = Y(i − 1)I(i);    i>0


 (B)      X(i) = X(i − 1)I(i);         Y(i) = Y(i − 1) + I(i);    i>0


 (C)      X(i) = X(i − 1)I(i);         Y(i) = Y(i − 1)I(i);      i>0


 (D)      X(i) = X(i − 1) + I(i);         Y(i) = Y(i − 1)I(i − 1);      i>0




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 Q.9      In the given figure, PQRS is a square of side 2 cm and PLMN is a rectangle. The
          corner L of the rectangle is on the side QR. Side MN of the rectangle passes through
          the corner S of the square.

          What is the area (in cm2) of the rectangle PLMN?

          Note: The figure shown is representative.


                                               N

                                    P              S


                                                       M

                                    Q     L        R



 (A)      2√2


 (B)      2


 (C)      8


 (D)      4




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 Q.10     The diagram below shows a river system consisting of 7 segments, marked P, Q, R,
          S, T, U, and V. It splits the land into 5 zones, marked Z1, Z2, Z3, Z4, and Z5. We
          need to connect these zones using the least number of bridges. Out of the following
          options, which one is correct?

          Note: The figure shown is representative.



                                Z2                         Z3
                                            R
                                                                    V

                            P                          T
                                          Q                             Z4

                                     Z1                           U
                                              S        Z5




 (A)      Bridges on P, Q, and T


 (B)      Bridges on P, Q, S, and T


 (C)      Bridges on Q, R, T, and V


 (D)      Bridges on P, Q, S, U, and V




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Q.11 – Q.35 Carry ONE mark Each

 Q.11     A 2n  2n matrix A = [aij ] has its elements as

                                               if (i + j ) is odd,
                                    aij = 
                                          −    if (i + j ) is even,

          where n is any integer greater than 2 and  is any non-zero real number. The rank
          of A is




 (A)       1


 (B)       2


 (C)       n


 (D)       2n




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 Q.12                                                 dy    x
          The solution of the differential equation      = 9 represents
                                                      dx    y




 (A)      a hyperbola


 (B)      a parabola


 (C)      an ellipse


 (D)      a circle




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 Q.13     The working of the hand-held metal detector most widely used by security
          personnel for human frisking is based on the principle of




 (A)      change in reluctance of an iron core in presence of a metallic object


 (B)      change in conductance of an iron core in presence of a metallic object


 (C)      electric field induced by a metallic object


 (D)      eddy current generation in a metallic object




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 Q.14     The primary coil of a linear variable differential transformer (LVDT) is supplied
          with AC voltage as shown in the figure. The secondary coils are connected in series
          opposition and the output is measured using a true RMS voltmeter.
          The displacement x of the core is indicated in mm on a linear scale. At the null
          position x = 0, the voltmeter reads 0 V. If the voltmeter reads 0.2 V for a
          displacement of x = +2 mm, then for a displacement of x = −3 mm, the voltmeter
          reading, in V, is




 (A)       − 0.3


 (B)       − 0.1


 (C)      0.3


 (D)      0.5




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 Q.15     In the force transducer shown in Figure (a), four identical strain gauges S1, S2, S3,
          and S4 are mounted on a cantilever at equal distance from its base. S1 and S2 are
          mounted on the top surface and S3 and S4 are mounted on the bottom surface, as
          shown in the Figure (a). These strain gauges are to be connected to form a
          Wheatstone bridge consisting of four arms A, B, C, and D, as shown in the
          Figure (b). From the following options, the correct order to maximize the
          measurement sensitivity is




 (A)       A → S1, B → S2, C → S4, D → S3


 (B)       A → S1, B → S4, C → S3, D → S2


 (C)       A → S1, B → S2, C → S3, D → S4


 (D)       A → S1, B → S4, C → S2, D → S3




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 Q.16     Let a continuous-time signal be x (t ) = e j 9t + e j 5t , where j = −1 and t is in
          seconds. The fundamental period of magnitude of x (t ) , in seconds, is




 (A)       

 (B)       
           2

 (C)       
           5

 (D)       
           9




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 Q.17     The minimized expression of the Boolean function Y(P, Q, R) implemented by the
          multiplexer (MUX) circuit shown in the figure is




 (A)      Y = R + (P  Q)


 (B)      Y = R (P  Q)


 (C)      Y = R + (PQ )


 (D)      Y = R  (P  Q)




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 Q.18     The 4-bit signed 2’s complement form of ( 5)10 + ( 5)10 is




 (A)       ( −6)10

 (B)       ( −7 )10

 (C)       ( −5)10

 (D)       ( −8)10




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 Q.19     An infinite sheet of uniform charge  s = 10 C/m2 is placed on z = 0 plane. The
          medium surrounding the sheet has a relative permittivity of 10. The electric flux
          density, in C/m2, at a point P(0, 0, 5), is

          Note: â , bˆ, and ĉ are unit vectors along the x , y, and z directions, respectively.




