EC-GATE-2015 PAPER-02 General Aptitude. Q. No. 1 5 Carry One Mark Each

Transcription

1 EC-GATE-5 PAPER- General Aptitude Q. No. 5 Carry One Mark Each. What is the adverb for the given word below? Misogynous (A) Misogynousness (B) Misogynity (C) Misogynously (D) Misogynous Answer: (C). Choose the appropriate word phrase out of the four options given below, to complete the following sentence Dhoni, as well as the other ream members of Indian team present on the occasion (A) Were (B) Was (C) Has (D) Have Answer: (A) 3. Ram and Ramesh appeared in an interview for two vacancies in the same department. The probability of Ram s selection is /6 and that of Ramesh is /8. What is the probability that only one of them will be selected? (A) 47/48 (B) /4 (C) 3/48 (D) 35/48 Answer: (B) Exp: PRam ; pramesh ponly at pram pnot ramesh pramesh pn Ram Choose he word most similar in meaning to the given word: Awkward (A) Inept (B) Graceful (C) Suitable (D) Dreadful Answer: (A) 5. An electric bus has onboard instruments that report the total electricity consumed since the start of the trip as well as the total distance covered. During a single day of operation, the bus travels on stretches M, N, O and P, in that order. The cumulative distances traveled and the corresponding electricity consumption are shown in the Table below Stretch Cumulative distance (km) Electricity used (kwh) M N 45 5 O P 57 The stretch where the electricity consumption per km is minimum is (A) M (B) N (C) O (D) P

2 EC-GATE-5 PAPER- Answer: (B) Exp: For M 6 N O P Q. No. 6 Carry Two Marks Each 6. Given below are two statements followed by two conclusions. Assuming these statements to be true, decide which one logically follows. Answer: Statements: I. All film stars are playback singers. II. All film directors are film stars Conclusions: I. All film directors are playback singers. II. Some film stars are film directors. (A) Only conclusion I follows (C) Neither conclusion I nor II follows (D) (B) Only conclusion II follows (D) Both conclusions I and II follow 7. Lamenting the gradual sidelining of the arts ill school curricula, a group of prominent artists wrote to the Chief Minister last year, asking him to allocate rnore funds to support arts education in schools. However, no such increase has been announced in this year s Budget. The artists expressed their deep anguish at their request not being approved, but many of them remain optimistic about funding in the future Answer: Which of the staternent(s) below is/are logically valid and can be inferred from the above statements? (i) The artists expected funding for the arts to increase this year (ii) The Chief Minister was receptive to the idea of increasing funding for the arts (iii) The Chief Minister is a prominent artist (iv) Schools are giving less importance to arts education nowadays (A) (iii) and (iv) (B) (i) and (iv) (C) (i), (ii) and (iv) (D) (i) and (iii) (C) 8. A tiger is 5 leaps of its own behind a deer. The tiger takes 5 leaps per minute to the deer s 4. If the tiger and the deer cover 8 metre and 5 metre per leap respectively. What distance in metres will be tiger have to run before it catches the deer?

3 EC-GATE-5 PAPER- Answer: 8 Exp: Tiger leap 8 meter Speed 5leap hr 4m min Deer leap 5meter speed 4hr m min Let at time t the tiger catches the deer. Distance travelled by deer + initial distance between them 58 4m = distance covered by tiger. 4 t 4 t 4 t min total dis tance 4 t 8 ms 9. If a b c, then ab bc ac lies in the interval (A) [, /3] (B) [ /, ] (C) [, /] (D) [, 4] Answer: (B). In the following sentence certain parts are underlined and marked P, Q and R. One of the parts may contain certain error or may not be acceptable in standard written communication. Select the part containing an error. Choose D as your answer if there is no error. The student corrected all the errors that the instructor marked on the answer book P Q R (A) P (B) Q (C) R (D) No error Answer: (B) Exp: The is not required in Q Electronics and Communication Engineering Q. No. 5 Carry One Mark Each. Let the signal f t outside the interval T,T, where T and T are finite. Furthermore, ft. The region of convergence (RoC) of the signal s bilateral Laplace transform F(s) Answer: Exp: is. A parallel strip containing the j axis. A parallel strip not containing the j axis 3. The entire s plane 4. A half plane containing the j axis (A) (B) (C) 3 (D) 4 (C) For a finite duration time domain signal ROC is entire s-plane. 3

