General Aptitude. Q. No. 1 5 Carry One Mark Each

Transcription

1 EC GATE-05-PAPER-03 General Aptitude Q. No. 5 Carry One Mark Each. An apple costs Rs. 0. An onion costs Rs. 8. Select the most suitable sentence with respect to grammar and usage. (A) The price of an apple is greater than an onion. (B) The price of an apple is more than onion. The price of an apple is greater than that of an onion. (D) Apples are more costlier than onions.. The Buddha said, Holding on to anger is like grasping a hot coal with the intent of throwing it at someone else; you are the one who gets burnt. Select the word below which is closest in meaning to the word underlined above. (A) burning (B) igniting clutching (D) flinging 3. M has a son Q and a daughter R. He has no other children. E is the mother of P and daughter-in-law of M. How is P related to M? (A) P is the son-in-law of M. (B) P is the grandchild of M. P is the daughter-in law of M. (D) P is the grandfather of M. (B) 4. The number that least fits this set: (34, 44, 97 and 64) is. (A) 34 (B) (D) ;44 ;64 8 but i.e. 97 is odd man out 97 x for any positive integer 5. It takes 0 s and 5 s, respectively, for two trains travelling at different constant speeds to completely pass a telegraph post. The length of the first train is 0 m and that of the second train is 50 m. The magnitude of the difference in the speeds of the two trains (in m/s) is. (A).0 (B) (D).0 (A) Speed length length speed time time 0 0s s 50 5s s 0 s s ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

2 EC GATE-05-PAPER-03 Q. No. 6 0 Carry Two Marks Each 6. The velocity V of a vehicle along a straight line is measured in m/s and plotted as shown with respect to time in seconds. At the end of the 7 seconds, how much will the odometer reading increase by (in m)? (A) 0 (B) 3 4 (D) 5 (B) At the end of 7 seconds, the odometer reading increase by 7 t0 V.dt V V V V V V V V meters 7. The overwhelming number of people infected with rabies in India has been flagged by the World Health Organization as a source of concern. It is estimated that inoculating 70% of pets and stray dogs against rabies can lead to a significant reduction in the number of people infected with rabies. Which of the following can be logically inferred from the above sentences? (A) The number of people in India infected with rabies is high. (B) The number of people in other parts of the world who are infected with rabies is low. Rabies can be eradicated in India by vaccinating 70% of stray dogs (D) Stray dogs are the main sources of rabies worldwide. (A) 8. A flat is shared by four first year undergraduate students. They agreed to allow the oldest of them to enjoy some extra space in the flat. Manu is two months older than Sravan, who is three months younger than Trideep. Pavan is one month older than Sravan. Who should occupy the extra space in the flat? (A) Manu (B) Sravan Trideep (D) Pavan ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

3 EC GATE-05-PAPER Find the area bounded by the lines 3x+y=4, x-3y=5 in the first quadrant. (A) 4.95 (B) (D) 0.35 Exp (B) 4 A,0 3 B 0, 7 5 C, 0 5 D 0, 3 E 4, Required area is area of OAB area of CEA sq.units 3 6 B D O y R 3x y 4 C E A x 3y 5 x 0. A straight line is fit to a data set (ln x, y). This line intercepts the abscissa at ln x = 0. and has a slope of 0.0. What is the value of y at x = 5 from the fit? (A) (B) (D) (A) a y a bx, where x ln x and 0., b 0.0 b a 0.0 x a x at x 5, y Electronics and Communication Engineering Q. No. 5 Carry One Mark Each. x Consider a square matrix A, Where x is unknown. If the eigenvalues of the matrix A are jand j, the x is equal to (A) j (B) j (D) (D) Product of eigen values = det j j x x x ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3 33/3