 (A)      5 ĉ


 (B)      0.25 ĉ


 (C)      10 ĉ


 (D)      0.5 ĉ




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 Q.20                                                                        V
          For the ideal opamp based circuit shown in the figure, the ratio     is
                                                                             I




 (A)        R3 + R4 
                    R
            R +R  1
            1     3 



 (B)        R2 + R4 
                    R
            R +R  3
             1    3 


 (C)       R1 + R3


 (D)       R3 + R4




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 Q.21     In a single-phase AC circuit, the power consumed by load resistance RL for an
          excitation VS is measured using a wattmeter. The same wattmeter is connected in
          two different topologies, Topology-A and Topology-B, as shown in the figure.
          Different branch currents and voltage drops are also marked in the figure. Among
          the following options, the condition that ensures low error in the wattmeter reading
          for both the topologies is




 (A)      VL ≫ VC for Topology-A and IL ≫ IP for Topology-B


 (B)      VL ≫ VC for Topology-A and IL ≪ IP for Topology-B


 (C)      VL ≪ VC for Topology-A and IL ≪ IP for Topology-B


 (D)      VL ≪ VC for Topology-A and IL ≫ IP for Topology-B




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 Q.22     Match the following sensors with their most suitable applications.


                            Sensor                                    Application
            P       Rotary Variable Differential       I     Vacuum measurement
                    Transformer
            Q       Thermocouple                       II    Force measurement
            R       Ionization Gauge                   III   Angular displacement measurement
            S       Strain Gauge                       IV    Temperature measurement


 (A)      P – II,     Q – III,     R – I,     S – IV


 (B)      P – II,     Q – IV,      R – III,    S–I


 (C)      P – III,     Q – IV,      R – II,    S–I


 (D)      P – III,     Q – IV,      R – I,    S – II




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 Q.23     A 3 1 2 digit digital voltmeter has a specified accuracy of  (0.5% + 1) . If it is used
          to measure 10 V DC voltage, the error in the measurement would be

          Note: Accuracy of the digital voltmeter is expressed as  ( % of reading + digit).




 (A)        0.4 %


 (B)        1.5 %


 (C)        0.6 %

 (D)        1%




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 Q.24     The circuit shown in Figure (a) can be represented using its equivalent T-model as
          shown in Figure (b). The values of the inductances L1 , L2 , and L3 in the equivalent
          T-model are




 (A)       L1 = 7 H, L2 = 6 H, L3 = − 4 H


 (B)       L1 = −1 H, L2 = − 2 H, L3 = 4 H


 (C)       L1 = 3 H, L2 = 2 H, L3 = 9 H


 (D)       L1 = 1 H, L2 = − 2 H, L3 = − 4 H




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 Q.25     Three     parallel   admittances   Ya = − j 0.2 S, Yb = 0.3 S, and Yc = j 0.4 S
          connected in parallel with a voltage source Vs = 1045 V, draw a total current I s
          from the source. The currents flowing through each of these admittances are
           I a , Ib , and I c , respectively. Let I = Ib + I c . The phase relation between I and I s
          is




 (A)       I leads I s by 19.44

 (B)       I lags I s by 19.44

 (C)       I leads I s by 33.69

 (D)       I lags I s by 33.69




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 Q.26       An oscilloscope has an input resistance of 1 MΩ . A 10X passive attenuating probe
            is connected to it to increase the input voltage range as well as the effective input
            resistance. The effective input resistance, in MΩ, seen into the probe tip is




 (A)        0.9


 (B)        9.1


 (C)        10


 (D)        11




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 Q.27                                                     2s − 1
            For the transfer function G ( s) = 1 +                      , the number of zeros lying
                                                     s + 5s 2 + 3s + 22
                                                       3

            in the left half of the s-plane is




 (A)        0


 (B)        1


 (C)        2


 (D)        3




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 Q.28       Consider the control system block diagram given in Figure (a). The loop transfer
            function G(s) H (s) does not have any pole on the j -axis. The counterclockwise
            contour with infinite radius, as shown in Figure (b), encircles two poles of
            G(s) H (s) . Choose the correct statement from the following options for
            closed loop stability of the system.




