GATE_2015_ECE_Morning

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3 Section - I (Geneal Aptitude). Choose the appopiate wod/phase, out of the fou options given below, to complete the following sentence : Fogs coak (c) hiss oa patte. If logx (5/7) = /3, then the value of x is 343/5 5/343 (c) 5/49 49/5 3. Opeates, and ae defined by : a b a b ; a b ab. a b Find the value of 66 6 (66 6) (c) a b a b ; a b 4. Choose the wod most simila meaning to the given wod: Educe Exet (c) Extact Educate Extend 5. Choose the most appopiate wod fom the options given below to complete the following sentence. The pincipal pesented the chief guest with a, as token of appeciation. momento (c) momentum memento moment 6. The following question pesents a sentence, pat of which is undelined. Beneath the sentence you find fou ways of phasing the undelined pat. Following the equiements of the standad witten English, select the answe that poduces the most effective sentence. Tubeculosis, togethe with its effects, anks one of the leading causes of death in India. anks as one of the leading causes of death GATE_05_ECE_Moning ank as one of the leading causes of death (c) has the ank of one of the leading causes of death ae one of the leading causes of death 7. Humpty Dumpty sits on a wall evey day while having lunch. The wall sometimes beaks. A peson sitting on the wall falls if the wall beaks. Which one of the statements below is logically valid and can be infeed fom the above sentences? Humpty Dumpty always falls white having lunch Humpty Dumpty does not fall sometimes while having be suitable scientific innovations, while the othe may be 007 All ight eseved. ECT Publications. Mob lunch (c) Humpty Dumpty neve falls duing dinne When Humpty Dumpty does not sit on the wall, the wall does not beak 8. A cube side 3 units is fomed using a set of smalle cubes of side unit. Find the popotion of the numbe of faces of the smalle cubes visible to those which ae NOT visible. : 4 : 3 (c) : : 3 9. Fill in the missing value Ans. (3) 0. ead the following paagaph and choose the coect statement. Climate change has educed human secuity and theatened human well being. An ignoed eality of human pogess is that human secuity lagely depends upon envionmental secuity. But on the contay, human pogess seems contadictoy to envionmental secuity. To keep up both at the equied level is a challenge to be addessed by one and all. One of the ways to cub the climate change may

4 Gate_05_ECE_Moning the Gandhian pespective on small scale pogess with focus on sustainability. Human pogess and secuity ae positively associated with envionmental secuity. Human pogess is contadictoy to envionmental secuity. (c) Human secuity is contadictoy to envionmental secuity. Human pogess depends upon envionmental secuity. Section - II (Electonics and Communication Engineeing). A silicon sample is unifomly doped with dono type impuities with a concentation of 0 6 /cm 3. The electon and hole mobilities in the sample ae00 cm /V-s and 400 cm /V-s espectively. Assume complete ionization of impuities. The chage of an electon is C. The esistivity of the sample (in -cm) is. Ans. (0.50). Negative feedback in a closed-loop contol system DOES NOT educe the oveall gain educe bandwidth (c) impove distubance ejection educe sensitivity to paamete vaiation 3. In the netwok shown in the figue, all esistos ae identical with 300. The esistance ab (in ) of the netwok is. a ab b Ans. (00) In the cicuit shown, at esonance, the amplitude of the sinusoidal voltage (in Volts) acoss the capacito is. 00cos t (V) Ans. (5) m F 5. Suppose A and B ae two independent events with pobabilities P(A) 0 and P(B) 0. Let A and B be thei complements. Which one of the following statements is FALSE? P A B P(A)P(B) P(A/B) = P(A) (c) P(A B) P(A) P(B) P(A B) P(A) P(B) 6. In the cicuit shown, the switch SW is thown fom position A to position B at time t = 0. The enegy (in J ) taken fom the 3V souce to chage the 0. F capacito fom 0V to 3 V is 3V 0 SW B A t 0 0.F (c) Let z = x + i y be a complex vaiable. Conside that contou integation is pefomed along the unit cicle in anticlockwise diection. Which one of the following statements is NOT TUE? z The esidue of at z = is / z (c) C z dz 0 dz i z C z (complex conjugate of z) is analytical function Ans. 007 All ight eseved. ECT Publications. Mob