4 EC-GATE-5 PAPER- A unity negative feedback system has an open loop transfer function Gs gain K for the system to have a damping ratio of.5 is Answer: 4 k Exp: G(s) s s CLTF k s s k.5 k n n k.5 k k.5 k () k 4 K s s. The 3. A mod n counter using a synchronous binary up counter with synchronous clear input is shown in the figure. The value of n is CLOCK 4 Bit Binary Counter CLK CLEAR Q A Q B Q C Q D Q A Q B Q C Q D Answer: 6 Exp: To find the modulus of the counter, consider the status of the inputs (Q B, Q C ) as. Q Q Q Q So, A B C D So, it is a MOD-6 counter 4. By performing cascading and/or summing/differencing operations using transfer function G s and G s, one CANNOT realize a transfer function of the form Answer: blocks (A) GsGs (B) (C) Gs Gs G s (B) G G s s (D) Gs Gs G s 4

5 Mobility (cm. V -. s - ) EC-GATE-5 PAPER The electric field of a uniform plane electromagnetic wave is 7 E ax j4a yexp j t.z The polarization of the wave is (A) Right handed circular (B) Right handed elliptical (C) Left handed circular (D) Left handed elliptical Answer: (D) E a 4ja e Exp: x y E cost z y 7 j t.z E 4cos 4sin t So, it left hand elliptical polrization. 6. A piece of silicon is doped uniformly with phosphorous with a doping concentration of 6 3 / cm. The expected value of mobility versus doping concentration for silicon assuming 9 full dopant ionization is shown below. The charge of an electron is.6 C. The conductivity in S cm of the silicon sample at 3 K is Hole and Electron Mobility in Silicon at 3 K 7 4 Electron Hole Answer:.9 Exp: E 3.E 4.E 5.E 6.E 7.E 8.E 9.E As per the graph mobility of electrons at the concentration 6 /cm 3 is cm So, n V s N q N D n S cm Doping concentration cm 3 cm V s 5

6 EC-GATE-5 PAPER In the figure shown, the output Y is required to be Y AB CD. The gates G and G must be, respectively, Answer: (A) NOR, OR (B) OR, NAND (C) NAND, OR (D) AND, NAND (A) A B C D Exp: Given expression is Y AB CD The first term can be obtained by considering G as NOR gate, and second term CD is obtained from another lower NOR-Gate. So, final expression can be implemented by considering G as OR-Gate. G G Y 8. In the bistable circuit shown, the ideal opamp has saturation level of 5V. The value of R in k that gives a hysteresis width of 5 mv is. R k R v in v out Answer: Exp: V L VTL VTH V I L 6

7 EC-GATE-5 PAPER- Hysteresis V V TH R R L L R R R R 5mV ( 5) 5 k k R k TL R 5 k 3 3 n 9. Two causal discrete time signal xnand yn are related as yn xm It the z transform of yn is zz Answer: n Exp: yn xm m According to accumulation property of z-transform Y z z 3 z z, the value of x is X z z X z z z z z X z z x n u n3 thus x m. The bilateral Laplace transform of a function ft (A) a b (B) s Answer: (C) Exp: Given ft e a b a t b otherwise st L f t e f t dt s (C) if a t b otherwise e as e s bs a st st st e f t e f t dt e f t dt a b (D) e sab s 7