                            Figure (a)                           Figure (b)

 (A)        The locus of G (s) H (s) should encircle the origin twice in the counterclockwise
            direction


 (B)        The locus of 1 + G (s) H (s) should encircle the origin twice in the clockwise
            direction


 (C)        The locus of G (s) H (s) should encircle the −1 + j 0 point twice in the
            counterclockwise direction


 (D)        The locus of 1 + G (s) H (s) should encircle the −1 + j 0 point twice in the
            clockwise direction




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 Q.29       A Boolean function X is given as X = A B + A C . The reduced form of X is




 (A)        A+B+C


 (B)        A+BC


 (C)        A+B+C


 (D)        B + AC




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 Q.30       A 60 V DC source with an internal resistance Ri nt = 0.5  is connected through a
            switch to a pair of infinitely long rails separated by l = 1 m as shown in the figure.
            The rails are placed in a constant, uniform magnetic field of flux density
            B = 0.5 T, directed into the page. A conducting bar placed on these rails is free to
            move. At the instant of closing the switch, the force induced on the bar is

            Note: Assume there is no friction between the bar and the rails. The resistances of
            the conducting bar and the rails are zero.




 (A)        60 N in the direction of x̂


 (B)        60 N opposite to the direction of x̂


 (C)        120 N in the direction of x̂


 (D)        120 N opposite to the direction of x̂




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 Q.31       The circuits mentioned in the following options are realized using ideal opamp.
            Among these, the circuit(s) performing non-linear operation on the input signal
            is/are




 (A)        Instrumentation amplifier


 (B)        Schmitt trigger


 (C)        Logarithmic amplifier


 (D)        Precision rectifier




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 Q.32                                                     −1 −1
            If one of the eigenvectors of the matrix A =        is along the direction
                                                          x −4 
                  
            of   , where  is any non-zero real number, then the value of x
                  2 
            is ______ (in integer).




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 Q.33                                             2z +1
            Consider the function      f ( z) =          , where z is a complex variable.
                                                  z2 − z
            The sum of the residues at singular points of f ( z ) is ________ (in integer).




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 Q.34       A dual-slope ADC has a fixed integration time of 100 ms. The reference voltage
            of the ADC is − 5 V. The time taken by the ADC to measure an input voltage of
            1.25 V is __________ ms (rounded off to the nearest integer).




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 Q.35       In the circuit shown, assume that the BJT in the circuit has very high β and
            VBE = 0.7 V, and the Zener diode has VZ = 4.7 V. The current I through the LED is
            ___________ mA (rounded off to two decimal places).




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Q.36 – Q.65 Carry TWO marks Each

 Q.36     The value of the surface integral  (2 x + z )dy dz + (2 x + z )dx dz + (2 z + y)dx dy
                                                 S

          over the sphere S : x + y + z = 9 is
                                    2   2   2




 (A)      72π


 (B)      144π


 (C)      36π


 (D)      432π




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 Q.37     Newton-Raphson method is used to compute the inverse of the number 1.6. Among
          the following options, the initial guess of the solution that results in
          non-convergence of the iterative process is




 (A)      0.55


 (B)      0.75


 (C)      1.15


 (D)      1.25




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 Q.38                                
          The value of the integral  ( cos6 x + cos4 x ) dx is
                                     −




 (A)       
           2


 (B)       5
            8


 (C)       11
            8


 (D)       9
            8




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 Q.39                   1
          Let y [n] =       y [n − 1] + x [n] , where   1 and real, represent a difference equation
                        
          of a causal discrete-time linear time invariant system. The system is initially at rest.
          If x [n] =  [n − p] where p  10 , the value of y [ p + 1] is




 (A)      0


 (B)      1


 (C)       1
           

 (D)       1
           2




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 Q.41     A chopper amplifier shown in the figure is designed to process a biomedical signal
          vin (t ) to generate conditioned output vout (t ) . The signals vin (t ) and vos (t ) are
          band limited to 50 Hz and 10 Hz, respectively. For the system to operate as a linear
          amplifier, choose the correct statement from the following options.




