Articles

## GATE-2012 ECE Q28 (electromagnetics)

Question 28 on electromagnetics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q28. A transmission line with a characteristic impedance of 100 is used to match a 50 section to a 200 section. If the matching is to be done both at 429MHz and 1GHz, the length of the transmission line can be approximately (A) 82.5cm…

## GATE-2012 ECE Q15 (communication)

Question 15 on communication from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q15. A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount  and decreases that of the…

## GATE-2012 ECE Q7 (digital)

Question 7 on digital from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q7. The output Y of a 2-bit comparator is logic 1 whenever the 2 bit input A is greater than 2 bit input B. The number of combinations for which output is logic 1 is (A) 4 (B)…

## GATE-2012 ECE Q13 (circuits)

Question 13 on analog electronics from GATE (Graduate Aptitude Test in Engineering) 2012 Electronics and Communication Engineering paper. Q13. The diodes and the capacitors in the circuit shown are ideal. The voltage  across the diode  is (A)  (B)   (C)  (D) Solution The first half of the circuit is a negative clamper circuit and the second half…

## 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…

## 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)…