One Stop GATE Forum: Instrumentation Engg GATE sample paper

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1
          A surface height profile is given by, y = a + b
            sin 
            
                
              
                  2p x
                
                
                  l
                
              
            
             (0x l)
            where a, b, l are constants and x is the horizontal coordinate.
            The roughness of the surface, based on absolute deviation, is
        
        
          Options
          
            
                
              
                  A)
                    
                        
                      
                          2b
                        
                        
                          p 
                        
                      
                    
                  
                  B)
                    
                        
                      
                          4b
                        
                        
                          p 
                        
                      
                    
                  
                
                
                  C)
                    
                        
                      
                          6b
                        
                        
                          p 
                        
                      
                    
                  
                  D)
                    
                        
                      
                          8b
                        
                        
                          p 
                        
                      
                    
                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          A
        
        
          

        
        
          2
          For N-bit Successive Approximation ADCs, other
            parameters such as clock frequency remaining constant, the
            conversion time is proportional to

          
        
        
          Options
          
            
                
              
                  A) N² 
                  B)
                    
                        
                      
                          Ö
                          N
                        
                      
                    
                  
                
                
                  C) log N
                  D) N
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          3
          The radius of a sphere is given as (40.0 ±
            0.5)mm.  The estimated error in its mass is:
        
        
          Options
          
            
                
              
                  A) ± 3.75%
                  B) ± 1.25%
                
                
                  C) ± 12.5%
                  D) ± 0/125%
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          4
          A zero error in a vernier caliper is termed as
        
        
          Options
          
            
                
              
                  A) accidental error 
                  B) interference error 
                
                
                  C) systematic error

                  
                  D) random error
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          5
          Given the discrete-time sequence x[n] = [2, 0,
            -1,-3, 4, 1, -l, X(e^jp) is
        
        
          Options
          
            
                
              
                  A) 8
                  B) 6p
                
                
                  C) 8p
                  D) 6
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          6
          Linear variable differential transformer has 
        
        
          Options
          
            
                
              
                  A) two primary coils connected in phase and a
                    secondary coil
                  B) two primary coils connected in opposition and a
                    secondary coil
                
                
                  C) one primary coil and two secondary coils
                    connected in phase
                  D) one primary coil and two secondary coils
                    connected in opposition
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          D
        
        
          

        
        
          7
          Position sensor units having a constant
            sensitivity of lV/mm are used for feedback in number of position
            controlled system units, each having an overall forward path dc gain
            of 50. If the random dc bias errors in the outputs of various sensor
            units are characterized as normal with mean 0 and standard deviation
            (s) 0.01V, for a constant set point of
            5V, the true position outputs of the various controlled system units
            can be characterized as normal with

          
        
        
          Options
          
            
                
              
                  A) mean of 5.0, s
                    of 0.01

                  
                  B) mean of 0.0, s
                    of 0.01

                  
                
                
                  C) mean of 5.0, s
                    of 0.0098

                  
                  D) mean of 4.902, s
                    of 0.0098

                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          8
          The refractive index of the core of an optical
            fiber is n₁and that of the cladding is nf If (n₁
            – n₂) = Dn, then the fiber
            can be made single mode with numerical aperture unchanged by
        
        
          Options
          
            
                
              
                  A) reducing core diameter and increasing Dn
                  B) reducing both core diameter and Dn

                  
                
                
                  C) reducing core diameter alone

                  
                  D) reducing Dn alone
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          D
        
        
          

        
        
          9
          
            For a suppressed carrier amplitude modulator (AM-SC) system, the
            carrier and the modulating inputs are x_c (t) = cos w_c
            t and x_m(t) = 0.5 sin w_m
            t, respectively. The output of the system is proportional to
          
        
        
          Options
          
            
                
              
                  A) sin (w_c +
                    w_m) t – sin (w_c
                    - w_m) t
                  B) sin (w_c 
                    + w_m) t  + 
                    cos (w_c  -w_m)
                    t
                
                
                  C) (1 + 0.5 sin w_m 
                    t) cos w_c t
                  D) (1- 0.5 sin w_m
                    t) cos w_c t
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          10
          
            The 3-dB cut-off frequency of a first analog high pas filter is w_cthe
            output will have a phase shift of
          
        
        
          Options
          
            
                
              
                  A)
                    
                        
                      
                          -p 
                        
                        
                          2
                        
                      
                    
                  
                  B)
                     
                    

                        
                      
                          -p 
                        
                        
                          4
                        
                      
                    
                  
                
                
                  C)
                    
                        
                      
                          p 
                        
                        
                          2
                        
                      
                    
                  
                  D)
                    
                        
                      
                          p 
                        
                        
                          2
                        
                      
                    
                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B


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