Page 1 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/GATE question papers: Electronics and Communication Engineering 2010 (EC) Q. No. 1 – 25 Carry One Mark Each 1. The eigen values of a skew-symmetric matrix are (A) always zero (B) always pure imaginary (C) either zero or pure imaginary (D) always real 2. The trigonometric Fourier series for the waveform f(t) shown below contains (A) only cosine terms and zero value for the dc component (B) only cosine terms and a positive value for the dc component (C) only cosine terms and a negative value for the dc component (D) only sine terms and a negative for the dc component 3. A function n(x) satisfied the differential equation 0 L ) x ( n dx ) x ( n d 2 2 2 where L is a constant. The boundary conditions are: n(0)=K and n ( ∞ ) = 0. The solution to this equation is (A) n(x) = K exp(x/L) (B) n(x) = K exp(-x/L ) (C) n(x) = K2 exp(-x/L) (D) n(x) = K exp(-x/L) 4. For the two-port network shown below, the short-circuit admittance parameter matrix is (A) (B) (C) (D) S 4 2 2 4 S 1 5 . 0 5 . 0 1 S 1 5 . 0 5 . 0 1 S 4 2 2 4 5. For parallel RLC circuit, which one of the following statements is NOT correct? (A) The bandwidth of the circuit deceases if R is increased (B) The bandwidth of the circuit remains same if L is increased (C) At resonance, input impedance is a real quantity (D) At resonance, the magnitude of input impedance attains its minimum value. Page 2 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/6. At room temperature, a possible value for the mobility of electrons in the inversion layer of a silicon n-channel MOSFET is (A) 450 cm2/V-s (B) 1350 cm2/V-s (C) 1800 cm2/V-s (D) 3600 cm2/V-s 7. Thin gate oxide in a CMOS process in preferably grown using (A) wet oxidation (B) dry oxidation (C) epitaxial deposition (D) ion implantation 8. In the silicon BJT circuit shown below, assume that the emitter area of transistor Q1 is half that of transistor Q2. The value of current I0 is approximately (A) 0.5 mA (B) 2mA (C) 9.3 mA (D) 15mA 9. The amplifier circuit shown below uses a silicon transistor. The capacitors CC and CE can be assumed to be short at signal frequency and the effect of output resistance r0 can be ignored. If CE is disconnected from the circuit, which one of the following statements is TRUE? (A) The input resistance Ri increases and the magnitude of voltage gain AV decreases (B) The input resistance Ri decreases and the magnitude of voltage gain AV decreases (C) Both input resistance Ri and the magnitude of voltage gain AV decrease (D) Both input resistance Ri and the magnitude of voltage gain AV increase R=9.3K I0 (2=715)= (1=700) Q1 Q2 -10 V Page 3 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/10. Assuming the OP-AMP to be ideal, the voltage gain of the amplifier shown below is (A) 12 RR (B) 13 RR (C) 1 3 2R R R (D) 1 3 2R R R 11. Match the logic ga5tes in Column A with their equivalents in Column B. (A) P–2, Q-4, R-1, S-3 (B) P-4, Q-2, R-1, S-3 (C) P–2, Q-4, R-3, S-1 (D) P-4, Q-2, R-3, S-1 Page 4 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/12. For the output F to be 1 in the logic circuit shown, the input combination should be (A) A = 1, B= 1. C = 0 (B) A = 1, B= 0,C = 0 (C) A = 0, B= 1. C = 0 (D) A = 0, B= 0, C = 1 13. In the circuit shown, the device connected to Y5 can have address in the range (A) 2000 -20FF (B) 2D00 – 2DFF (C) 2E00 – 2EFF (D) FD00 -FDFF 14. Consider the z-transform X(z) = 5z2 + 4z-1 + 3; 0<|z| < ∞ . The inverse z transform x[n] is (A) 5[n + 2] + 3 [n] + 4 [n – 1] (B) 5 [n -2] + 3 [n] + 4 [n + 1] (C) 5 u[n + 2] + 3 u[n] + 4 u[n – 1] (D) 5 u[n -2] + 3 u[n] + 4 u[n + 1] 15. Two discrete time systems with impulse responses h1[n] = [n -1] and h2[n] = [n – 2] are connected in cascade. The overall impulse response of the cascaded system is (A) [n -1] + [n -2] (B) [n -4] (C) [n -3] (D) [n -1] [n -2] 16. For an N-point FFT algorithm with N = 2m which one of the following statements is