5 8. Conside a staight, infinitely long, cuent caying conducto lying on the zaxis. Which one of the following plots (in linea scale) qualitatively epesents the dependence of H on, whee H is the magnitude of the azimuthal component of magnetic field outside the conducto and is the adial distance fom the conducto? H H GATE_05_ECE_Moning. A sinusoidal signal of khz fequency is applied to a delta modulato. The sampling ate and step-size of the delta modulato ae 0,000 samples pe second and 0. V, espectively. To pevent slope oveload, the maximum amplitude of the sinusoidal signal (in Volts) is (c) H H (c) 9. The wavefom of apeiodic signal x(t) is shown in the figue. x(t) 3. The electic field component of a plane wave tavelling in a lossless dielectic medium is given by 8 z E(z, t) aˆ ycos 0 t V/m. The wavelength (in m) fo the wave is. Ans. (8.89) 4. In the given cicuit, the values of V and V espectively ae t I A signal g(t) is defined by powe of g(t) is. Ans. (.5) 0. Conside a system of linea equations : x y + 3z =, x 3y + 4z =, and x + 4y 6z = k t g(t) x. The aveage The value of k fo which the system has infinitely many solution is. Ans. (). A function f(x) = x + x 3 is defined in the closed inteval [, ]. The value of x, in the open inteval (, ) fo which the mean value theoem is satisfied, is / /3 (c) /3 / 007 All ight eseved. ECT Publications. Mob V 5 V, 5 V (c) 5 V, 35 V 0 V, 30 V 0 V, 0 V 5. Conside a fou bit D to A convete. The analog value coesponding to a digital signals of values 0000 and 000 ae 0 V and V espectively. The analog value (in Volts) coesponding to the digital signal is. Ans. (0.9375) 6. In an 8085 micopocesso, the shift egistes which stoe the esult of an addition and the oveflow bit ae, espectively B and F (c) H and F A and F A and C V 3

6 Gate_05_ECE_Moning 7. A egion of negative diffeential esistance is obseved in the cuent voltage chaacteistics of a silicon PN junction if both the P-egion and the N-egion ae heavily doped the N-egion is heavily doped compaed to the P-egion (c) the P-egion is heavily doped compaed to the N-egion an intinsic silicon egion is inseted between the P- egion and the N-egion 8. Conside the signal s(t) m(t) cos f t m(t) ˆ sin( f t) c whee ˆm(t) denotes the Hilbe tansfom of m(t) and the bandwidth of m(t) is vey small compaed to f c. The signal s(t) is a high-pass signal low-pass signal (c) band-pass signal double sideband suppessed caie signal 0(s ) 9. The pola plot of the tansfe function G(s) fo s 0 will be in the fist quadant second quadant (c) thid quadant fouth quadant * 0. The esult of the convolution x( t)( t t) is x(t + t 0 ) x(t t 0 ) (c) x( t + t 0 ) x( t t 0 ) Ans.. A 6 Kb (=6,384 bit) memoy aay is designed as a squae with an aspect atio of one (numbe of ows is equal to the numbe of columns). The minimum numbe of addess lines needed fo the ow decode is. Ans. (7). Fo the cicuit with ideal diodes shown in the figue, the shape of the output (v out ) fo the given sine wave input (v in ) will be c 0 T 0 0.5T V i V o T 0 0.5T T 0 0.5T (c) T 0 T 0.5T 0 0.5T 3. The value of p such that the vecto is an eigenvecto 3 of the matix Ans. (7) 4 p In the cicuit shown below, the Zene diode is ideal and the Zene voltage is 6 V. The output voltage V 0 (in volts) is. k 0V k Ans. (5) 5. A unity negative feedback system has the open-loop K tansfe function G(s). The value of the s(s )(s 3) gain K (>0) at which the oot locus cosses the imaginay axis is Ans. () 6. Fo the NMOSFET in the cicuit shown, the theshold voltage is V th, whee V th > 0. The souce voltage V SS is vaied fom 0 to V DD. Neglecting the channel length modulation, the dain cuent I D as a function of V SS is epesented by V o All ight eseved. ECT Publications. Mob