8 EC-GATE-5 PAPER- b st e dt a st e b e bs e as s a s e as e s bs. The port admittance matrix of the circuit shown is given by (A)..3 (B) (C) (D).4.3 Answer: Exp: Correct answer not given in options The value of x for which all the eigen values of the matrix given below are real is 5 j 4 x 4 (A) 5 + j (B) 5 j (C) 5j (D) + 5 j Answer: (B) 5J 4 Exp: Let A x 4 Given that all eigen values of A are real. A is Hermitian T A A ie. A A x 4 5 j 4 5 j x x5 j 4 4 8

9 EC-GATE-5 PAPER The signal cos t is ideally sampled at a sampling frequency of 5 Hz. The sampled 4 signal is passed through a filter with impulse response output is (A) 5 cos4 t 4 (C) 5 cos t 4 (B) (D) sin t cos 4 t. The filter t 5 sin t cos t t 4 5 sin t cos 4 t t Answer: (A) Exp: Given signal is x t cos t 4 Neglect the phase-shift and it can be inserted at the end result. 4 L If xt cos t Xf f 5 f 5 Given filter impulse response is, sin t h t cos 4t t sin c t sin 4t Hf rect f * f f j rect f rect f j X f repeats with a value fo 5Hz and each impulse value is 5 Thus the sampled signal spectrum and the spectrum of the filter are as follows: Xs f 5 / f H(f Hf 9

10 5 Xs f Hf f f 4j 5 xr t sin 4t recovered signal 5 = cos 4 t Insert the neglected phase shift xr t cos 4t cos 4t 4 4 EC-GATE-5 PAPER A sinusoidal signal of amplitude A is quantized by a uniform quantizer Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 3.8 db, the number of levels in the quantizer is Answer: 3 Exp: Signal power A A Quantization step size, L Quantization noise power 4A A L 3L 3 Signal to quantiation noise ratio L Given signal to quantization noise ratio 3.8dB or L L The magnitude and phase of the complex Fourier series coefficients a k of a periodic signal x(t) are shown in the figure. Choose the correct statement form the four chices given. Notation: C is the set of complex numbers, R is the set of purely real numbers, and P is the set purely imaginary numbers. (A) x t R (B) xt P (C) xtc R (D) The information given is not sufficient to draw any conclusion about x(t) 3 a k a k k k

11 EC-GATE-5 PAPER- Answer: (A) Exp: a k only changes the sign of the magnitude a k. Since the magnitude spectrum a k is even the corresponding time-domain signal is real. 6. The general solution of the differential equation dy cosy is dx cos x tan x cot y c c is a constan t (A) tan y cot x cc is a constan t (B) (C) tan y cot x cc is a constan t (D) tan x coty cc is a constan t Answer: (D) dy cos y Exp: Given dx cos x dy dx cos y cos x dy dx sin y cos x cosec ydy cot y tan x k tan x cot yk sec x dx tan x cot y c where c k Variable - Separable 7. An n type silicon sample is uniformly illuminated with light which generates electron hole pairs per cm 3 per second. The minority carrier lifetime in the sample is s. Int eh steady state, the hole concentration in the sample is approximately The value of x is Answer: 4 Exp: The concentration of hole-electron pair in sec cm So, the power of is 4. x 4 x, where x is an integer. 8. If the circuit shown has to function as a clamping circuit, which one of the following conditions should be satisfied for sinusoidal signal of period T? C v R (A) RC<<T (B) RC =.35T (C) RC T (D) RC >> T Answer: (D)

12 EC-GATE-5 PAPER In a source free region in vacuum, if the electrostatic potential constant c must be Answer: 3 Exp: x y cz E 4xa ya cza.e 4 c c 3 x y z x y cz, the value of. In an 885 microprocessor, which one of the following instructions changes the content of the accumulator? Answer: Exp: (A) MOV B, M (B) PCHL (C) RNZ (D) SBI BEH (D) Generally arithmetic or logical instructions update the data of accumulator and flags. So, in the given option only SBT BE H is arithmetic instruction. SBI BEH Add the content of accumulator with immediate data BE H and store the result in accumulator.. The voltage V C across the capacitor (in Volts) in the network shown is 8V 4V Vc Answer: Exp: V V V V R c L () (8) Vc 4 c c c c c c V 4 (8)() V 4 9 V 4 6 V 6 4 V 6 4 V V V, 5 H z

