Articles

GATE-2012 ECE Q34 (signals)

Question 34 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q34. Consider the differential equation  with  and  The numerical value of  is (A) -2 (B) -1 (C) 0 (D) 1

GATE-2012 ECE Q12 (math)

Question 12 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q12. With initial condition  the solution of the differential equation,  is (A) (B) (C) (D) Solution From the product rule used to find the derivative of product of two or more functions, Applying this to the above equation, we…

GATE-2012 ECE Q11 (signals)

Question 11 on signals from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q11. The unilateral Laplace transform of is . The unilateral Laplace transform ofis (A)  (B)  (C)  (D)  Solution From the definition of Laplace transform for a function defined for all real numbers  is,  , where  with real numbers  and . To find the Laplace…

GATE-2012 ECE Q2 (communication)

Question 52 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q2. The power spectral density of a real process for positive frequencies is shown below. The values of  and , respectively are (A)  (B)  (C)  (D)  Solution For a wide sense stationary function, the auto-correlation with delay  is defined as,…

GATE-2012 ECE Q52 (electromagnetics)

Question 52 on electromagnetics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. An infinitely long uniform solid wire of radius  carries a uniform dc current of density . Q52. The magnetic field at a distance  from the center of the wire is proportional to (A)  for and for (B)  for  and  for  (C)  for  and  for  (D)  for  and  for  Solution…

GATE-2012 ECE Q16 (electromagnetics)

Question 16 on electromagnetics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q16. A coaxial cable with an inner diameter of 1mm and outer diameter of 2.4mm is filled with a dielectric of relative permittivity 10.89. Given ,  the characteristic impedance of the cable is (A)  (B)  (C)  (D)  Solution To…

GATE-2012 ECE Q39 (communication)

Question 39 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q39. The signal  as shown is applied both to  a phase modulator (with  as the phase constant) and a frequency modulator (with as the frequency constant) having the same carrier frequency.  The ratio  for the same maximum phase deviation is,…

GATE-2012 ECE Q47 (math)

Question 47 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q47. Given that and , the value of is (A)  (B)  (C)  (D)  Solution To answer this question, we need to refer to Cayley Hamilton Theorem. This is discussed briefly in Pages 310-311 of Introduction to Linear Algebra, Glibert Strang (buy…

Update : Correction to solution of GATE-2012 ECE Q38

Thanks to Mr. Raghava G D’s comments on the post discussing Question 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper, realized that I had made an error in the solution. Have the updated the post with the right answer and additional explanations.

GATE-2012 ECE Q38 (communication)

Question 38 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q38. A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0)=9/10, then the probability of error for an optimum receiver will be (A) 7/80 (B) 63/80 (C)…

GATE-2012 ECE Q3 (communication)

Question 3 on Communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q3. In a baseband communications link, frequencies upto 3500Hz are used for signalling. Using a raised cosine pulse with 75% excess bandwidth and for no inter-symbol interference, the maximum possible signaling rate in symbols per second is, (A)…

GATE-2012 ECE Q26 (electronic devices)

Question 26 on Electronic Devices from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q26. The source of a silicon (), n-channel MOS transistor has an area of and a depth of  . If the dopant density in the source is , the number of holes in the source region with…

GATE-2012 ECE Q36 (math)

Question 36 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q36. A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is (A) 1/3 (B) 1/2 (C) 2/3 (D) 3/4 Solution Let us start by…

GATE-2012 ECE Q46 (math)

Question 46 on math from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q46. The maximum value of  in the interval [1, 6] is (A) 21 (B) 25 (C) 41 (D) 46 Solution Let us start by finding the critical points of the function . The first derivative is, . Solving by…