EC GATE-7-PAPER-II www.gateforum.com Electronics and Communication Engineering Q. No. to 5 Carry One Mark Each. Consider the circuit shown in the figure. Y MUX Key X Z The Boolean expression F implemented by the circuit is (A) XYZ XY YZ (B) XYZ XZ YZ (C) XYZ XY YZ (D) XYZ XY YZ (B) F xyz zxy F xyz x y z F xyz xz yz y xy MUX F F x z. An LTI system with unit sample response hn 5n 7n 7n 5n 4 is a (A) Low pass filter (B) high pass filter (C) band pass filter (D) band stop filter (C) hn 5n 7n 7n 5n 4 Obtain h e 5 7e 7e 5 j j j 4 j At and ; j h e For at a frequency maximum value of j h e j h e is obtained Thus Ideal behaviour of h[n] 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
EC GATE-7-PAPER-II www.gateforum.com. In the circuit shown, V is a sinusoidal voltage source. The current I is in phase with voltage V. amplitude of voltage across the capacitor The ratio is. amplitude of voltage across the resistor 5 5H I V 5F (.9 to.) If I &V are in phase then the circuit is in resonance At resonance VC L 5 Q. V R C 5 5 R 4. In a DRAM, (A) periodic refreshing is not required (B) information is stored in a capacitor (C) information is stored in a latch (D) both read and write operations can be performed simultaneously (B) n 5. Consider an n-channel MOSFET having width W, length L, electron mobility in the channel and oxide capacitance per unit area C. If gate-to-source voltage V GS =.7V, drain-tosource voltage V DS =.V, n ox ox C A / V, threshold voltage V TH =. V and (W/L) =5, then the transconductance g m (in ma/v) is. (.45 to.55) Here, VDS VGS V PH, so n-channel MOSFET is working in linear region. W V ID ncox VGS V TH.VDS L So, transconductance I DS g m is in linear region and is given by W D 6 4 gm nc ox.vds 5. 5.5 ma V VGS L VDS const 6. Two conducting spheres S and S of radii a and b (b>a) respectively, are placed far apart and connected by a long, thin conducting wire, as shown in the figure. S Wire S Radius b Radius a ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com For some charge placed on this structure, the potential and surface electric field on S are V a and E a, and that on S are V b and E b, respectively, which of the following is CORRECT? (A) Va Vb and Ea Eb (B) Va Vb and Ea Eb (C) Va Vb and Ea Eb (D) Va Vb and Ea Eb (C) bc two spheres are joined with a conducting wire, the voltage on two spheres is same. V V The capacitance of sphere radius C C a b a a b We know Q CV b b b Qa Ca a Q C b Ea 4o a b E E b a E a b 4 b b o a 7. For the circuit shown in the figure, P and Q are the inputs and Y is the output. PMOS Y P Q NMOS The logic implemented by the circuit is (A) XNOR (B) XOR (C) NOR (D) OR (B) 8. An n-channel enhancement mode MOSFET is biased at V V and V V V (C), where GS TH DS GS TH V GS is the gate-to-source voltage, V DS is the drain-to-source voltage and V TH is the threshold voltage. Considering channel length modulation effect to be significant, the MOSFET behaves as a (A) voltage source with zero output impedance (B) voltage source with non-zero output impedance (C) current source with finite output impedance (D) current source with infinite output impedance If channel length modulation is considered and significant it means ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com VA early voltage and r A e V I D Vgs gmvgs re Vo If VAS VTH and VDS VDS VTH then it indicates that MOSFET is working in saturation region and it can be used as an amplifier. So it can act as current source with finite output impedance. 9. A connection is made consisting of resistance A in series with a parallel combination of resistances B and C. Three resistors of value, 5, are provided. Consider all possible permutations of the given resistors into the positions A, B, C, and identify the configurations with maximum possible overall resistance, and also the ones with minimum possible overall resistance. The ratio of maximum to minimum values of the resistances (up to second decimal place) is. (. to.6) The maximum resistance 5 R.48 max The minimum resistance 5 R 5. min R R max min.4 5. An npn bipolar junction transistor (BJT) is operating in the active region. If the reverse bias across the base collector junction is increased, then (A) the effective base width increases and common emitter current gain increases (B) the effective base width increases and common emitter current gain decreases (C) the effective base width decreases and common emitter current gain increases (D) the effective base width decreases and common emitter current gain decreases (C) If the reverse bias voltage across the base collector junction is increased, then their effective base width will decrease and collector current will increase, therefore their common-emitter current gain increases. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4