4 . For EC GATE-05-PAPER-03 sin z f z, the residue of the pole at z = 0 is. z 3 5 sin z z z z z f z z z z 3! 5! z 3! 5! Resideu coefficient of z 3. The probability of getting a head in a single toss of a biased coin is 0.3. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting head for the first time in the fifth toss is Required probability = TTTTH The integral dx x is equal to. 0 x x x dx x Consider the first order initial value problem 3 y' y x x, y 0, 0 x x with exact solution yx x e. For x = 0., the percentage difference between the exact solution and the solution obtained using a single iteration of the second-order Runge-Kutta method with stepsize h = 0.is 5. y0 0 x Given y f x,y y x x, By nd order R K method y y k k where 0 k hf x, y 0.f 0, h k k h.f x 0, y f 0, 0.f 0.05, ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4 44/4

5 EC GATE-05-PAPER-03 y Exact solution, 0. y e.57 % difference % Consider the signal x t cos6t sin 8 t, where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(t+5) is (A) 8 (B) 6 (D) 3 Shifting doesn t effects the sampling rate due to scaling by a factor spectral components are doubled. X(f ) Thus maximum frequency of Y(f) 8. Nyquist rate 8 6Hz 7. If the signal (A) (A) sin t t sin t sa t t sa t sin t sin t x t * t t with * denoting the convolution operation, then x(t) is equal to F sa t rect (B) F rect sin t t sin t t Convolution in time domain leads to multiplication in frequency domain sin t rect rect X xt sa t t sin t (D) t ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5 55/5

6 EC GATE-05-PAPER A discrete-time signal xn n 3 n 5 has z-transform X(z). If Y(z) = X(-z) is the z- transform of another signal y[n], then (A) y[n] = x[n] (B) y[n] = x[-n] y[n] = -x[n] (D) y[n] = -x[-n] xn n 3 n x z z z yn n 3 n 5 yn xn x z z y z z z 9. In the RLC circuit shown in the figure, the input voltage is given by i t cos 00t 4sin 500t The output voltage 0 t is Key (A) cos (00t) + sin (500t) (B) cos (00t) + 4sin (500t) sin (00t) + cos (500t) (D) sin (00t) + 4cos (500t) (B) V i (t) = cos 00t + 4 sin 500t, since there are frequency term output will also have frequency term. If we take 4sin500t first i.e. W = 500 then on the output section, this parallel LC combination have Z, so it is open circuit and V 0 = V i LC j00 j00 So w.r.t. 4sin500t output must be 4sin500t without any change in amplitude and phase, this is satisfied by only option B. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6 66/6

7 EC GATE-05-PAPER The I-V characteristics of three types of diodes at the room temperature, made of semiconductors X, Y and Z, are shown in the figure. Assume that the diodes are uniformly doped and identical in all respects except their materials. If EgX, EgY and EgZ are the band gaps of X, Y and Z, respectively, then I X Y Z V (A) EgX > EgY > EgZ EgX < EgY < EgZ (B) EgX = EgY = EgZ (D) no relationship among these band gaps exists. The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in (A) inversion (B) accumulation depletion (D) flat band (A) The semiconductor used in the MOSFET is n-type. At the surface the intrinsic level is above E F as it is found at the distance of below E F, So, the surface is in inversion region.. The figure shows the I-V characteristics of a solar cell illuminated uniformly with solar light of power 00 mw/cm. The solar cell has an area of 3 cm and a fill factor of 0.7. The maximum efficiency (in %) of the device is. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7 77/7

8 EC GATE-05-PAPER-03 FF.V I P (00 3) oc sc Efficiency 00% in = %. 3. The diodes D and D in the figure are ideal and the capacitors are identical. The product RC is very large compared to the time period of the ac voltage. Assuming that the diodes do not breakdown in the reverse bias, the output voltage V 0 (in volt) at the steady state is 0 Vo 0volts 0V 0V Vo 0V 4. Consider the circuit shown in the figure. Assuming V BE = V EB = 0.7 volt, the value of the dc voltage V C (in volt) is 0.5 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8 88/8

9 VE.5 VBE.8V V V 0.7.V I I B E B C 0. 0k EC GATE-05-PAPER A A 4 3 VC V 5. In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in khz) at the output pin 3 is f 5.64kHz R R C [ ] A B 6. In an 8085 microprocessor, the contents of the accumulator and the carry flag are A7 (in hex) and 0, respectively. If the instruction RLC is executed, then the contents of the accumulator (in hex) and the carry flag, respectively, will be (A) 4E and 0 (B) 4E and 4F and 0 (D) 4F and (D) Accumulator CY ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9 99/9