TRUE? (A) It is not possible to construct a signal flow graph with both input and output in normal order (B) The number of butterflies in the mth stage is N/m (C) In-place computation requires storage of only 2N node data (D) Computation of a butterfly requires only one complex multiplication To device Chip select VCC GND A11 A12 A13 A14 A15 A B A8 A9 A10 Y5 74LS138 3-to-8 decoder G2 G2 G1 10 /MPage 5 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/17. The transfer function Y(s)/R(s) of the system shown is (A) 0 (B) 1 s 1 (C) 1 s 2 (D) 3 s 2 18. A system with transfer function p s s ) s ( X ) s ( Y has an output y(t) = cos 3 t 2 for the input signal x(t) = p cos 2 t 2 . Then, the system parameter ‘p’ is (A) 3 (B) 3 2 (C) 1 (D) 23 19. For the asymptotic Bode magnitude plot shown below, the system transfer function can be (A) 1 s 1 . 0 1 s 10 (B) 1 s 1 . 0 1 s 100 (C) 1 s 10 s 100 (D) 1 s 10 1 s 1 . 0 20. Suppose that the modulating signal is m(t) = 2cos (2 fmt) and the carrier signal is xC(t) = AC cos(2fct), which one of the following is a conventional AM signal without over-modulation? (A) x(t) = Acm(t) cos(2fct) (B) x(t) = Ac[1 + m(t)]cos(2fct) (C) x(t) = Ac cos(2fct) + 4 Ac m(t) cos(2fct) (D) x(t) = Ac cos(2fmt) cos(2fct) + Ac sin(2fmt) sin(2fct) Page 6 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.n t.i e n/http://w w. w questionpapers.net.in/21. Consider an angle modulated signal x(t) = 6cos[2x106t+2sin(8000t) + 4cos(8000pt)] V. The average power of x(t) is. (A) 10W (B) 18W (C) 20W (D) 28W 22. If the scattering matrix [S] of a two port network is[S] = then the network is 0 0 0 0 90 1 . 0 90 9 . 0 90 9 . 0 0 2 . 0 (A) lossless and reciprocal (B) lossless but not reciprocal (C) not lossless but reciprocal (D) neither lossless nor reciprocal 23. A transmission line has a characteristic impedance of 50 and a resistance of 0.1 /m. if the line is distortion less, the attenuation constant (in Np/m) is (A) 500 (B) 5 (C) 0.014 (D) 0.002 24. Consider the pulse shape s(t) as shown. The impulse response h(t) of the filter matched to this pulse is s(t) 1 0 t T h( t ) (B) t T 0 1 h( t ) (A) 1 t 0 -T (C) (D) h( t ) h( t ) 1 T 2T 0 T t 1 0 25. The electric field component of a time harmonic plane EM wave traveling in a nonmagnetic lossless dielectric medium has an amplitude of 1 V/m. If the relative permittivity of the medium is 4, the magnitude of the time-average power density vector (in W/m2) is (A) 301 (B) 601 (C) 120 1 (D) 240 1 Page 7 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.qu tion es papers.net.in/http://www.questionpapers et.in/.n Q. No. 26 – 51 Carry Two Marks Each 26. If ey = x1 X then y has a (A) maximum at x= e (B) minimum at x= e (C) maximum at x= e-1 (D) minimum at x= e-1 27. A fair coin is tossed independently four times. The probability of the event “the number of time heads shown up is more than the number of times tails shown up” is (A) 16 1 (B) 81 (C) 41 (D) 16 5 28. If A aˆ = xy + x2 then x y aˆ c l d . A over the path shown in the figure is y 3 -1 -0 1 3 2 3 C x (A) 0 (B) 3 2 (C) 1 (D) 2 3 29. The residues of a complex function X(z) = ) 2 z )( 1 z ( z z 12 1 at its poles are (A) 21 , 21 and 1 (B) 21 , 21 and 1 (C) 2 1 , 1 and 23 (D) 2 1 , 1 and 23 30. Consider differential equation x ) x ( y dx ) x ( dy with the initial condition y(0) = 0. Using Euler’s first order method with a step size of 0.1, the value of y (0.3) is (A) 0.01 (B) 0.031 (C) 0.0631 (D) 0.1 31. Given f(t) = L-1 1 ) ft ( if . s ) 3 K ( 2 s 4 3 s 1 s 3 lim x , then the value of K is (A) 1 (B) 2 (C) 3 (D) 4 Page 8 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/32. In the circuit shown, the switch S is open for a long time and is closed at t=0. The current i(t) for t≥0+ is (A) i(t)=0.5-0.125e-1000t A (B) i(t)=1.5-0.125e-1000t A (C) i(t)=0.5-0.5e-1000t A (D) i(t)=0.375e-1000t A 33. The current I in the circuit shown is (A) -j1A (B) J1A (C) 0A (D) 20A 34. In the circuit shown, the