13 EC-GATE-5 PAPER- az b f z. If f z f z for all z z,a,b 4 and c 5, cz d equal to.. Let Answer: az b f z if f z f z, for z z cz d Exp: a, b 4, c5 f z z 4 5z d f z f z z4 z4 5z d 5z d z z z dz 4d z z z dz 4d z z d z z d then d should be 3. In the circuit shown the average value of the voltage V ab (in Volts) in steady state condition is. 5sin 5t k b F V ab a mh k 5V Answer: 5 4. For the signal flow graph shown in the figure, the value of Cs R s is H 3 X Rs G X3 4 G X G3 X5 G4 X Cs H H 3

14 EC-GATE-5 PAPER- G G G G G G H G G H G G H G G G G H H (A) G G G G G G H G G H G G H G G G G H H (B) (C) GG H G3G4H GG3H3 GG G3G4HH (D) GG H G3G4H GG3H3 GG G3G4HH Answer: (B) Exp: Using mason gain formula we get it directly. 5. In the circuit shown, V VA for switch SW in position A and V VB for SW in position VB B. Assume that the opamp is ideal. The value of is V A k 5V k B A k SW k V V k Answer:.5 k Exp: VOB 5 k k 6V k k VOA 5 4V V V k k V V OB OA.5 4

15 EC-GATE-5 PAPER- Q. No carry Two Marks Each 6. Let X, and Y, be two independent binary random variables. If P (X = ) = p and P(Y = ) = q, then PX Y is equal to Answer: (A) pq p q (B) pq (C) p q (D) (D) pq Exp: P x P P x p P y q P y q Let Z X Y X Y Z From above table, PX and Y P X Y Z P Z B P Z P X and Y P X and Y P X and Y pq 7. An LC tank circuit consists of an ideal capacitor C connected in parallel with a coil of inductance L having an internal resistance R. The resonant frequency of the tank circuit is Answer: Exp: (A) LC L (C) RC LC (D) Y Y Y c LR R jl Y jc jc jl R R L (B) (D) Placing Imaginary part to zero we get option (D). C R LC L C R LC L C L R 5

16 EC-GATE-5 PAPER X n n n is an independent and identically distributed (i,i,d,) random process with n equally likely to be n Yn Xn.5Xn or. Y is another random process obtained as n n. The autocorrelation function of Y n n n denoted by RY k is X (A) RY k (B) RY k k 3 3 k (C) RY k (D) k RY k k Answer: (B) Exp: R Yk R yn, n k E Yn.Y n k Yn xn.5xn y E x n.x n k x n.5 x n k.5 x n.x n k.5x n x n k E xn.x n k.5e x nx n k.5e xn x n k R k E x n.5x n x n k.5x n k.5e x n x n k R X k.5r x k.5r x k.5r x k.5r x k R k.5r k.5r k y x x R x k E x n.x n k 6

17 if k, R x E x n. if k, R x k E x n.e x n k E x n E x n k R.5R.5R.5R y x x x.5 EC-GATE-5 PAPER- R.5R.5R.5R y x x x.5 R.5R.5R.5R y x x x.5 Ry k for k other than, and = Ry k k 9. In a MOS capacitor with an oxide layer thickness of nm, the maximum depletion layer thickness is nm. The permittivities of the semiconductor and the oxide layer are s and ox respectively. Assuming s / ox 3, the ratio of the maximum capacitance to the minimum capacitance of this MOS capacitor is Answer: 4.33 Exp: ox Cmax tox Xdmax ox 4.33 C min ox s tox s 3 tox Xdmax ox s t X ox dmax 7

