Γενεραλ Απτιτυδε ΓΑ Σετ 4. Σελεχτ τηε mοστ συιταβλε σεντενχε ωιτη ρεσπεχτ το γραmmαρ ανδ υσαγε. (Α) Τηε πριχε οφ αν αππλε ισ γρεατερ τηαν αν ονιον.

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1 ΓΑΤΕ 06 Γενεραλ Απτιτυδε ΓΑ Σετ 4 Q. Q. 5 carry one mark each. Θ. Αν αππλε χοστσ Ρσ. 0. Αν ονιον χοστσ Ρσ. 8. Σελεχτ τηε mοστ συιταβλε σεντενχε ωιτη ρεσπεχτ το γραmmαρ ανδ υσαγε. (Α) Τηε πριχε οφ αν αππλε ισ γρεατερ τηαν αν ονιον. (Β) Τηε πριχε οφ αν αππλε ισ mορε τηαν ονιον. (Χ) Τηε πριχε οφ αν αππλε ισ γρεατερ τηαν τηατ οφ αν ονιον. (D) Αππλεσ αρε mορε χοστλιερ τηαν ονιονσ. Θ. Τηε Βυδδηα σαιδ, Ηολδινγ ον το ανγερ ισ λικε γρασπινγ α ηοτ χοαλ ωιτη τηε ιντεντ οφ τηροωινγ ιτ ατ σοmεονε ελσε; ψου αρε τηε ονε ωηο γετσ βυρντ. Σελεχτ τηε ωορδ βελοω ωηιχη ισ χλοσεστ ιν mεανινγ το τηε ωορδ υνδερλινεδ αβοϖε. (Α) βυρνινγ (Β) ιγνιτινγ (Χ) χλυτχηινγ (D) φλινγινγ Θ.3 M ηασ α σον Q ανδ α δαυγητερ R. Ηε ηασ νο οτηερ χηιλδρεν. E ισ τηε mοτηερ οφ P ανδ δαυγητερ ιν λαω οφ M. Ηοω ισ P ρελατεδ το M? (Α) P ισ τηε σον ιν λαω οφ M. (Β) P ισ τηε γρανδχηιλδ οφ M. (Χ) P ισ τηε δαυγητερ ιν λαω οφ M. (D) P ισ τηε γρανδφατηερ οφ M. Θ.4 Τηε νυmβερ τηατ λεαστ φιτσ τηισ σετ: (34, 44, 97 ανδ 64) ισ. (Α) 34 (Β) 44 (Χ) 97 (D) 64 Θ.5 Ιτ τακεσ 0 σ ανδ 5 σ, ρεσπεχτιϖελψ, φορ τωο τραινσ τραϖελλινγ ατ διφφερεντ χονσταντ σπεεδσ το χοmπλετελψ πασσ α τελεγραπη ποστ. Τηε λενγτη οφ τηε φιρστ τραιν ισ 0 m ανδ τηατ οφ τηε σεχονδ τραιν ισ 50 m. Τηε mαγνιτυδε οφ τηε διφφερενχε ιν τηε σπεεδσ οφ τηε τωο τραινσ (ιν m/σ) ισ. (Α).0 (Β) 0.0 (Χ).0 (D).0 /3