 (A)      The minimum frequency of s(t) required is 100 Hz and vos (t ) gets attenuated by
          the system


 (B)      The minimum frequency of s(t) required is 100 Hz and vos (t ) also gets amplified
                                    200
          by the system by a factor
                                        

 (C)      The minimum frequency of s(t) required is 80 Hz and vos (t ) gets attenuated by the
          system


 (D)      The minimum frequency of s(t) required is 80 Hz and vos (t ) also gets amplified by
                                 200
          the system by a factor
                                    




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 Q.42     An 8-bit microprocessor has 16-bit address bus (A15 − A0) where A0 is the LSB. As
          shown in Figure (a), it has a pre-installed 4 KB ROM whose starting address is
          0000 H. The processor needs to be upgraded by adding a 16 KB RAM as shown in
          Figure (b). The address range for the newly added RAM is




 (A)      1000 H – 4FFF H


 (B)      3000 H – 6FFF H


 (C)      4000 H – 7FFF H


 (D)      8000 H – BFFF H




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 Q.43     A 3-bit DAC is implemented using ideal opamp and switches as shown in the figure.
          Each of the switches gets closed when its corresponding digital input is at logic 1.
          For a digital input of 110, the resistance Rin seen from the reference source and the
          current I, are




 (A)      Rin = 2 kΩ and I = 3 mA


 (B)      Rin = 12 kΩ and I = 0.5 mA


 (C)      Rin =  Ω and I = 1 mA


 (D)      Rin =  Ω and I = 3 mA




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 Q.45     The bridge circuit, shown in Figure (a), can be equivalently represented using the
          circuit shown in Figure (b). The values of R1, R2, and VC in the equivalent circuit
          are




 (A)      R1 = 6 kΩ, R2 = 3 kΩ, and VC = 9 V


 (B)      R1 = 3 kΩ, R2 = 6 kΩ, and VC = 4.5 V


 (C)      R1 = 2 kΩ, R2 = 2 kΩ, and VC = 9 V


 (D)      R1 = 2 kΩ, R2 = 2 kΩ, and VC = 4.5 V




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 Q.46     A 2-pole, 50 Hz, 3-phase induction motor supplies power to a certain load at
          2970 rpm. The torque-speed curve of this machine follows a linear relationship
          between synchronous speed and 95 % of synchronous speed. Assume mechanical
          and stray losses to be zero. If the load torque of the motor is doubled, the new
          operating speed of the motor, in rpm, is




 (A)      2940


 (B)      2812


 (C)      2970


 (D)      2850




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 Q.47                                                                       1
          The figure shows a closed-loop system with a plant G ( s ) =          and a lead
                                                                           s2
          compensator C(s). The compensator is designed to place the dominant closed-loop
                             27
          poles at − 1.5  j    . From the following options, choose the phase lead that the
                             2
          compensator needs to contribute.




 (A)      30


 (B)      60


 (C)      90


 (D)      120




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 Q.48     Let f (t ) and g (t ) represent continuous-time real-valued signals. If h (t ) denotes
          cross-correlation between f (t ) and g (−t ) , its continuous-time Fourier transform
          H ( j) equals

          Note: F ( j) and G( j) denote the continuous-time Fourier transforms of f (t )
          and g (t ) , respectively.




 (A)      F ( j) G( j)


 (B)      F (− j) G( j)


 (C)      F ( j) G(− j)


 (D)      −F ( j) G(− j)




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 Q.49     Choose the correct statement(s) from the following options, regarding Cauchy’s
          theorem on complex integration ∮C f(z) dz where C is a simple closed path in a
          simply connected domain D.




 (A)      Cauchy’s theorem cannot be directly applied to conclude that ∮C f(z) dz = 0 when
                     1
          f(z) = 2, and C is the unit circle
                    z


 (B)      If f(z) is analytic in D, then it can be concluded that ∮C f(z) dz = 0 for any simple
          closed path C in D


 (C)      The function f(z) must be analytic in D to conclude ∮C f(z) dz = 0 for any simple
          closed path C in D


 (D)                                     1
          ∮C f(z) dz ≠ 0 when f(z) = z2 , since the function is not analytic at z = 0




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 Q.50                                                                          a
          The plant in the feedback control system shown in the figure is P( s) =   , where
                                                                            s − b2  2

           a  0 and b  0 . The type(s) of controller C(s) that CANNOT stabilize the plant
          is/are




 (A)      proportional (P) controller


 (B)      integral (I) controller


 (C)      proportional-integral (PI) controller


 (D)      proportional-derivative (PD) controller




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 Q. 51    Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems
          from the following options.




 (A)       j 2 t
          e 3

 (B)            2 
          cos     t
                3 


 (C)      2t

 (D)            2 
          sin     t
                3 




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 Q.52      The probability of a student missing a class is 0.1. In a total number of 10 classes,
           the probability that the student will not miss more than one class is ___ (rounded
           off to two decimal places).




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 Q.53      A metallic strain-gauge (SG) with resistance RSG is connected as shown in the
           figure, where RL1, RL2, RL3 represent the lead wire resistances. The SG has a gauge
           factor of 2 and nominal resistance RN of 125 Ω. When the SG is subjected to a
           tensile strain of 2  10-3, the resulting change in RSG is ΔR. The ΔR value is measured
           as ΔRMEAS = REQ2 – REQ1. The REQ1 and REQ2 are the equivalent resistances measured
           between the terminals 1 and 2, and terminals 2 and 3, respectively.