power supplied by the voltage source is (A) 0W (B) 5W (C) 10W (D) 100W 35. In a uniformly doped BJT, assume that NE, NB and NC are the emitter, base and collector dopings in atoms/cm3, respectively. If the emitter injection efficiency of the BJT is close unity, which one of the following conditions is TRUE? (A) NE=NB=NC (B) NE >>NB and NB>NC (C) NE=NB and NB½ S2: The system is stable but not causal for ROC:|z|<¼ S3: The system is neither stable nor causal for ROC: ¼<|z|<½ Which one of the following statements is valid? (A) Both S1 and S2 are true (B) Both S2 and S3 are true (C) Both S1 and S3 are true (D) S1, S2 and S3 are all true 43. The Nyquist sampling rate for the signal s(t) = t t ) 700 sin( t ) t 500 sin( is given by (A) 400 Hz (B) 600 Hz (C) 1200Hz (D) 1400 Hz C D A B F(A,B,C,D) Y I0 I1 I2 I3 4x1 MUX Page 11 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/44. A unity negative feedback closed loop system has a plant with the transfer function 2 s 2 s 1 ) s ( G 2 and a controller Gc(S) in the feed forward path. For a unit set input, the transfer function of the controller that gives minimum steady state error is (A) 2 s 1 s ) s ( Gc (B) 1 s 2 s ) s ( Gc (C) ) 3 s )( 2 s ( ) 4 S )( 1 s ( ) s ( Gc (D) s 3 s2 1 ) s ( Gc 45. X(t) is a stationary process with the power spectral density Sx(f)>0 for all f. The process is passed through a system shown below. Let Sy(f) be the power spectral density of Y(t). Which one of the following statements is correct? (A) Sy(f)>0 for all f (B) Sy(f)=0 for |f|>1kHz (C) Sy(f)=0 for f=nf0, f0=2kHz, n any integer (D) Sy(f)=0 for f=(2n+1)f0=1kHz, n any integer 46. A plane wave having the electric field component z 8 i aˆ ) y t 10 3 cos( 24 E V/M and traveling in free space is incident normally on a lossless medium with m= m0 and e=9e0 which occupies the region y≥0. The reflected magnetic field component is given by (A) 101 x 8 aˆ ) y t 10 3 cos( A/M (B) 201 x 8 aˆ ) y t 10 3 cos( A/M (C) 201 x 8 aˆ ) y t 10 3 cos( A/M (D) 101 x 8 aˆ ) y t 10 3 cos( A/M 47. In the circuit shown, all the transmission line sections are lossless. The Voltage Standing Wave Ra (VSWR) on the 60W line is tion (A) 1.00 (B) 1.64 (C) 2.50 (D) 3.00 Z0=30 Short /8 /4 Z0=60 ZL=30 0 Z30 2 = Delay=0.5ms d dt Y(t) X(t) + + + Page 12 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/Common Data Questions: 48 & 49 Consider the common emitter amplifier shown below with the following circuit parameters: b=100, gm=0.3861 A/V, r0=∞, rp=259 W, RS=1k W, RB=93K W, RC=250 W, RL=1k W, C1=∞ and C2=4.7mF. +10V R C R B R S RL C 2 C1 + s -+ 0 -48. The resistance seen by the source Vs is (A) 258 (B) 1258 (C) 93 K (D) ∞ 49. The lower cut-off frequency due to C2 is (A) 33.9 Hz (B) 27.1 Hz (C) 13.6 Hz (D) 16.9 Hz Common Data Questions: 50 & 51 The signal flow graph of a system is shown below. U(s) 2 1/s 1/s 1 0.5 1 -1 -1 Y(s) 50. The state variable representation of the system can be (A) x = u 20 x 0 1 1 1 Y = [0 0.5]x (B) x = u 20 x 0 1 1 1 y [0 0.5]x (C) x = u 20 x 0 1 1 1 y [0.5 0.5]x (D) x = u 20 x 0 1 1 1 y [0.5 0.5]x Page 13 of 14 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html http://www.questionpapers.net.in/http://www.questionpapers.net.in/51. The transf the system is er function of (A) 1 s 1 s2 (B) 1 s 1 s2 (C) 1 s s 1 s 2 (D) 1 s s 1 s 2 Questions: Q.52 to Q.55 Carry Two Marks Each Statement for Linked Answer Questions: 52 & 53 g 00K, electronic charge=1.6x10-19 C, thermal voltage=26mV and electron mobility = 1350cm2/V-s Linked Answer The silicon sample with unit cross-sectional area shown below is in thermal equilibrium. The followin information is given: T=3 ND=1016/cm3 x=0 x=1m= 1V= 5 The magnitude of ectric field at x=0. is 2. the el 5 m (A) 1kV/cm (B) 5kV/cm (C) 10 kV/cm (D) 26kV/cm (C) 4.32x103 A/cm2 (D) 6.48x102 A/cm2 Statement for Linked Answer Questions: 54 & 55 filter is ideal with unity gain and cutoff ent the random variable y(tk). nction, e 2/2). Assume transmitted