2 ΓΑΤΕ 06 Q. 6 Q. 0 carry two marks each. Γενεραλ Απτιτυδε ΓΑ Σετ 4 Θ.6 Τηε ϖελοχιτψ ς οφ α ϖεηιχλε αλονγ α στραιγητ λινε ισ mεασυρεδ ιν m/σ ανδ πλοττεδ ασ σηοων ωιτη ρεσπεχτ το τιmε ιν σεχονδσ. Ατ τηε ενδ οφ τηε 7 σεχονδσ, ηοω mυχη ωιλλλ τηε οδοmετερ ρεαδινγ ινχρεασε βψ (ιν m)? (Α) 0 (Β) 3 Θ.7 Τηε οϖερωηελmινγ νυmβερ οφ πεοπλε ινφεχτεδ ωιτη ραβιεσ ιν Ινδια ηασ βεεν φλαγγεδ βψ τηε Wορλδ Ηεαλτη Οργανιζατιον ασ α σουρχε οφ χονχερν. Ιτ ισ εστιmατεδ τηαττ ινοχυλατινγ 70% οφ πετσ ανδ στραψ δογσ αγαινστ ραβιεσ χαν λεαδ το α σιγνιφιχαντ ρεδυχτιον ιν τηε νυmβερ οφ πεοπλε ινφεχτεδ ωιτη ραβιεσ. Wηιχη οφ τηε φολλοωινγ χαν βε λογιχαλλψ ινφερρεδ φροm τηε αβοϖε σεντενχεσ? (Α) Τηε νυmβερ οφ πεοπλε ιν Ινδια ινφεχτεδ ωιτη ραβιεσ ισ ηιγη. (Β) Τηε νυmβερ οφ πεοπλε ιν οτηερ παρτσ οφ τηε ωορλδ ωηο αρε ινφεχτεδ ωιτη ραβιεσ ισ λοω. (Χ) Ραβιεσ χαν βε εραδιχατεδ ιν Ινδια βψ ϖαχχινατινγ 70% οφ στραψ δογσ. (D) Στραψ δογσ αρε τηε mαιν σουρχε οφ ραβιεσ ωορλδωιδε. Θ.8 Α φλατ ισ σηαρεδ βψ φουρ φιρστ ψεαρ υνδεργραδυατε στυδεντσ. Τηεψ αγρεεδ το αλλοω τηε ολδεστ οφ τηεm το ενϕοψ σοmε εξτρα σπαχε ιν τηε φλατ. Μανυ ισ τωο mοντησ ολδερ τηαν Σραϖαν, ωηο ισ τηρεε mοντησ ψουνγερ τηαν Τριδεεπ. Παϖαν ισ ονε mοντη ολδερ τηαν Σραϖαν. Wηο σηουλδ οχχυπψ τηε εξτρα σπαχε ιν τηε φλατ? (Χ) 4 (D) 5 (Α) Μανυ (Β) Σραϖαν (Χ) Τριδεεπ (D) Παϖαν Θ.9 Φινδ τηε αρεα βουνδεδ βψ τηε λινεσ 3ξ+ψ=4, ξ 3ψ=5 ιν τηε φιρστ θυαδραντ. (Α) 4.95 (Β) 5.5 (Χ) 5.70 (D) 0.35 /3

3 ΓΑΤΕ 06 Γενεραλ Απτιτυδε ΓΑ Σετ 4 Θ.0 Α στραιγητ λινε ισ φιτ το α δατα σετ (λν x, y). Τηισ λινε ιντερχεπτσ τηε αβσχισσα ατ λν x = 0. ανδ ηασ α σλοπε οφ 0.0. Wηατ ισ τηε ϖαλυε οφ y ατ x = 5 φροm τηε φιτ? (Α) (Β) 0.04 (Χ) 0.04 (D) END OF THE QUESTION PAPER 3/3

4 Q. Q. 5 carry one mark each. Q. Consider a square matrix σ x A =, ω σ where x is unknown. If the eigenvalues of the matrix A are ( σ + jω) and ( σ jω), then x is equal to (A) + jω (B) jω (C) + ω (D) ω Q. For ( z) ( z) sin f =, the residue of the pole at z = 0 is z Q.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 Q.4 The integral dx ( x 0 ) is equal to Q.5 Consider the first order initial value problem y' = y + x x, y(0) =, (0 x < ) with exact solution y(x) = x + e x. 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 step-size h = 0.is Q.6 Consider the signal ( ) = χοσ(6 ) + σιν(8 ), where is in seconds. The Nyquist sampling rate (in samples/second) for the signal ( ) = ( + 5) is (A) 8 (B) (C) 6 (D) 3 Q.7 If the signal ( ) = ( ) ( ) with denoting the convolution operation, then x(t) is equal to (A) ( ) (B) ( ) (C) ( ) (D) ( ) EC (3) /9

5 Q.8 A discrete-time signal [ ] = [ 3] + [ 5] has z-transform X(z). If ( ) = ( ) is the z-transform of another signal y[n], then (A) [ ] = [ ] (C) [ ] = [ ] (B) [ ] = [ ] (D) [ ] = [ ] Q.9 In the RLC circuit shown in the figure, the input voltage is given by The output voltage ( ) is ( ) = χοσ(00 ) + 4 σιν(500 ). 0.5 H 00 µf + v i (t) (A) χοσ(00 ) + σιν(500 ) (C) σιν(00 ) + χοσ(500 ) - Ω 0.4 H 0 µf Ω + v o (t) (B) χοσ(00 ) + 4 σιν(500 ) (D) σιν(00 ) + 4 χοσ(500 ) Q.0 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 E gx, E gy and E gz are the band gaps of X, Y and Z, respectively, then I X Y Z V - (A) E gx > E gy > E gz (C) E gx < E gy < E gz (B) E gx = E gy = E gz (D) no relationship among these band gaps exists. EC (3) /9