18 EC-GATE-5 PAPER Let the random variable X represent the number of times a fair coin needs to be tossed till two consecutive heads appear for the first time. The expectation of X is Answer:.5 Exp: Let x be a random variable which denotes number of tosses to get two heads. Px HH Px3 THH Px4 TTHH... Ex In the circuit shown, the Norton equivalent resistance in across terminals a b is. a 4I 4 Answer:.333 Exp: a Vth 4I Vth Vth 4 Also V 4I th 4 Vth 3 4 R th I 8 V th I b 4 I b a V th R th A V th

19 EC-GATE-5 PAPER The figure shows a binary counter with synchronous clear input. With the decoding logic shown, the counter works as a Binary Counter Q 3 Q CLK Q CLEAR Q Answer: (A) mod counter (B) mod 4 counter (C) mod 5 counter (D) mod 6 counter (B) Exp: Q3 Q Q Q Once the output of Ex-NOR gate is then counter will be RESET. So, Ex-NOR-gate will produce logic for Q 3 =, Q =. So, the counter will show the sequence like: 3 So, it is MOD-4 counter. 33. In the ac equivalent circuit shown, the two BJTs are bbiased in active region and have identical parameters with. The open circuit small signal voltage gain is approximately v out v in 9

20 EC-GATE-5 PAPER- Answer: - Exp: V out V in When Base and collector is shorted, it act as a diode. So V.7V. V.7V V.7V Gain, in 34. The state variable representation of a system is given as x x; x y x The response y(t) is (A) sin(t) Answer: (D) Exp: X AX X(s) si A X() s X(s) s X(s) s xt y(t) [ ] (B) (C) cost t e (D)

21 EC-GATE-5 PAPER Consider the differential equation Answer: response (A) xtfor t is e.t (B) (C) Exp: Given dx.x dt.t e (C) D.E dx.x dt x dx. x dt Auxiliary equation is m. Complementary solution Given m.. t x x c p C e. t t 5e 5. t x xc xp C e 5 with initial condition t e e D.. x C 5 C49 x 549 e 5 49e.t (D) t.t 5 49e x. The 36. For the voltage regulator circuit shown, the input voltage Vin is V % and the regulated output volage V out is V. Assume the opamp to be ideal. For a load R L drawing ma, the maximum power dissipation in Q (in Watts) is. Answer:.856 Exp: PQ (max) VCE(max) Icmax.(i) CE(max) V 4 V 4V I (.4)mA cmax I I ma.4ma E c 4.4mA IR IR ma Put values in Equation (), we get 3 PQ (max) 4.4 Watt.856 Watt V in V ref ref 4V Q R R k R L V out

22 EC-GATE-5 PAPER Input x(t) and output y(t) of an LTI system are related by the differential equation y" t y' t 6yt xt. If the system is neither causal nor stable, the impulse response h(t) of the system is t t 3t t (A) e ut e u t (B) e ut e u t t t 3t t (C) e ut e ut (D) e ut e ut Answer: Exp: (B) The given differential equation is, y" t y' t 6yt xt On applying Laplace transform on both sides, s y s sy y s y s y 6y s x s To calculate the transfer function all initial conditions are taken as. s s 6 ys x s Hs s3 s 5 s3 s s s 6 It is given that h(t) is non-casual and un-stable. To satisfy both the conditions ROC should be left of the left most pole. Using the following standard pair sa sa Hs at e u t ; a at e u t ; a 5 s3 s 3t t e u t e u t 5 3t t e u t e u t 5 5 So option (B) is correct.

