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 016 Γενεραλ Απτιτυδε ΓΑ Σετ 4 Q. 1 Q. 5 carry one mark each. Θ.1 Αν αππλε χοστσ Ρσ. 10. 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. 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 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. P ισ τηε γρανδφατηερ οφ M. Θ.4 Τηε νυmβερ τηατ λεαστ φιτσ τηισ σετ: (34, 441, 97 ανδ 64) ισ. (Α) 34 (Β) 441 (Χ) Θ.5 Ιτ τακεσ 10 σ ανδ 15 σ, ρεσπεχτιϖελψ, φορ τωο τραινσ τραϖελλινγ ατ διφφερεντ χονσταντ σπεεδσ το χοmπλετελψ πασσ α τελεγραπη ποστ. Τηε λενγτη οφ τηε φιρστ τραιν ισ 10 m ανδ τηατ οφ τηε σεχονδ τραιν ισ 150 m. Τηε mαγνιτυδε οφ τηε διφφερενχε ιν τηε σπεεδσ οφ τηε τωο τραινσ (ιν m/σ) ισ. (Α).0 (Β) 10.0 (Χ) /3

2 ΓΑΤΕ 016 Q. 6 Q. 10 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. 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 5 (Α) Μανυ (Β) Σραϖαν (Χ) Τριδεεπ Παϖαν Θ.9 Φινδ τηε αρεα βουνδεδ βψ τηε λινεσ 3ξ+ψ=14, ξ 3ψ=5 ιν τηε φιρστ θυαδραντ. (Α) (Β) 15.5 (Χ) /3

3 ΓΑΤΕ 016 Γενεραλ Απτιτυδε ΓΑ Σετ 4 Θ.10 Α στραιγητ λινε ισ φιτ το α δατα σετ (λν x, y). Τηισ λινε ιντερχεπτσ τηε αβσχισσα ατ λν x = 0.1 ανδ ηασ α σλοπε οφ 0.0. Wηατ ισ τηε ϖαλυε οφ y ατ x = 5 φροm τηε φιτ? (Α) (Β) (Χ) END OF THE QUESTION PAPER 3/3

4 Q. 1 Q. 5 carry one mark each. Q.1 A straight line of the form y = mx + c passes through the origin and the point (x, y) = (, 6). The value of m is. Q. lim ( n ) n n 1 n + + is. Q.3 A voltage V 1 is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V, which is independent of V 1, is measured 00 times and its average and standard deviation are 150 V and V respectively. V 3 is computed as: V 3 = V 1 + V. Then the standard deviation of V 3 in volt is. Q.4 The vector that is NOT perpendicular to the vectors (i + j + k) and (i + j + 3k) is. (A) (i j + k) (B) ( i + j k) (C) (0i + 0j + 0k) (4i +3 j + 5k) Q.5 In the neighborhood of z = 1, the function f(z) has a power series expansion of the form ( )=1+(1 )+(1 ) + Then f(z) is (A) 1 z (B) 1 z (C) z 1 z z 1 Q.6 Three currents i 1, i and i 3 meet at a node as shown in the figure below. If i 1 = 3 cos(ωt) ampere, i = 4 sin(ωt) ampere and i 3 = I 3 cos(ωt + θ) ampere, the value of I 3 in ampere is. Q.7 An air cored coil has a Q of 5 at a frequency of 100 khz. The Q of the coil at 0 khz (neglecting skin effect) will be. Q.8 A current i(t) shown in the figure below is passed through a 1 F capacitor that had zero initial charge. The voltage across the capacitor for t > s in volt is IN 1/1

5 Q.9 The signal x [n] shown in the figure below is convolved with itself to get y[n]. The value of y [ 1] is. Q.10 In the circuit shown below (v 1 + v ) = [1 sin(π10000t) + 1 sin(π30000t)] V. The RMS value of the current through the resistor R will be minimum if the value of the capacitor C in microfarad is. Q.11 If X (s), the Laplace transform of signal x(t) is given by of x(t) as t is. ( s + ) X ( s) = ( s + 1)( s + 3), then the value s 1 Q.1 The number of times the Nyquist plot of Gs () = will encircle the origin clockwise is. s + 1 Q.13 The value of a 0 which will ensure that the polynomial s 3 + 3s + s + a 0 has roots on the left half of the s-plane is (A) 11 (B) 9 (C) 7 5 Q.14 The input it ( ) = sin(3 t+ π ) is applied to a system whose transfer function The amplitude of the output of the system is. 8 Gs () =. ( s + 10) Q.15 The diode D used in the circuit below is ideal. The voltage drop V ab across the 1 kω resistor in volt is. IN /1