6 Q. The figure shows the band diagram of a Metal Oxide Semiconductor (MOS). The surface region of this MOS is in SiO E M Φ Β Φ Β E C E FS E i E V (A) inversion (B) accumulation (C) depletion (D) flat band Q. 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 I SC = 80mA I (0, 0) V OC =0.5V V EC (3) 3/9

7 Q.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 O (in volt) at the steady state is D 0sin t ac C C + R - V o D Q.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 V CC =.5V Q β =00 V C β = 50 kω 0 kω Q V EC (3) 4/9

8 Q.5 In the astable multivibrator circuit shown in the figure, the frequency of oscillation (in khz) at the output pin 3 is V cc R A =. kω 7 Disch 8 Vcc 4 Res R B = 4.7 kω 6 Thresh 555 Timer Out 3 C = 0.0 µf Q.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 (C) 4F and 0 (D) 4F and Q.7 The logic functionality realized by the circuit shown below is (A) OR (B) XOR (C) NAND (D) AND Q.8 The minimum number of -input NAND gates required to implement a -input XOR gate is (A) 4 (B) 5 (C) 6 (D) 7 Trig Gnd EC (3) 5/9

9 Q.9 The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is X + G + G Y H GG GG (A) G = (B) G = + G H + G G + G H GG GG (C) G = (D) G = + G G H + G G + G G H Q.0 For the unity feedback control system shown in the figure, the open-loop transfer function G(s) is given as G ( s) =. s( s + ) The steady state error e ss due to a unit step input is x(t) + e(t) G(s) y(t) (A) 0 (B) 0.5 (C).0 (D) Q. 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 Q. An analog baseband signal, bandlimited 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 EC (3) 6/9

10 Q.3 A binary baseband digital communication system employs the signal p (t) = T 0, S, 0 t T S otherwise for transmission of bits. The graphical representation of the matched filter output y(t) for this signal will be (A) y(t) (B) y(t) /T s 0.5 (C) 0 y(t) T s T s 0 T s T s t t 0 T s T s (D) y(t) 0 T s / T s Q.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 (B) left-handed circularly polarized (C) elliptically polarized with a tilt angle of 45 0 (D) horizontally polarized Q.5 Faraday s law of electromagnetic induction is mathematically described by which one of the following equations? (A) B = 0 (B) D = ρv B D (C) E = (D) H = σ E + t t t t EC (3) 7/9

11 Q. 6 Q. 55 carry two marks each. Q.6 The particular solution of the initial value problem given below is d y dy dy y y dx dx dx x = = 0 with (0) = 3 and = 36 (A) (3 8x) e 6x (C) (3 + 0x) e 6x (B) (3 + 5x) e 6x (D) (3 x) e 6x Q.7 If the vectors e = (, 0, ), e = (0,, 0) and e 3 = (, 0, ) form an orthogonal basis of the threedimensional real space, then the vector u = (4, 3, 3) can be expressed as (A) u = e 3e e3 (B) u = e 3e + e (C) u = e + 3e + e3 (D) u = e + 3e e Q.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 Q.9 z e The values of the integral dz π j along a closed contour c in anti-clockwise direction for z (i) the point z 0 = inside the contour c, and (ii) the point z 0 = outside the contour c, respectively, are c (A) (i).7, (ii) 0 (B) (i) 7.39, (ii) 0 (C) (i) 0, (ii).7 (D) (i) 0, (ii) 7.39 EC (3) 8/9

12 Q.30 A signal χοσ χοσ ( ) is the input to an LTI system with the transfer function ( ) = +. If denotes the k th coefficient in the exponential Fourier series of the output signal, then is equal to (A) 0 (B) (C) (D) 3 Q.3 The ROC (region of convergence) of the z-transform of a discrete-time signal is represented by the n xn [ ] =.0, < n< +, then the ROC of its shaded region in the z-plane. If the signal ( ) z-transform is represented by (A) Im (B) Im (C) Unit circle Unit circle Im z-plane 0.5 z-plane 0.5 Re Re Unit circle z-plane 0.5 (D) Im Unit circle z-plane 0.5 Re Re (ROC does not exist) EC (3) 9/9