EC GATE-7-PAPER-II www.gateforum.com. Consider the state space realization x t x t u t, 9 x t 45 x t with the initial condition x x, where u(t) denotes the unit step function. The value of lim x t x t (4.99 to 5.) x t... x t 9x t 45u t.... Apply L.T to above equation x t because initial conditions are zero 45 Sx s x 9X s S 45 X ss 9 45 X s s s 9 S 5 X s 5 s 9 X t 5u t 5e u t t 9t It x t x t It x t 5 t t is.. The rank of the matrix (4 to 4) R 4 R 4 R ~ 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
EC GATE-7-PAPER-II www.gateforum.com R 4 R 4 R ~ R R ~ R 4 R 4 R ~ R 5 R 5 R 4 ~ Which is in Echelon form Rank No.of non zero rows 4. A two wire transmission line terminates in a television set. The VSWR measured on the line is 5.8. The percentage of power that is reflected from the television set is (48. to 5.) Percentage of power reflected is VSWR 5.8 4.8.758 VSWR 5.8 6.8 % Power reflected = 49.8% 4. The input x(t) and the output y (t) of a continuous-time system are related as y t t tt x u du. The system is (A) Linear and time-variant (C) Non-linear and time-variant (B) (B) Linear and time-invariant (D) Non-linear and time-invariant Given Input-output relationship describes integration over a fundamental period T. The integration over one period is linear and time-invariant. ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6
EC GATE-7-PAPER-II www.gateforum.com 5. Which of the following statements is incorrect? (A) Lead compensator is used to reduce the settling time. (B) Lag compensator is used to reduce the steady state error. (C) Lead compensator may increase the order of a system. (D) Lag compensator always stabilizes an unstable system. (D) The phase-lead controller adds zero and a pole, with the zero to the right of the pole, to the forward-path transfer function. The general effect is to add more damping to the closed-loop system. The rise time and settling time are reduced in general. Reduces the steady state error Reduces the speed of response (i.e decreases) Increases the gain of original network without affecting stability Permits the increases of gain if phase margin is acceptable System becomes lesser stable Reduces the effect of noise Decrease the bandwidth 6. The residues of a function fz z 4z are (A) (B) and 7 5 (B) and 5 5 Z = 4 is a pole of order (or) simple pole (C) and 7 5 Residue of f(z) at z= 4 = Res f z lim z 4. z = is a pole of order. z4 d Res f z lim z. z z! dz z 4 z d lim z dz z 4 5 (D) and 5 5 and z4 z 4 z 5 5 7. A sinusoidal message signal is converted to a PCM signal using a uniform quantizer. The required signal-to-quantization noise ratio (SQNR) at the output of the quantizer is 4dB. The minimum number of bits per sample needed to achieve the desired SQNR is (7 to 7) For sinusoidal signal SNR in db 6. n.75 Q Given required SNR Q 4dB ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7
EC GATE-7-PAPER-II www.gateforum.com 6. n.75 4dB 6.n 4.75 4.75 n 6. n 7 Since 'n' must be an int eger 8. The general solution of the differential equation constants K and K is (A) (C) 6x 6x K e K e (B) 6x 6x K e K e (D) d y dx dy 5y in terms of arbitrary dx K e K e 8 x 8 x K e K e 8 x 8 x (A) D D 5 y k.e k e D 6 roots are real and distinct 6 x 6 x Where k, k are arbitrary constants. 9. Which one of the following graphs shows the Shannon capacity (channel capacity) in bits of a memory less binary symmetric channel with crossover probability P? (A) Capacity (B) Capacity p p (C) Capacity (D) Capacity p p (C) For memory less binary Symmetric channel Channel capacity C H p Hp plog plog p p p Cross over probability C plog p p log p At p ; C At p C At p C C P ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8
EC GATE-7-PAPER-II www.gateforum.com. The output V of the diode circuit shown in the figure is connected to an averaging DC voltmeter. The reading on the DC voltmeter in Volts, neglecting the voltage drop across the diode, is. (.5 to.) V sin t f 5Hz m Vo.847V k V. Consider the random process Xt U Vt, where U is a zero-mean Gaussian random variable and V is a random variable uniformly distributed between and. Assume that U and V are statistically independent. The mean value of the random process at t = is () Given x t U Vt x U V E x E U V E U E V. For the system shown in the figure, Y (s) / X (s) =. Xs Gs Ys (.95 to.5) Ys X s Xs Gs Ys. The smaller angle (in degrees) between the planes x + y + z = and x y + z = is. (54. to 55.) x y x y z We have angle between two planes a x b y c y d a x b y c y d x is cos a a b b c c a b c a b c cos 54.7 4 4 9 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9