6 Q.16 In the circuit given below, the opamp is ideal. The output voltage V O in volt is. Q.17 In the circuit given below, the diodes D 1 and D have a forward voltage drop of 0.6 V. The opamp used is ideal. The magnitude of the negative peak value of the output V O in volt is. Q.18 The Boolean expression XY + ( X + Y )Z is equivalent to (A) XYZ + X Y Z (B) X Y Z + XYZ (C) ( X + Z )( Y+Z ) ( X + Z )( Y + Z ) Q.19 In the digital circuit given below, F is (A) XY + YZ (B) XY + YZ (C) XY + YZ XZ + Y Q.0 A 3 ½ digit DMM has an accuracy specification of ± 1 % of full scale (accuracy class 1). A reading of ma is obtained on its 00 ma full scale range. The worst case error in the reading in milliampere is ±. IN 3/1

7 Q.1 A dc potentiometer, shown in figure below, is made by connecting fifteen 10 Ω resistors and a 10 Ω slide wire of length 1000 mm in series. The potentiometer is standardized with the current I p = ma. Balance for an unknown voltage is obtained when the dial is in position 11 (11 numbers of the fixed 10 Ω resistor are included) and the slide wire is on the 34th mm position. The unknown voltage (up to four decimal places) in volt is. Q. In the circuit given below, each input terminal of the opamp draws a bias current of 10 na. The effect due to these input bias currents on the output voltage V O will be zero, if the value of R chosen in kilo-ohm is. Q.3 A peizo-electric type pressure sensor has a sensitivity of 1 mv/kpa and a bandwidth of 300 Hz to 300 khz. For a constant (dc) pressure of 100 kpa, the steady state output of the sensor in mllivolt is. Q.4 The signal m(t) = cos(ω m t) is SSB (single side-band) modulated with a carrier cos(ω c t) to get s(t). The signal obtained by passing s(t) through an ideal envelope detector is (A) cos(ω m t) (B) sin(ω m t) (C) cos(ω m t) + sin(ω m t) 1 IN 4/1

8 t 3 Q.5 Let st ( ) = rect 3 be a signal passed through an AWGN (additive white Gaussian noise) N0 to get () channel with noise power spectral density (PSD) vt. If vt () is passed through a matched-filter that is matched to st ( ), then output signal-to noise ratio (SNR) of the matched-filter is (A) 1 N 0 (B) N 0 (C) 3 N 0 4 N 0 Q. 6 Q. 55 carry two marks each. Q.6 Let f : [ 1, 1], where 3 4 f( x) = x x 10. The minimum value of f( x) is. Q.7 An urn contains 5 red and 7 green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour. The probability of getting a red ball in the next draw is (A) (B) Q.8 Consider the matrix A = ( 3 ) A A is. (C) whose eigenvalues are 1, 1 and 3. Then Trace of Q.9 The relationship between the force f(t) and the displacement x(t) of a spring-mass system (with a mass M, viscous damping D and spring constant K) is d xt () dxt () M + D + Kx() t = f () t. dt dt X(s) and F(s) are the Laplace transforms of x(t) and f(t) respectively. With M = 0.1, D =, K =10 X() s in appropriate units, the transfer function Gs () = is Fs () 10 (A) s + 0s+ 100 (B) s + 0s+ 100 (C) s 10s + 0s+ 100 s s + 0s+ 100 Q.30 The value of the integral 1 z + 1 π j z 1 C dz where z is a complex number and C center at 1+ 0j in the complex plane is. is a unit circle with IN 5/1

9 Q.31 The current I X in the circuit given below in milliampere is. Q.3 In the circuit shown below, V S = V, R = 10 Ω and ωl= 100 Ω. The current I S is in phase with V S. The magnitude of I S in milliampere is. Q.33 A symmetrical three-phase three-wire RYB system is connected to a balanced delta-connected load. The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The power in the system is measured using the two wattmeter method. The first wattmeter connected between R-line and Y-line reads zero. The reading of the second wattmeter (connected between B- line and Y-line) in watt is. Q.34 In the strain gauge bridge circuit given below, R 1 = R 3 = R (1 x) and R = R 4 = R (1 + x), where R is 350 Ω. The voltage sources v s and v n represent the dc excitation and the undesired noise/interference, respectively. The value of capacitor C in microfarad that is required to ensure that the output across a and b is low-pass filtered with a cutoff frequency of 150 Hz is. IN 6/1

10 Q.35 The voltage v(t) shown below is applied to the given circuit. v( t) = 3 V for t < 0 and v( t) = 6 V for t > 0. The value of current i(t) at t = 1s, in ampere is. Q.36 For the periodic signal x(t) shown below with period T = 8 s, the power in the 10 th harmonic is (A) 0 (B) 1 10π (C) Q.37 The fundamental period N 0 of the discrete-time sinusoid π 1 4 5π 301 xn [ ] = sin π n is. 4 Q.38 The transfer function G(s) of a system which has the asymptotic Bode plot shown below is (A) 10 4 ( s 1) ( s + 100) (B) 10 4 ( s + 1) ( s + 100) (C) 10 4 ( s + 1) ( s + 100) 10 4 ( s 1) ( s 100) IN 7/1