10 EC GATE-05-PAPER-03 RLCRotate left accumulator content without carry CY Accumulator FH 7. The logic functionality realized by the circuit shown below is (A) OR (B) XOR NAND (D) AND (D) All the transistor are n-mos we know when input to gate is 0 n mos behave as open circuit. Input to Gate is n mos is short circuit. we can redraw the circuit as A B T Y B T to get the functionality get find its truth table A B T T Y 0 0 OFF ON 0 0 ON OFF A 0 0 OFF ON 0 ON OFF A So, Y satisfy AND gate table. 8. The minimum number of -input NAND gates required to implement a -input XOR gate is (A) 4 (B) 5 6 (D) 7 (A) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 0 00/

11 EC GATE-05-PAPER-03 A B Y AB AB AB 9. The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is GG GG (A) G (B) G G H G G G H GG GG G (D) G G G H G G G G H (B) G G G G H H Y GG x G H G G 0. For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as Gs s s ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

12 EC GATE-05-PAPER-03 The steady state error ess due to a unit step input is (A) 0 (B) (D) (A) For unit step input ess. k kp limg(s) lim s0 s0 s(s ) So, ess 0 p. For a superheterodyne receiver, the intermediate frequency is 5 MHz and the local oscillator frequency is 3.5 GHz. If the frequency of the received signal is greater than the local oscillator frequency, then the image frequency (in MHz) is f image =? f S = f L0 (fsi - f L0) f Si = Image freq f L0= Signal freq f S - f L0 f Si + fl0 fsi fl0 fs f S fl0 ff fsi fl0 ff fl0 fl0 ff =3485 mhz. An analog baseband signal, band limited to 00 Hz, is sampled at the Nyquist rate. The samples are quantized into four message symbols that occur independently with probabilities p = p 4 = 0.5 and p = p 3. The information rate (bits/sec) of the message source is 3.9 Information rate = rh ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

13 EC GATE-05-PAPER-03 H bits symbol r symbols sec If we assume each sample is mapped to symbol Then r = 00 MHz P P P 4 3 P P 8 3 P P H log8 log I.R 3.9 Mbps 3. A binary baseband digital communication system employs the signal p t, 0 t T T S S 0, otherwise for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be (A) (B) (D) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3 33/

14 EC GATE-05-PAPER-03 P(t) h(t) y(t) h(t) = P(t S-t) T S 0 T S t 4. If a right-handed circularly polarized wave is incident normally on a plane perfect conductor, then the reflected wave will be (A) right-handed circularly polarized elliptically polarized with a tilt angle of 45 0 (B) 0 T S (B) left-handed circularly polarized (D) horizontally polarized If incident wave is right handed polarized then the reflected wave is left handed polarized. 5. Faraday s law of electromagnetic induction is mathematically described by which one of the following equations? B D (A).B 0 (B).D V E (D) H E t t Q. No carry Two Marks Each 6. The particular solution of the initial value problem given below is d y dy dy dx dx dx x 0 36y 0 with y 0 3 and 36 6x (A) 3 8xe 6x (B) 3 5xe 6x 3 0xe 6x (D) 3 xe (A) D D 36 0 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4 44/

15 D 6, 6 y0 3 EC GATE-05-PAPER-03 C.F C C x e 6x 6x 6x y C C x e 3C 6x dy 6x Ce C Cx e 6 dx dy 36 dx x0 36 C C 8 y 3 8x e 7. If the vectors e = (, 0, ), e = (0,, 0) and e 3 = (, 0, ) form an orthogonal basis of the threedimensional real space R 3 3, then the vector u 4,3, 3 R can be expressed as u e 3e e (B) u e 3e e (A) 3 u e 3e e (D) u e 3e e (D) From option (D), u e 3e e ,3, 3,0, 30,,0,0, 8. A triangle in the xy-plane is bounded by the straight lines x = 3y, y = 0 and x = 3. The volume above the triangle and under the plane x + y + z = 6 is 0 Volume = R z dx dy y x 3y B R x b O A x x limits : 0 to 3 y limits: 0 to x 3 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5 55/