bits to be equiprobable and threshold z is set to a/2=10-6V. 53. The magnitude of the electron drift current density at x=0.5 m is (A) 2.16x104 A/cm2 (B) 1.08x104 A/cm2 Consider a baseband binary PAM receiver shown below. The additive channel noise n(t) is whit with power spectral density SN(f)=N0/2=10-20 W/Hz. The low-pass frequency 1MHz. Let Yk repres Yk=Nk if transmitted bit bk=0 Yk=a+Nk if transmitted bit bk=1 Where Nk represents the noise sample value. The noise sample has a probability density fu PNk(n)=0.5e-|n| (This has mean zero and varianc 54. The value of the parameter V-1) (in is (A) 1010 (B) 107 (C) 1.414x10-10 (D) 2x10-20 GATE question papers: Electronics and Communication Engineering 2010 (EC) Download more GATE question papers and read GATE articles at: http://www.questionpapers.net.in/gate-question-papers-download.html Page 14 of 14 http://www.questionpapers.net.in/http://www.questionpapers.net.in/5 skilled workers can build a wall in 20 days; 8 semi-skilled worker can build a wall in 25days; 10 unskilled workers can build a wall in 30 days. If a 55. The probability of bit error is (A) 0.5xe-3.5 (B) 0.5xe-5 (C) 0.5xe-7 (D) 0.5xe-10 Q. No. 56 – 60 Carry One Mark Each 6. s is st in m g (A) Cyclic (B) indirect (C) confusing (D) crooked 57. words. xpresses the re tion in orig ed: Worker (C) wit : jester (D) renovated : house 8. : ces wo (A) uphold (B) restrain (C) Cherish (D) conserve 9. g sentence: th emark pol ___ his lack of ss abo su (A) masked (B) belied (C) cherish (D) conserve 60. m play both y foot ll. The nu r o erson ockey otball is: (A) 2 (B) 17 (C) 13 (D) 3 61. s for their cause. meaning of the above passage: (D) People in military establishments like to use chemical agents in war. 2. (A) 534 (B) 1403 (C) 1623 (D) 1513 63. team has 2 killed, 6 semi-skilled and 5 unskilled ers wall? 4. 3,3,4, ny istinct t n rs eater than 3000 can be formed? (A) 50 (B) 51 (C) 52 (D) 54 65. o successive siblings (that is born one after another) is tha ii. 1 year. However, Gita is not the oldest and est. . rder w ey ) HSIG (B) SGHI (C) IGSH (D) IHSG End of Question Papers 5 Which of the following option the close eanin to the world below: Circuitous The question below consists of a pair of related of related words followed by four pairs of Select the pair that best e la the inal pair. Unemploy (A) fallow : land (B) unaware : sleeper 5 Choose the most appropriate word from the options given below to complete the following sentence If we manage to ________ our natural resour , we uld leave a better planet for our children. 5 Choose the most appropriate word from the options given below to complete the followin His ra er casual r s on itics ____ seriousne ut the bject. 25 persons are in a room. 15 of them play hockey, 17 of them play football and 10 of the hocke and ba n the mbe f p s playing neither h nor fo Q. No. 61 – 65 Carry Two Marks Each Modern warfare has changed from large scale clashes of armies to suppression of civilian populations. Chemical agents that do their work silently appear to be suited to such warfare; and regretfully, there exist people in military establishments who think that chemical agents are useful tool which of the following statements best sums up the (A) Modern warfare has resulted in civil strife. (B) Chemical agents are useful in modern warfare. (C) Use of chemical agents in warfare would be undesirable. 6 If 137+276=435 how much is 731+672? work , how long will it take to build the (A) 20 days (B) 18 days (C) 16 days (D) 15 days 6 Given digits 2,2,3, 4,4,4 how ma d 4 digi umbe gr Hari (H), Gita (G), Irfan (I) and Saira (S) are sibiligs (i.e. brothers and sisters). All were born on 1st January. The age difference between any tw less n3 years. Given the following facts: i. Hair’s age + Gita’s age > Irfan’s age + Saira’s age. The age difference between Gita and Saira is Saira is not the young iii There are not twins. In what o ere th born (0ldest first)? (A