23 EC-GATE-5 PAPER The diode in the circuit given below has VON.7V but is ideal otherwise. The current (in ma) in the 4k resistor is. k D k 3k ma 4k 6k Answer:.6 N 39. A zero mean white Gaussian noise having power spectral density is passed through an LTI filter whose impulse response h(t) is shown in the figure. The variance of the filtered noise at t = 4 is A ht 3 t A (A) 3 AN (A) (B) 3 AN 4 Answer: Exp: Let N(t) be the noise at the output of filter. Variance of N t E N t E N Since the input noise is zero mean, Output noise mean is also zero. ENt EWt. h tdt E W t W t is white noise R var N t E N t N (C) AN (D) AN 3

24 Since R h * h * R N N N R N h * h. o Since R N. No R N h k.h kdk No No R N h k dk 3A EC-GATE-5 PAPER- o 3.A.N o 4. Assuming that the opamp in the circuit shown below is ideal, the output voltage V (in volts) is k k V V o Answer: 3 Exp: V k V k V V o V V k k V 3V V 4

25 EC-GATE-5 PAPER A to 8 demultiplexer with data input D in, address inputs S,S,S (with S as the LSB) and Y to Y 7 as the eight demultiplexed output, is to be designed using two to 4 decoders (with enable input E and address input A and A ) as shown in the figure D in, S,S and S are to be connected to P, Q, R and S, but not necessarily in this order. The respective input connections to P, Q, R and S terminals should be P Q R S E A A to4 Decoder Y o Y Y Y 3 Y o Y Y Y 3 A A7 to4 Decoder Y o Y Y Y 3 Y 4 Y 5 Y 6 Y 7 Answer: Exp: (A) S,D in,s,s (B) S,D in,s,s (C) D in,s,s,s (D) D in,s,s,s (D) We need to implement : 8 DEMUX Select lines of DEMUX should be mapped to address lines of decoder. So, LSB of DEMUX should be connected to LSB of address lines of decoder. R S S S Input to both the decoder should be same so P D in NOT gate along with OR gate in case to select one decoder at a time so Q S. P D Q S in R S S S a D in S S S Y Y Y 7 5

26 4 t EC-GATE-5 PAPER- sin 4t 4. The value of the integral cos t dt is 4t Answer: 3 sin 4 t Exp: cos t dt 4 t cos t sin 4t dt 3 sin 6t dt sin t dt sin A cos B sin AB sin AB t t 3 t 6sin 6 t t sin t e dt e dt t t 3 sin 6t sin t L L with s t t 3 6 ds ds with s s s s 36 s 4 3 s s 6 6 s 6. tan. tan with s 3 s s tan tan tan tan 6 3 tan tan A function of Boolean variables X, Y and Z is expressed in terms of the min terms as F X,Y, Z,,5,6,7 Answer: Which one of the product of sums given below is equal to the function FX,Y,Z? (A) X Y Z. X Y Z. X Y Z (B) 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 (D) X Y Z. X Y Z. X Y Z. X Y Z. X Y Z (B) Exp: Given minterm is:fx,y,z,,5,6,7 So, maxterm is :FX,Y,Z M,3,4 POS X Y Z X Y Z X Y Z 6

27 EC-GATE-5 PAPER The transfer function of a mass spring damper system is given by Gs Ms Bs K The frequency response data for the system are given in the following table. in rad/s G j in db arg G j in deg The unit step response of the system approaches a steady state value of Answer:. 45. Two half wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz and phase shift of /between them (the element at the origin leads in phase). If the maximum radiated E field at the point P in the x y plane o. occurs at an azimuthal angle of 6 the distance d (in meters) between the antennas is. z d O 6 y OP d Answer: 5 x Exp: = δ+βdcosθ For maximum field, = δ+βdcosθ = dcos6 d d 5m m 6 7

28 EC-GATE-5 PAPER An air filled rectangular waveguide of internal dimensions a cmbcma b has a cutoff frequency of 6 GHz for the dominant TE mode. For the same waveguide, if the cutoff frequency of the TM mode is 5 GHz, the cutoff frequency of the TE mode in GHz is. Answer: 3.7 Exp: TE f f c c 6GHz 8 m n a b a 4 TM a b 9.65 b TE c 8 3 f c. b f 3.7 GHz 47. Consider two real sequences with time origin marked by the bold value x n,,3,, x n,3,, Let Xk and Xk be 4 point DFTs of xn and x Another sequence The value of Answer: x3 n, respectively x3 n is derived by taking 4 point inverse DFT of x3 k x kx k is Exp: xn,,3,, xn,3,, X k X k X k 3 Based on the properties of DFT, x n x n X k X k x n 3 Circular convolution between two 4-point signals is as follows: x 3. 8