16 3 x 3 y0 x0 EC GATE-05-PAPER x y dy dx 3 x 3 y 6 x y.dx z x0 y0 3 x x x x dx x x dx x 8 3 x cubic units The values of the integral z e dz j along a closed contour c in anti-clockwise direction for z c (i) The point z 0 = inside the contour c, and (ii) The point z 0 = outside the contour c, Respectively, are (A) (i).7, (ii) 0 (B) (i) 7.39, (ii) 0 (i) 0, (ii).7 (D) (i) 0, (ii) 7.39 (B) e (i) jf j z j (ii) 0 e A signal cos t cos t s s H s e e. nd rd harmonic 3 harmonic is the input to an LTI system with the transfer function If C k denotes the k th coefficient in the exponential Fourier series of the output signal, then C 3 is equal to (A) 0 (B) (D) 3 (B) output cos t cos t In E.F.S 3 rd harmonic j 3t j 3t j 3t 3 3 cos t e e 3 The coefficient of e isso C. 3 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6 66/

17 EC GATE-05-PAPER The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the shaded region in the z-plane. If the signal xn.0 n, n, then the ROC of its z-transform is represented by (A) (B) (D) (D) n n n u n ; ROC : z n x n, n x n u n u n n u n ; ROC : z 0.5 Thus combined ROC does not exist for x[n] ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7 77/

18 EC GATE-05-PAPER Assume that the circuit in the figure has reached the steady state before time t = 0 when the 3 resistor suddenly burns out, resulting in an open circuit. The current i(t) (in ampere) at t = 0 + is. At t 0, the circuit is on steady state i.e. the capacitor is open circuited so the circuit will be V V V V 4V 3F 3 3 V V 6V F 3 at t = 0 + when is open circuited, the capacitors will have an ideal voltage source of values 4V and 6V so the circuit will be A 3F V F 3 So the current through resistor at t = 0 + should be 4 A 4V 4V 6V Burn out 6V at t 0 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8 88/

19 EC GATE-05-PAPER In the figure shown, the current i (in ampere) is. - Nodal equation at V V 8 V V 8 V 0 4V 6 V 4V By using KCL at node a. A 5 8V i a 8V v b 0V 8 4 i 0 i 5A i KCL at b 4 i i i 0 i A 34. The z-parameter matrix z z z z for the two-port network shown in (A) (A) (B) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India (D) /

20 EC GATE-05-PAPER-03 Since the given network is symmetric and reciprocal Z Z Z Z input 3 output V 36 Z I 3 6 I 0 V Z I So I 0 We know V V Z Z Z Z Z V I 3 6 IL 0 V 35. A continuous-time speech signal xa(t) is sampled at a rate of 8 khz and the samples are subsequently 4096 grouped in blocks, each of size N. The DFT of each block is to be computed in real time using the radix- decimation-in-frequency FFT algorithm. If the processor performs all operations sequentially, and takes 0 s for computing each complex multiplication (including multiplications by and ) and the time required for addition/subtraction is negligible, then the maximum value of N is 36. The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a (A) low-pass filter (B) high-pass filter band-pass filter (D) band-stop filter yn 5xn 5xn j j j j H e 5 e At 0, H e 0 At ; H e 0 Thus the filter is band pass filter ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 0 00/

21 EC GATE-05-PAPER The injected excess electron concentration profile in the base region of an npn BJT, biased in the active region, is linear, as shown in the figure. If the area of the emitter-base junction is 0.00 cm, n 800 cm V s in the base region and depletion layer widths are negligible, then the collector current I c (in ma) at room temperature is. 9 (Given: thermal voltage V T = 6 mv at room temperature, electronic charge q.6 0 C ) 6.65 dn dx Ic qadn qa nvt dn dx Ic 6.65mA 38. Figures I and II show two MOS capacitors of unit area. The capacitor in Figure I has insulator materials X (of thickness t = nm and dielectric constant 4 ) and Y (of thickness t = 3 nm and dielectric constant 0). The capacitor in Figure II has only insulator material X of thickness t Eq. If the capacitors are of equal capacitance, then the value of t Eq (in nm) is..6 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