13 Q.3 Assume that the circuit in the figure has reached the steady state before time = 0 when the 3 resistor suddenly burns out, resulting in an open circuit. The current ( ) (in ampere) at = 0 is Ω 3 F Ω V i(t) Ω F 3 Ω Q.33 In the figure shown, the current (in ampere) is A 5 Ω Ω Ω Ω 8 V Ω 8 V i EC (3) 0/9

14 Q.34 The z-parameter matrix z z z z for the two-port network shown is 3 Ω input port output port 6 Ω (A) (B) Q.35 A continuous-time speech signal x a (t) is sampled at a rate of 8 khz and the samples are subsequently 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 µs 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 (C) Q.36 The direct form structure of an FIR (finite impulse response) filter is shown in the figure. x[n] The filter can be used to approximate a (A) low-pass filter (C) band-pass filter Unit Delay Unit Delay (B) high-pass filter (D) band-stop filter (D) y[n] EC (3) /9

15 Q.37 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, µ 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 (Given: thermal voltage V T = 6 mv at room temperature, electronic charge q = C) I B I E n p n 0 4 cm -3 Excess electron profile I C 0 0.5µm Q.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 ε = 4) and Y (of thickness t = 3 nm and dielectric constant ε = 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 t Metal t ε ε Si Si Figure I Metal ε Si Si Figure II t Eq EC (3) /9

16 Q.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 I -80V -70V V D D D 0-00V D Figure I Figure II (A) D only (C) both Dand D (B) D only (D) none of D and D Q.40 For the circuit shown in the figure, R = R = R 3 = Ω, L = µh and C = µf. If the input V = cos 6 t, then the overall voltage gain (V out /V in ) of the circuit is ( ) in 0 L V in - + R R C - + R3 V out EC (3) 3/9

17 Q.4 In the circuit shown in the figure, the channel length modulation of all transistors is non-zero (λ 0). Also, all transistors operate in saturation and have negligible body effect. The ac small signal voltage gain (V o /V in ) of the circuit is V DD M3 M V G v o v in M (A) ( ) (B) ( ) (C) (D) ( ) Q.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 λ to be zero, the small signal input pole frequency (in khz) is v in 5kΩ 50pF kω V DD v o M EC (3) 4/9

18 Q.43 Following is the K-map of a Boolean function of five variables P, Q, R, S and X. The minimum sum-of-product (SOP) expression for the function is PQ RS PQ RS X=0 X= (A) PQSX + PQSX + QRSX + QRSX (B) QSX + QSX (C) QSX + QSX (D) QS + QS Q.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 P Q R S T 0 MUX 0 MUX S 0 S 0 Y EC (3) 5/9

19 Q.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. Q 0 (LSB) 3-bit Synchronous Counter Q Q (MSB) Clk RESET If the clock (Clk) frequency is GHz, then the counter behaves as a (A) mod-5 counter (B) mod-6 counter (C) mod-7 counter (D) mod-8 counter Q.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 s 3 (K + 3) s K 4 (A).0 < K < 0.5 (B) 0 < K < 0.5 (C) 0 < K < (D) 0.5 < K < Q.47 A second-order linear time-invariant system is described by the following state equations d x dt d x dt ( t) + x ( t) 3u( t) = ( t) x ( t) = u( t) + 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 (C) both controllable and observable (D) neither controllable nor observable EC (3) 6/9

20 Q.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 Q.49 A wide sense stationary random process ( ) passes through the LTI system shown in the figure. If the autocorrelation function of ( ) is ( ), then the autocorrelation function ( ) of the output ( ) is equal to X(t) Delay = T 0 Y(t) (A) ( ) + ( ) + ( + ) (B) ( ) ( ) ( + ) (C) ( ) + ( ) (D) ( ) ( ) Q.50 A voice-grade AWGN (additive white Gaussian noise) telephone channel has a bandwidth of η khz and two-sided noise power spectral density =.5 0 Watt per Hz. If information at the rate 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 Q.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 Q.5 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 EC (3) 7/9

21 Q.53 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 (C) TE 0 < TE 0 < TE 0 < TE (D) TE 0 < TE < TE 0 < TE 0 Q.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 µw) is EC (3) 8/9

22 Q.55 Consider the charge profile shown in the figure. The resultant potential distribution is best described by (A) (C) (B) (D) END OF THE QUESTION PAPER EC (3) 9/9