One Stop GATE Forum: ECE GATE sample paper

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1
          Consider a lossless antenna with a directive
            gain of +6dB. If 1 mW of power is fed to it the total power radiated
            by the antenna will be
        
        
          Options
          
            
                
              
                  A) 4 mW
                  B) 1 mW
                
                
                  C)

                    7 mW                                                      
                  D) 1/4 mW
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          A
        
        
          

        
        
          2
          The bandgap of Silicon at room temperature is
        
        
          Options
          
            
                
              
                  A) 1.3 eV
                  B) 0.7 eV
                
                
                  C) 1.1 eV
                  D) 1.4 eV
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          3
          For a signal x(t) the fourier transform is X(f).
            Then the inverse Fourier transform of X(3f + 2) is given by
        
        
          Options
          
            
                
              
                  A)
                    
                        
                      
                          1
                        
                        
                          2
                        
                      
                    
                    x(
                    
                        
                      
                          t
                        
                        
                          2
                        
                      
                    
                    )e^(j3p t) 
                  B)
                    
                        
                      
                          1
                        
                        
                          3
                        
                      
                    
                    x(
                    
                        
                      
                          t
                        
                        
                          3
                        
                      
                    
                    )e^-j4pt/3
                
                
                  C) 3x(3t)e^-j4p t 
                  D) x(3t+2)
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          4
          In a PCM system, if the code word length is
            increased from 6 to 8 bits, the signal to quantization noise ratio
            improves by the factor

          
        
        
          Options
          
            
                
              
                  A) 8/6 
                  B) 12

                     
                
                
                  C) 16 
                  D) 8
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          5
          
            Match the following and choose the correct combination:
             
            

                
              
                  Group 1
                  Group 2
                
                
                  E. Newton-Raphson method 

                    F. Runge-kutta method 

                    G. Simpson^,s Rule 

                    H. Gauss elimination
                  1. Solving nonlinear equations

                    2. Solving linear simultaneous equations

                    3. Solving ordinary differential equations

                    4. Numerical integration

                    5. Interpolation

                    6. Calculation of Eigenvalues
                
              
            
          
        
        
          Options
          
            
                
              
                  A) E-6, F-1, G-5, H-3
                  B) E-1, F-6, G-4, H-3
                
                
                  C) E-1, F-3, G-4, H-2
                  D) E-5, F-3, G-4, H-1
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          6
          The Fourier transform of a conjugate symmetric
            function is always

          
        
        
          Options
          
            
                
              
                  A) imaginary 
                  B) conjugate anti-symmetric 

                  
                
                
                  C) real
                  D) conjugate symmetric
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          7
          
            Match the following and choose the correct combination.
             
            

                
              
                  Group 1
                  Group 2
                
                
                  E - continuous and aperiodic signal      

                    F - continuous and periodic signal 

                    G - Discrete and aperiodic signal 

                    H - Discrete and periodic signal
                  1 - Fourier representation is continuous and aperiodic

                    2 - Fourier representation is discrete and aperiodic

                    3 - Fourier representation is continu-ous and periodic

                    4 - Fourier representation is discrete and periodic
                
              
            
          
        
        
          Options
          
            
                
              
                  A) E - 3, F - 2, G - 4, H -1
                  B) E -1, F - 3, G - 2, H - 4
                
                
                  C) E -1, F - 2, G - 3, H - 4
                  D) E - 2, F - 1, G - 4, H - 3
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          8
          A device with input x(t) and output y(t) is
            characterized by:   y(t) = x²(t).

            An FM signal with frequency deviation of 90 kHz and modulating
            signal bandwidth of 5 kHz is applied to this device. The bandwidth
            of the output signal is

             
        
        
          Options
          
            
                
              
                  A) 370 kHz  
                  B) 190 kHz 
                
                
                  C) 380kHz 
                  D) 95kHz
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          C
        
        
          

        
        
          9
          For the polynomial P(s) = s⁵  +
            s⁴ + 2s³ + 2s² + 3s + 15, the
            number of roots which lie in the right half of the s-plane is

          
        
        
          Options
          
            
                
              
                  A) 4
                  B) 2
                
                
                  C) 3
                  D) 1
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B
        
        
          

        
        
          10
          An AM signal is detected using an envelope
            detector The carrier frequency and modulating signal frequency are 1
            MHz and 2 kHz respectively. An appropriate value for the time
            constant of the envelope detector is

          
        
        
          Options
          
            
                
              
                  A) 500 msec
                  B) 20 msec
                
                
                  C) 0.2 msec
                  D) 1 msec
                
              
            
          
        
        
          

          

        
        
          Correct Answer
          B


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