22 EC GATE-05-PAPER-03 E E. t t E E 4 0 CI.5 E E Et Et (4 ) (0) C t t E 4 II t Eq t.5 t Eq Eq.6nm 39. The I-V characteristics of the zener diodes D and D are shown in Figure I. These diodes are used in the circuit given in Figure II. If the supply voltage is varied from 0 to 00 V, then breakdown occurs in (A) D only (B) D only both Dand D (D) none of D and D (D) When two diodes are connected in series, the effective breakdown voltages becomes equal to the sum of their individual breakdown voltage. Vb Vb Vb V Since the applied voltage has a maximum of 00V (00<V b ), No diodes will be in breakdown region. 40. For the circuit shown in the figure, R R R3, L H and C F. If the input 6 Vin cos 0 t, then the overall voltage gain V V of the circuit is. out in - ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

23 EC GATE-05-PAPER-03 R A 6 6 j L 0 0 A R R X 3 C The overall voltage gain Vout V in V A A A out v Vin 4. In the circuit shown in the figure, the channel length modulation of all transistors is non-zero 0. Also, all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain V V of the circuit is 0 in (A) g r r r g r r m (B) m 0 03 gm3 g r r r m gm (A) Drawing a small signal model g r r r (D) m gm3 V g3 _ G 3 g V m g3 r 03 S D 3 g V m g r o V 0 V in r o V g g V m g ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3 33/

24 EC GATE-05-PAPER-03 V in V g g m V in r o r o V 0 r o3 V o AV= o 0 03 V in = - gm (r r r ) 4. In the circuit shown in the figure, transistor M is in saturation and has transconductance g m = 0.0 siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation to be zero, the small signal input pole frequency (in khz) is C 50PF g R 550PF in m g 0.05 m R k R k g R R f in in m 5k R C in in 57.9 khz ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4 44/

25 EC GATE-05-PAPER Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sumof-product (SOP) expression for the function is (A) PQSX PQSX QRSX QRSX (B) QSX QSX QSX QSX (D) QS QS QJ RS PQ RS PQ QS X 0 X F QSX QSX 44. For the circuit shown in the figure, the delays of NOR gates, multiplexers and inverters are ns,.5 ns and ns, respectively. If all the inputs P, Q, R, S and T are applied at the same time instant, the maximum propagation delay (in ns) of the circuit is. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5 55/

26 EC GATE-05-PAPER-03 (6) Case (i) When T = 0 T total = delay of NOR + delay of st MUX + delay of nd MUX= = 5ns Case (ii) When T = T total = delay of st NOT-gate + delay of st MUX + delay of nd NOR-gate + delay of nd MUX = = 6 ns So, the maximum delay = 6 ns. 45. For the circuit shown in the figure, the delay of the bubbled NAND gate is ns and that of the counter is assumed to be zero. If the clock (Clk) frequency is GHz, then the counter behaves as a (A) mod-5 counter (B) mod-6 counter mod-7 counter (D) mod-8 counter (D) The time period of clock is nsec and that of nand gate is n sec. The time period of clock n sec and that of nand gate is n.sec. If the nand gate would have 0 delay then the counter must be MOD 6 because on 6 th CP it will be rejected. But as the delay is nsec, the effect of 6 th CP will be observed on reset in after nsec, but in this additional n.sec, more clock cycle would passed in total 8 cycles are needed to rest the counter so MOD8 counter. 46. The first two rows in the Routh table for the characteristic equation of a certain closed-loop control system are given as The range of K for which the system is stable is (A).0 < K < 0.5 (B) 0 < K < K (D) 0.5 K ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6 66/