11 1 Q.39 For the feedback system given below, the transfer function Gs () =. The system CANNOT ( s + 1) be stabilized with 3 (A) Cs () = 1+ s (B) 9 (C) Cs () = 3+ s Cs () = 3+ Cs ()= Q.40 Match the unit-step responses (1), () and (3) with the transfer functions P(s), Q(s) and R(s), given below. (A) P(s) (3), Q(s) (), R(s) (1) (B) P(s) (1), Q(s) (), R(s) (3) (C) P(s) (), Q(s) (1), R(s) (3) P(s) (1), Q(s) (3), R(s) () Q.41 An ideal opamp is used to realize a difference amplifier circuit given below having a gain of 10. If x = 0.05, the CMRR of the circuit in db is. 1 s 7 s 1 P(s) = ( s + 1 ) ( s 1) Q(s) = ( s ) s R(s) = ( ) + 10 ( + ) 1 s +1 IN 8/1

12 Q.4 In the circuit given below, the opamp is ideal. The input v x is a sinusoid. To ensure v y = v x, the value of C N in picofarad is. Q.43 In the circuit given below, the opamp is ideal. The value of current I L in microampere is. Q.44 A 4 to 1 multiplexer to realize a Boolean function F (X, Y, Z) is shown in the figure below. The inputs Y and Z are connected to the selectors of the MUX (Y is more significant). The canonical sum-of-product expression for F ( X, Y, Z ) is (A) m (, 3, 4, 7 ) (B) m ( 1, 3, 5, 7) (C) m ( 0,, 4, 6 ) m (, 3, 5, 6 ) IN 9/1

13 Q.45 A synchronous counter using two J - K flip flops that goes through the sequence of states: Q 1 Q = is required. To achieve this, the inputs to the flip flops are (A) J 1 = Q, K 1 = 0 ; J = Q 1, K = Q 1 (B) J 1 = 1, K 1 = 1 ; J = Q 1, K = Q 1 (C) J 1 = Q, K 1 = Q ; J = 1, K = 1 J 1 = Q, K 1 = Q ; J = Q 1, K = Q 1 Q.46 A 1 Kbyte memory module has to be interfaced with an 8-bit microprocessor that has 16 address lines. The address lines A 0 to A 9 of the processor are connected to the corresponding address lines of the memory module. The active low chip select CS of the memory module is connected to the y 5 output of a 3 to 8 decoder with active low outputs. S 0, S 1, and S are the input lines to the decoder, with S as the MSB. The decoder has one active low EN 1 and one active high EN enable lines as shown below. The address range(s) that gets mapped onto this memory module is (are) (A) 3000 H to 33FF H and E000 H to E3FF H (C) 5300 H to 53FF H and A300 H to A3FF H (B) 1400 H to 17FF H 5800 H to 5BFF H and D800 H to DBFF H Q.47 A coil is tested with a series type Q-meter. Resonance at a particular frequency is obtained with a capacitance of 110 pf. When the frequency is doubled, the capacitance required for resonance is 0 pf. The distributed capacitance of the coil in pico farad is. IN 10/1

14 Q.48 The comparators (output = 1, when input 0 and output = 0, when input < 0), exclusive-or gate and the unity gain low-pass filter given in the circuit are ideal. The logic output voltages of the exclusive-or gate are 0 V and 5 V. The cutoff frequency of the low-pass filter is 0.1 Hz. For V 1 = 1 sin (3000t + 36 o ) V and V = 1 sin (3000t) V, the value of V O in volt is. Q.49 A 00 mv full scale dual-slope 3 ½ digit DMM has a reference voltage of 100 mv and a first integration time of 100 ms. For an input of [ Cos(100πt)] mv, the conversion time (without taking the auto-zero phase time into consideration) in millisecond is. Q.50 In the circuit below, the opamp is ideal and the sensor is an RTD whose resistance R θ = 1000 ( θ) Ω, where θ is temperature in C. The output sensitivity in mv/ C is. Q.51 The photo diode in the figure below has an active sensing area of 10 mm, a sensitivity of 0.5 A/W and a dark current of 1 µa. The i-to-v converter has a sensitivity of 100 mv/µa. For an input light intensity of 4 W/m, the output V O in volt is. IN 11/1

15 Q.5 The velocity of flow of water (density 1000 kg/m 3 ) in a horizontal pipe is measured using the PITOT tube shown below. The fluid in the U-tube manometer is mercury with a density of kg/m 3. Assume g = 9.81 m/s. If the height difference (h) is measured as 94.1 mm, the velocity of flow of water in m/s is. Q.53 The bandgap in ev of a semiconductor material required to construct an LED that emits peak power at the wavelength of 60 nm is. (Plank constant h = ev s and speed of light c = m/s). sin(100 πt) Q.54 The signal mt () = is frequency modulated (FM) with an FM modulator of frequency 100 π t deviation constant of 30 khz/v. Using Carson s rule, the approximate bandwidth of the modulated wave in kilohertz is. Q.55 A signal m(t) varies from 3.5 V to V with an average power of 3 W. The signal is quantized using a midtread type quantizer and subsequently binary encoded. With the codeword of length 3, the signal to quantization noise ratio in db is. END OF THE QUESTION PAPER IN 1/1