29 4t 48. Let xt ast s t with st e ut, where ut EC-GATE-5 PAPER- is unit step function. If the bilateral Lapalce transform of x(t) is 6 X s 4 Re s 4 Answer: - s 6 Then the value of is 4t Exp: x t st st & st e u t 4t 4t x t e u t e u t 4t L e u t s 4 s 4 4t L e u t B Xs s4 s4 s4s4 6 ; 4 4 s 6 s 6 On solving the numerator 49. Consider a binary, digital communication system which used pulses gt and gt for transmitting bits over an AWGN channel. If the receiver uses a matched filter, which one of the following pulses will give the minimum probability of bit error? (A) gt (B) gt t t (C) gt (D) gt t t 9

30 EC-GATE-5 PAPER- Answer: (A) Exp: Optimum receiver for AWGN channel is given by matched filter. In case of matched filter receiver, E Probability of error Q N u Probability of error is minimum for which E is maximum. Now looking at options Energy in option A Energy in option (C) and (D) is same = /3 t dt Energy in option (B) 4t dt 3 t Thus option (A) is correct answer. 5. The electric field of a plane wave propagating in a lossless non magnetic medium is given by the following expression Answer: 9 9 Ez,t a x5cos t z a y3cos t z The type of the polarization is (A) Right Hand Circular. (C) Right Hand Elliptical (B) Exp: E 5cost z x Ey 3cost z But the wave is propagating along negative z-direction So, Left hand elliptical (LED). (B) Left Hand Elliptical (D) Linear 3

31 EC-GATE-5 PAPER The energy band diagram and electron density profile n(x) in a semiconductor are shown in the figure. Assume that qx cm 3 5 kt Gvien kt D kt.6v, Dn 36cm s, and q q at x = is EeV n x e, with.v / cm and x expressed in cm. Slope.eV/cm. The electron current density in A / cm log n x Ec Ev x x x x (A) 4.4 (B). (C) (D). Answer: (B) OR (D) dn x Exp: Jn,diff qdn () dx x Given : n x e qax 5 kt qax 5 qa kt d n x e dx kt d n x 5. dx.6 n cm 9 5 J, diff A cm 5. A dc voltage of V is applied across an n type silicon bar having a rectangular cross section and a length of cm as shown in figure. The donor doping concentration N and the mobility of electrons D 6 3 n are cm and cm V s, respectively. The average time in s taken by the electrons to move from one end of the bar to other end is. V n Si cm 3

32 EC-GATE-5 PAPER- Answer: Exp: V V m d v cm s d L L v T s d 4 T Vd In the circuit shown, the initial voltages across the capacitors C and C are V and 3V, respectively. The switch is closed at time t =. The total energy dissipated (in Joules) in the resistor R until steady state is reached is t R C 3F C F Answer:.5 Exp: 3 s s I(s) 3 3s 3s I(s) 4 4 s s t 3 i(t) e ; t 5 E R i (t)dt 5 e 4 t 5 4 t 5 e dt s 3s I(s) 3 s s J 3

33 EC-GATE-5 PAPER The output of a standard second order system for a unit step input is given as t yt e cos 3t. The transfer function of the system is 3 6 (A) s s (B) (C) (D) s s s s 3 s s 4 Answer: (D) Exp: Here n n If C denotes the counterclockwise unit circle, the value of the contour integral Rezdz j is. C Answer:.5 Exp: J e Re z dz where C is z j j Put z e d je d j j j Re e je d cos. jcos jsin d j j cos d cos sin d j j j 33