EC GATE-7-PAPER-II www.gateforum.com 4. Consider the circuit shown in the figure. Assume base-to- emitter voltage V BE =.8 V and common base current gain of the transistor is unity. 8V 44k 4k 6k k The value of the collector- to emitter voltage V CE (in volt) is. (5.5 to 6.5) Given V.8V; BE As ; is very large So IE I CE C 86 VB 4.8V 6 4.8 8 IC ma V 8 6 8 6V 5. In the figure, D is a real silicon pn junction diode with a drop of.7v under forward bias condition and D is a zener diode with breakdown voltage of -6.8 V. The input V in (t) is a periodic square wave of period T, whose one period is shown in the figure. Vin t F 4V t sec onds 4V D D Vout t Assuming T. where is the time constant of the circuit, the maximum and minimum values of the output waveform are respectively, (A) 7.5 V and.5v (C) 7.5 V and. V (A) When Vi 4V, the equivalent circuit is (B) 6. V and.9v (D) 6. V and.6 V ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com V C Vi.7V 6.8V Vo V V V i C o V V V C i o C V 4 6.8.7 4 7.5 6.5V Maximum Vo 7.5V When Vi 4V, the equivalent circuit is V C V i Vo V V V 4V 6.5.5V o i C Minimum V.5V o Q. No. 6 to 55 Carry Two Marks Each 6. If the vector function F a x y kz a y k x z a z ky z is irrotational, then the values of the constants k, k and k respectively, are (A).,.5,.5 (B).,.,. (C).,.,.5 (D) 4.,.,. (B) curl F i j k x y z y k z k x z k y z i k j k k k k, k, k 7. The un-modulated carrier power in an AM transmitter is 5kW. This carrier is modulated by a sinusoidal modulating signal. The maximum percentage of modulation is 5%. If it is reduced to 4%, then the maximum un-modulated carrier power (in kw) that can be used without overloading the transmitter is (5.9 to 5.) Total power when 5% is PT PC ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
T EC GATE-7-PAPER-II www.gateforum.com.5 PT 5 5.5 5.5 P 5.65 When 4% Total power remains 5.65 C.4 5.65 PC 5.65 PC.8 P 5. 8. Consider an LTI system with magnitude response f, f Hf, f And phase response Arg If the input to the system is H f f. x t 8cos t 6sin 4t 4 cos 8t. 4 8 6 Then the average power of the output signal y (t) is. (7.95 to 8.5) Consider an LTI system with magnitude response f, f Hf, f And phase response Arg If the input to the system is H f f. x t 8cos t 6sin 4t 4 cos 8t. 4 8 6 Then the average power of the output signal y (t) is. 8. Obtain Xf for the given x(t) X f 4 f f 8 f f f 4 f 4 Xf Hf 8 4 multiply 4 4 4 f f ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com 4 f f Yf f f y t 4cos t Thus max power 6 8 9. A MOS capacitor is fabricated on p-type Si (silicon) where the metal work function is 4. ev and electron affinity of Si is 4. ev. E C -F F =.9 ev, where E C and E F are the conduction band 4 minimum and the Fermi energy levels of Si, respectively. Oxide.9, 8.85 F / cm. r -9 oxide thickness t ox =. m and electronic charge q =.6 C.If the measured flat band voltage of the capacitor is V, then the magnitude of the fixed charge at the oxidesemiconductor interface, in nc/cm, is. (6.85 to 6.95) V FB Q MS C F ox q q q MS M S M xo c f q q E E 4.4..9..9.8eV.8q V MS.8V q ox 9 Cox 4.5 F cm tox F.8 4.5 9 F E Q QF. 4.5 Q 6.9nc cm 9. An electron (q ) is moving in free space with velocity 5 m/s towards a stationary electron (q ) far away. The closest distance that this moving electron gets to the stationary electron before the repulsive force diverts its path is -8 m. [Given, mass of electron m = 9. - kg, charge of electron 9 permittivity / 6 F / m] (4.55 to 5.55) Work done due to field and external agent must be zero qv MV.6.6 m 4 9 9 5 8 5.58 m o -9 e = -.6 C, and ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