7 (c) I D I D V DD V V DD th V th V SS V SS V SS V DD I D I D V th V DD V th V SS V SS 7. The longitudinal component of the magnetic field inside an ai-filled ectangula waveguide made of a pefect electic conducto is given by the following expession H(x, z y, z, t) 0.cos(5 x) cos(30.3 y) TM TM (c) TE TE 9 cos(0 t z)(a/m) 8. The input X to Binay Symmetic Channel (BSC) shown in the figue is with pobability of 0.8. The coss-ove pobability is /7. If the eceived bit Y = 0, the conditional pobability that was tansmitted is. PX 0 0. PX 0.8 Ans. (0.4) x 0 6/7 /7 /7 Y 0 6/7 GATE_05_ECE_Moning 9. The tansmitted signal in a GSM system is of 00 khz bandwidth and 8 uses shae a common bandwidth using TDMA. If at a given time uses ae talking in a cell, the total bandwidth of the signal eceived by the base station of the cell will be at least (in khz). Ans. (*) 30. A lead compensato netwok includes a paallel combination of and C in the feed-fowad path. If the tansfe function of the compensato is is. Ans. (0.5) G(s) c s the value of C s 4 3. Conside a unifom plane wave with amplitude (E 0 ) of 0 V/m and. GHz fequency tavelling an ai, and incident nomally on a dielectic medium with complex elative pemittivity ( ) and pemeability ( ) as shown in the figue. E0 0 V/m Feq.. GHz Ai Dielectic j j 0cm E The magnitude of the tansmitted electic field component (in V/m) afte it has tavelled a distance of 0 cm inside the dielectic egion is. Ans. (0.) 3. Fo a silicon diode with long P and N egions, the accepte and done impuity concentations ae cm and cm, espectively. The lifetimes of electons in P egion and holes in N egion ae both 00 s. The electon and hole diffusion coefficients ae 49cm /s and 36cm /s, espectively. Assume kt/q 6 mv, the intinsic caie concentation is cm 9, and q.6 0 C. When a fowad voltage of 08 mv is applied acoss the diode, the hole cuent density (in na/cm ) injected fom P egion to N egion is. 007 All ight eseved. ECT Publications. Mob

8 Gate_05_ECE_Moning Ans. (86.7) 33. A plant tansfe function is given as G(s) K p K s s(s ) When the plant opeates in a unity feedback configuation, the condition fo the stability of the closed loop system is K K I K p 0 Kp 0 (c) KI Kp KI Kp 34. Which one of the following gaphs descibes the function f(x) = e x(x + x + )? f(x) f(x) x(t) m(t) cos(400t) y(t) 0x(t) x (t) H(f) z(t) Fig. H(f) f(hz) Ans. (350) 37. A MOSFET in satuation has a dain cuent of ma fo V DS = 0.5 V. If the channel length modulation coefficient is 0.05 V, the output esistance (in k ) of the MOSFET is. Ans. (0) x x 38. Fo the discete-time system shown in the figue, the poles of the system tansfe function ae located at f(x) f(x) x[n] y[n] (c) x x z z 35. A 3-input majoity gate is defined by the logic function M(a, b, c) = ab + bc + ca. Which one of the following gate is epesented by the function M(M(a,b,c),M(a,b,c)c)? 3-input NAND gate 3-input XO gate (c) 3-input NO gate 3-input XNO gate 36. In the system shown in Figue, m(t) is a low-pass signal with bandwidth W Hz. The fequency esponse of the bandpass filte H(f) is shown in Figue. If it is desied that the output signal z(t) = 0 x(t), the maximum value of W(in Hz) should be stictly less than., 3,3 (c), 3, A vecto 3 P is given by P x ya x y a x yza x y z Which of the following statements is TUE? P is solenoidal, but not iotational P is iotational, but not solensoidal (c) P is neithe solenoidal no iotational P is both solenoidal and iotational 40. In the cicuit shown, assume that the opamp is ideal. The bidge output voltage V 0 (in mv) fo 0.05 is All ight eseved. ECT Publications. Mob

