One Stop GATE Forum: E&E GATE Sample paper

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1
          For the scalar field u =
            
                
              
                  x² 
                
                
                  2
                
              
            
            +
            
                
              
                  y² 
                
                
                  3
                
              
            
            , magnitude of the gradient at the point (1,3) is
        
        
          Options
          
            
                
              
                  A)
                    
                        
                      
                          Ö
                          13/9
                        
                      
                    
                  
                  B)
                    
                        
                      
                          Ö
                          9/2
                        
                      
                    
                  
                
                
                  C)
                    
                        
                      
                          Ö
                          5
                        
                      
                    
                  
                  D)
                    
                        
                      
                          9
                        
                        
                          2
                        
                      
                    
                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          2
          A digital-to-analog converter with a full-scale
            output voltage of 3.5 V has a resolution close to 14m V. Its bit
            size is
        
        
          Options
          
            
                
              
                  A) 4
                  B) 8
                
                
                  C) 16
                  D) 32
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          3
          
            A single-phase half-controlled rectifier is driving a separately
            excited dc motor. The dc motor has a back emf constant of 0.5 V/rpm.
            The armature current is 5 A without any ripple. The armature
            resistance is 2W. The converter is
            working from a 280 V, single phase ac source with a firing angle of
            80°. Under this operating condition, the speed of the motor will be
          
        
        
          Options
          
            
                
              
                  A) 339 rpm
                  B) 359 rpm
                
                
                  C) 366 rpm
                  D) 386 rpm
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          4
          
            In relation to the synchronous machines, which one of the
            following statements is false?
          
        
        
          Options
          
            
                
              
                  A) In salient pole machines, the direct-axis
                    synchronous reactance is greater than the quadrature-axis
                    synchronous reactance
                  B) The damper bars help the synchronous motor self
                    start
                
                
                  C) Short circuit ratio is the ratio of the field
                    current required to produce the rated voltage on open
                    circuit to the rated armature current

                  
                  D) The V-curve of a synchronous motor represents
                    the variation in the armature current with field excitation,
                    at a given output power
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          5
          The 8085 assembly language instruction that
            stores the content of H and L registers into the memory locations
            2050_H and 2051_H, respectively, is

          
        
        
          Options
          
            
                
              
                  A) SPHL 2050_H 
                  B) SPHL2051_H
                
                
                  C) SHLD 2050_H
                  D) STAX 2050_H

                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          6
          If
            
                
              
                   E
                
              
            
             is the electric field intensity, Ñ(Ñ x
            
                
              
                   E
                
              
            
             ) is equal to  
        
        
          Options
          
            
                
              
                  A)
                    
                        
                      
                           E
                        
                      
                    
                     
                  B) |
                    
                        
                      
                           E
                        
                      
                    
                     | 
                
                
                  C) null vector
                  D) zero
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          D
        
        
          

        
        
          7
          For the function f(x) = x² e^-x,
            the maximum occurs when x is equal to  
        
        
          Options
          
            
                
              
                  A) 2
                  B) 1
                
                
                  C) 0
                  D) -1
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          8
          
            Two wattmeters, which are connected to measure the total power on
            a three -phase system supplying a balanced load, read 10.5 kW and -
            2.5 kW, respectively. The total powere and the power factor,
            respectively, are
          
        
        
          Options
          
            
                
              
                  A) 13.0 kW, 0.334 
                  B) 13.0 kW, 0.684

                  
                
                
                  C) 8.0 kW, 0.52 
                  D) 8.0 kW, 0.334
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          D
        
        
          

        
        
          9
          The insulation strength of an EHV transmission
            line is mainly governed by
        
        
          Options
          
            
                
              
                  A) load power factor 
                  B) switching over-voltages

                  
                
                
                  C) harmonics 
                  D) corona
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          10
          For the equation,

            s³- 4s²+ s + 6 = 0

            the number of roots in the left half of s-plane will be
        
        
          Options
          
            
                
              
                  A) zero
                  B) one

                  
                
                
                  C) two 
                  D) three

                  
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C


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