. The values of the integrals EC GATE-7-PAPER-II www.gateforum.com x y dy dx and x y are x y x y dx dy (A) same and equal to.5 (B) same and equal to -.5 (C).5 and.5, respectively (C) To find Consider x y dy dx x y x y y dy x dy dy x y x y x y x y x. x y x y x dy x dy x dy x x x y x y x x y x x x x x x x x x x x x y dy dx dx x y x x Similarly x y dx dy x y (D) -.5 and.5, respectively. Passengers try repeatedly to get a seat reservation in any train running between two stations until they are successful. If there is 4% chance of getting reservation in any attempt by a passenger, then the average number of attempts that passengers need to make to get a seat reserved is. (.4 to.6) Let X is a random variable which takes number of attempts Given probability of any attempts to be successful, 4 p 4%, q 5 5 5 X 4 px 5 5 5 5 5 5 5 5 5 5 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4
EC GATE-7-PAPER-II www.gateforum.com EX XpX 4... 5 5 5 5 5 5 5 4... x x x 4x... 5 5 5 5 5 5 5.5 5 4 Average number of attempts that passengers need to make to get seat reserved is.5. Figure I shows a 4-bits ripple carry adder realized using full adders and Figure II shows the circuit of a full-adder (FA). The propagation delay of the XOR, AND and OR gates in Figure II are ns, 5 ns and ns respectively. Assume all the inputs to the 4-bit adder are initially reset to. Y X Y X Y X Y X X n Y n S n Z 4 Z FA FA Z Z FA FA Z Zn S S S S Figure I Z n Figure II At t=, the inputs to the 4-bit adder are changed to XXXX, Y Y YY and Z. The output of the ripple carry adder will be stable at t (in ns) = (7. to 7.) 4. The permittivity of water at optical frequencies is.75. It is found that an isotropic light source at a distance d under water forms an illuminated circular area of radius 5m, as shown in the figure. The critical angle is. c Air 5m Water C d Light Source The value of d (in meter) is (4. to 4.4) C sin sin 49.6.75 5 5 tan C d 4.m d tan C ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5
EC GATE-7-PAPER-II www.gateforum.com 5. A unity feedback control system is characterized by the open-loop transfer function K s Gs s s The Nyquist path and the corresponding Nyquist plot of G(s) are shown in the figures below. j j s R j Re s plane j5.4k K j j Gs plane Re G K j Nyquist path for Gs j5.4k Nyquist Plot of Gs If < K <, then the number of poles of the closed-loop transfer function that lie in the right half of the s-plane is (A) (B) (C) (D) (C) N=, Because < L < There are no encircles around (Y, ) And K S K S GS S S S.7 S..598i So, P N P Z Z OR C.E S S KS K If stable K > K+ K> Here, in the question asking < K < So, System is unstable 6. The signal xt sin 4 t, where t is in seconds is sampled at a rate of 9 samples per second. The sampled signal is the input to an ideal low pass filter with frequency response H(f) as follows : Hf, f khz, f khz. What is the number of sinusoids in the output and their frequencies in khz? (A) Number =, frequency = 7 (B) Number =, frequencies=,7, (C) Number =, frequencies =, 7 (D) Number =, frequencies =, (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
EC GATE-7-PAPER-II www.gateforum.com Given input signal xt sin 4 t Input signal spectrum 7 Xf 7 f khz Sampled signal spectrum is the spectrum of X(f) which repeats with integer multiples of 9 khz. Sampled signal spectrum: Xs f 6 7 9 7 9 6 f The sampled signal spectrum is passed through a LPF of cutoff frequency KHz. Thus the filtered out sinusoids are of KHz 7 KHz and KHz frequency. 7. A unity feedback control system is characterized by the open-loop transfer function s Gs s ks s The value of k for which the system oscillates at rad/s is. (.74 to.76) Gs rad sec K?? s s ks s G s H s k s ks 4s s ks s s 4 s k 4k k s s For marginal stable 4k k.75 k 4 Cross check ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7
EC GATE-7-PAPER-II www.gateforum.com Take auxiliary equation ks s 4 s j rad sec k 4 8. Consider the circuit shown in the figure. i V i P Q The Thevenin equivalent resistance (in ) across P Q is. (-. to -.99) V To find R th I V Here i o V Nodal at V V i o V I I I V V V I R th i o V 9. The transfer function of a causal LTI system is H(s) = /s. If the input to the system is x(t) = [sin(t) / t]u(t), where u(t) is a unit step function, the system output y(t) as t is. (.45 to.55) Given xt sin t ut t By using frequency integration property, x t t s L X u du s L Consider x t sin t ut X s s du tan s u ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8