27 EC GATE-05-PAPER-03 (D) S S 3 k 3 k 4 From the table we can find characteristic equation 3 s ks k 3s 4 0 For stability kk 3 4 4k 6k 4 0 k k 0 So the conditions are k and k combiningly k > 47. A second-order linear time-invariant system is described by the following state equations d x t x t 3u t dt d x t x t u t dt where x (t) and x (t) are the two state variables and u(t) denotes the input. If the output c(t) = x (t), then the system is (A) controllable but not observable (B) observable but not controllable both controllable and observable (D) neither controllable nor observable (A) The set of equation of the system are dx t dt t i x t 3u t x t x t 0x t 3u t dx x t u t x t 0 x t x t u t dt c t x t 0x t we can frame the state space of the system as x x y 0 x x 0 x x ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7 77/

28 EC GATE-05-PAPER A matrix is 0 3 Bmatrix is C matrix is 0 for controllability determinant of B AB so controllable for observability determinant of so not observable final controllable but not observable C 0 Ca 48. The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as K s G s and H s, s s Respectively, If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is. To find break point, from characteristic equation we need to arrange k as function of s, then the root of dk 0 gives break point. ds Characteristic equation is given by s s k k 0 ks s s s s k s d d s s s s s s dk ds ds ds s dk s s s s ds s dk 0 ds ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8 88/

29 EC GATE-05-PAPER-03 s s 4s 4 s s 0 s 4s 0 s 0.58 and 3.44 j j To find the valid break point we need to find that lies on root locus 3.44 lies on root locus So break point A wide sense stationary random process X(t) passes through the LTI system shown in the figure. If the autocorrelation function of X(t) is R X, equal to then the autocorrelation function R Y of the output Y(t) is (A) R R T R T (B) R R T R T X X 0 X 0 X X 0 X 0 R R T (D) R R T X X 0 X X 0 (B) R YY(τ) = E[Y(t)Y(t - τ)] E[{X(t)-X(t - T 0)}{X(t-τ)-X(t -τ T 0)}] = R X(τ) - R X(-τ-T 0)-R X(-T+T 0)+R X(-τ) R YY(τ) = R X(τ) - R X(τ + T 0)-R X(τ-T 0) 50. A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of 4.0 khz and two-sided noise power spectral density 5 Watt per Hz. If information at the rate.5 0 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9 99/

30 3.5 EC GATE-05-PAPER-03 of 5 kbps is to be transmitted over this channel with arbitrarily small bit error rate, then the minimum bit-energy E b (in mj/bit) necessary is. Information rate R C Channel capacity For Error free transmission S C = B log N B = 4KHz S = E / T E R b b b b η N =.B = ηb S R b B log N ER b b R b B log + ηb E 3.5mJ/bit b E bmin 3.5mJ/bit 5. The bit error probability of a memoryless binary symmetric channel is 0 5. If 0 5 bits are sent over this channel, then the probability that not more than one bit will be in error is. Pebit n 0 bits x no. of bits error Px Px 0 Px very close ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India /

31 EC GATE-05-PAPER Consider an air-filled rectangular waveguide with dimensions a =.86 cm and b =.06 cm. At 0 GHz operating frequency, the value of the propagation constant (per meter) of the corresponding propagating mode is Consider an air-filled rectangular waveguide with dimensions a =.86 cm and b =.06 cm. The increasing order of the cut-off frequencies for different modes is (A) TE 0 < TE 0 < TE < TE 0 (B) TE 0 < TE < TE 0 < TE 0 TE 0 < TE 0 < TE 0 < TE (D) TE 0 < TE < TE 0 < TE 0 0 C m n fc a b for TE C C fc for TE 0 C C fc For TE C fc 07.7 For TE 0 C C fc TE 0 < TE 0 < TE 0 < TE 54. A radar operating at 5 GHz uses a common antenna for transmission and reception. The antenna has a gain of 50 and is aligned for maximum directional radiation and reception to a target km away having radar cross-section of 3 m. If it transmits 00 kw, then the received power in W is Consider the charge profile shown in the figure. The resultant potential distribution is best described by ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3 33/

32 EC GATE-05-PAPER-03 (A) (B) (D) (D) q q Electrical 0 Ndxno Ndxpo Potential (x) 0 P(x) x x w 0 V(x) P b a b a P P ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 3 33/