           If RL1 = RL2 = 5 Ω, and RL3 = 4.95 Ω, the measured value of tensile strain
           is ___ 10 −3 (rounded off to two decimal places).




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 Q.54             ( )
           Let X e j represent the discrete time Fourier transform of a 4-length sequence

                                                                      ( ) is sampled at
           x[n] , where x[0] = 1, x[1] = 2, x[2] = 2, and x[3] = 4 . X e j
                2 k
           k =      to generate a periodic sequence in k with period 3, where k represents
                  3
           an integer. Let y [n] represent another sequence such that its discrete Fourier

                                                  ( ) for 0  k  2 . The value of y[0]
                                                    j
           transform Y [k ] is given as Y [k ] = X e k
           is______ (in integer).




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 Q.55      A schematic of a Michelson interferometer, used for the measurement of refractive
           index of gas, is shown in the figure. The transparent chamber is filled with a gas of
           refractive index ng , where ng  1 , at atmospheric pressure. If a 532 nm laser beam
           produces 30 interference fringes on the screen, then the number of fringes produced
           by a 632.8 nm laser beam will be _____ (rounded off to one decimal place).

           Note: Assume that the effect of beamsplitter width is negligible. The setup is placed
           in air medium with refractive index equal to 1.




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 Q.56      Consider an AC bridge shown in the figure with R = 300 Ω , R1 = 1000 Ω ,
            R2 = 500 Ω , L= 30 mH, and a detector D. At the bridge balance condition,
           the frequency of the excitation source VS is _________ kHz (rounded off to two
           decimal places).




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 Q.57      An air filled parallel plate electrostatic actuator is shown in the figure. The area of
           each capacitor plate is 100 μm  100 μm . The distance between the plates
           d 0 = 1 µm when both the capacitor charge and spring restoring force are zero as
           shown in Figure (a). A linear spring of constant k = 0.01 N/m is connected to the
           movable plate. When charge is supplied to the capacitor using a current source, the
           top plate moves as shown in Figure (b). The magnitude of minimum charge (Q)
           required to momentarily close the gap between the plates is _______× 10−14 C
           (rounded off to two decimal places).

           Note: Assume a full range of motion is possible for the top plate and there is no
           fringe capacitance. The permittivity of free space is  o = 8.85 10−12 F/m and
           relative permittivity of air (  r ) is 1.




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 Q.58      The resistance of a thermistor is measured to be 2.25 kΩ at 30 °C and 1.17 kΩ at
           60 °C. Its material constant β is ___________ K (rounded off to two decimal
           places).




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 Q.59      A feedback control system is shown in the figure.




           The maximum allowable value of n such that the output y(t ) , due to any step
           disturbance signal d (t ) , becomes zero at steady-state, is ________
           (in integer).




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 Q.60      The circuit given in the figure is driven by a voltage source Vs = 25 230 V.
           The system is operating at a frequency of 50 Hz. The transformers are assumed to
           be ideal. The average power dissipated, in W, in the 50 kΩ resistance is _______
           (rounded off to two decimal places).




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 Q.61      In the circuit shown, the galvanometer (G) has an internal resistance of 100 Ω.
           The galvanometer current IG is ________ µA (rounded off to the nearest integer).




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 Q.62      A series RLC circuit resonates at 7500 rad/s for inductance
           L = 20 mH and resistance R = 10 Ω. The uncertainties in the measurement of L and
           R are 0.8 mH and 0.3 Ω, respectively. The percentage uncertainty in the
           measurement of quality factor is _________% (rounded off to one decimal
           place).




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           In the circuit shown, the switch is opened at t = 0 s. The current i(t )
 Q.63      at t = 2 ms is _____________ mA (rounded off to two decimal places).




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 Q.64      A signal VM = 5sin ( t 3) V is applied to the circuit consisting of a switch S and
           capacitor C = 0.1 µF, as shown in the figure. The output Vx of the circuit is fed to
           an ADC having an input impedance consisting of a 10 MΩ resistance in parallel
           with a 0.1 µF capacitor. If S is opened at t = 0.5 s, the value of Vx at
           t = 1.5 s will be ________ V (rounded off to two decimal places).

           Note: Assume all components are ideal.




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 Q.65      For the circuit shown in the figure, the active power supplied by the source
           is _______ W (rounded off to one decimal place).




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Source: GATE. Question paper published by GATE.