9 50 50( ) Ans. (50) V o 50( ) 50 Q.4 The cicuit shown in the figue has an ideal opamp. The oscillation fequency and the condition to sustain the oscillations, espectively, ae (c) C C and C and Ans. C V o C and 4 C and 4 4. In the cicuit shown, I = 80 ma and I = 4 ma. Tansistos T and T ae identical. Assume that the themal voltage V T is 6 mv at 7 C. At 50 C, the value of voltage V V V (in mv) is Ans. (83.5) V s I s V V V T T I GATE_05_ECE_Moning 43. The built-in potential of an abupt p-n junction is 0.75 V. If its junction capacitance (C J ) at a evese bias (V ) of.5v is 5pF, the value of C J (in pf) when V = 7.5 V is. Ans. (.5) 44. The electic field intensity of a plane wave taveling in fee space is given by the following expession E(x, t) a y4cos( t k 0x)(V/m) In this field, conside a squae aea 0cm 0cm on a plane x + y =. The total time-aveaged powe (in mw) passing though the squae aea is. Ans. (53.9) 45. The open-loop tansfe function of a unity feedback K(s 4) configuation is given as G(s). The value (s 8)(s 9) of a gain K(>0) fo which + j lies on the oot locus is. Ans. (5.54) Q.46 In the cicuit shown, switch SW is closed at t = 0. Assuming zeo initial conditions, the value of v c (t) (in Volts) at t = sec is. 0V Ans. (.58) t0 SW 3 5 F 6 V(t) c Q.47 The solution of the diffeential equation d y dt dy y 0 with y(0) y(0) is dt ( t)e t ( + t)e t (c) ( + t)e t ( t)e t Q.48 The maximum aea (in squae unit) of a ectangle whose vetices lies on the ellipse x + 4y = is Ans. () 49. The Boolean expession F(X,T,Z) X Y Z XY Z XY Z XYZ conveted into 007 All ight eseved. ECT Publications. Mob

10 Gate_05_ECE_Moning canonical poduct of sum (POS) fom is (X Y Z)(X Y Z)(X Y Z)(X Y Z) (X Y Z)(X Y Z)(X Y Z)(X Y Z) (c) (X Y Z)(X Y Z)(X Y Z)(X Y Z) (X Y Z)(X Y Z)(X Y Z)(X Y Z) 50. The damping atio of a seies LC cicuit can be expessed as C L (c) C L L C 5. The pole-zeo diagam of a causal and stable discete-time system is shown in the figue. The zeo at the oigin has multiplicity 4. The impulse esponse of the system is h[n]. If h[0] =, we can conclude L C p 0 0 A/3 q W3 W 3 0 W3 0 B/3 4 4 c W3 W W 3 C/3 then the elationship between the sequences [p, q, ] and [a, b, c] is [p, q, ] = [b, a, c] [p, q, ] = [b, c, a] (c) [p, q, ] = [c, a, b] [p, q, ] = [c, b, a] 53. All the logic gates shown in the figue have a popagation delay of 0 ns. Let A = C = 0 and B = until time t = 0. At t = 0, all the inputs flip (i.e. A = C = and B = 0) and emain in that state. Fo t > 0, output Z = fo a duation (in ns) of A B Z C Ans. (0) 54. In the given cicuit, the maximum powe (in Watts) that can be tansfeed to the load L is 40 V ms j L Ans A souce emits bit 0 with pobability 3 and bit with h[n] is eal fo all n h[n] is puely imaginay fo all n (c) h[n] is eal fo only even n h[n] is puely imaginay fo only odd n Q.5 Two sequences [a, b, c] and [A, B, C] ae elated as, A a B W3 W 3 b 4 C W3 W 3 c If anothe sequence [p, q, ] is deived as, pobability. The emitted bits ae communicated to the 3 eceive. The eceive decides fo eithe 0 o based on the eceived value. It is given that the conditional density functions of as, 3 x, x 5 f() 0 4 and f() 0 6 0, othewise 0, othewise The minimum decision eo pobability is 0 (c) 9 Ans. (*) All ight eseved. ECT Publications. Mob

Q. 1 Q. 25 carry one mark each.

Q. 1 Q. 25 carry one mark each. Q. Q. 5 carry one mark each. Q. Consider a system of linear equations: x y 3z =, x 3y 4z =, and x 4y 6 z = k. The value of k for which the system has infinitely many solutions is. Q. A function 3 = is