EC GATE-7-PAPER-II www.gateforum.com Lx t tan s X s Ys XsH j tan s s s By using final value theorem, lim yt lim sys lim tan s t s s 4. An integral I over a counter clock wise circle C is given by If C is defined as z =, then the value of I is (A) (D) I z z C z e dz. isin (B) isin (C) isin (D) 4 isin I z z e dz C z Consider z z z z iz i z z f z e e z i are simple poles of f(z) which lie inside z = Residue of f(z) at z z i lim z i e z i ie zi & Residue of f(z) at z iz i z z i lim z i e z i ie zi z iz i z i i i i By residue theorem, I e dz i ie ie e e C z z i i e e 4i 4isin i 4. Consider a binary memory less channel characterized by the transition probability diagram shown in the figure..5.5.75.75 The channel is (A) Lossless (B) Noiseless (C) Useless (D) Deterministic (C) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9
EC GATE-7-PAPER-II www.gateforum.com It is a useless channel as MAP criteria cannot decide anything on receiving we cannot decide what is transmitted. 4. An abrupt pn junction (located at x = ) is uniformly doped on both p and n sides. The width of the depletion region is W and the electric field variation in the x-direction is E(x). Which of the following figures represents the electric field profile near the pn junction? (A) Ex (B) Ex n side p side W, x n side p side W, x (C) E x n side W p side, x (D) E x n side W p side, x (A) If left side is p-region and right side is n-region then electric field triangle will be down warded and if the left side is n-region and right side is p-region, then electric field triangle will be upward. 4. A second order LTI system is described by the following state equations, d x t x t dt d x t x t x dt t r t Where xt and x t are the two state variables and r(t) denotes the input. The output c(t) = x (t). The system is. (A) Undamped (oscillatory) (C) Critically damped (D) x (t) x (t) sx (s) X (s) x (t) x (t) x (t) r(t) sx (s) X (s) X (s) R(s) s s X (s) R(s) R(s) C(s) X (s) s s C(s) R(s) (s )(s ) system is over damped (B) Under damped (D) Over damped ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com 44. Consider the parallel combination of two LTI systems shown in the figure. h t xt yt h t The impulse responses of the systems are h t t t h t t. If the input x(t) is a unit step signal, then the energy of y(t) is. (7. to 7.) Since h t and h xt t are connected in parallel the resultant system can be given as follows. h t h t yt y t x t * h t h t From the given h (t) & h (t) h t h t t t t x t u t yt ut u t u t Energy of y t dt dt 4 7 y(t) t 45. Assuming that transistors M and M are identical and have a threshold voltage of V, the state of transistors M and M are respectively. V (A) Saturation, Saturation.5V (B) Linear, Linear M (C) Linear, Saturation (D) Saturation, Linear V M (C) If VD VG V TH, then transistor is working in saturation region. So, For M transistor V V V D G TH V.5 V Assume that M is working in saturation, so that ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com I D I D V V V V GS TH GS TH V V V S G.5V V D S S V V.5V. Now, for M, transistor to work in saturation VD VG V TH, but it is not satisfied by M transistor and VG V TH, so, transistor M is ON but working in linear region. 46. A programmable logic array (PLA) is shown in the figure. P P Q Q R R * * * * * * * * * P F Q The Boolean function F implemented is (A) P Q R P Q R P Q R (B) P Q RP Q RP Q R (C) P Q R P Q R P Q R (C) PQR PQR PQR (D) P Q RP Q RP Q R 47. A modulating signal given By x(t) = 5 sin 4 t cos t V is fed to a phase modulator with phase deviation constant k p =.5rad/V. If the carrier frequency is khz, the instantaneous frequency (in khz) at t =.5 ms is (69.9 to 7.) xt 5sin4 t cos t Transform theorem frequency d f t fc k p. mt dt d m t 5cos 4 t cos t 4 sin t. dt t.5 R d m t 5cos 4 cos dt fi t 5 7 khz ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com 48. The minimum value of the function. (-. to -99.99) x f x x x x f x x x x x f x x f at x, f x has local minimum. f at x, f x has local maximum For x =, local minimum value Finding f 4. f. f x x x in the int erval x occurs at x = f x, are end points of interval Minimum occurs at x 49. The switch in the circuit, shown in the figure, was open for a long time and is closed at t =. The current i(t) (in ampere) at t =.5 seconds is it 5 A 5 t.5h (8. to 8.) At t= - At t A 5 5 i 5A L il O 5 it 5.5H 5A ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
L EC GATE-7-PAPER-II www.gateforum.com L.5 il R 5 t i 5e i t 5e At t.5s 5 i.5 8.6A e t 5. In the voltage reference circuit shown in the figure, the op-amp is ideal and the transistors Q Q.., Q are identical in all respects and have infinitely large values of common emitter current the relation I C =I S exp ((V BE /V T ), where I s is the saturation current. Assume that the voltage V P shown in the figure is.7 V and the thermal voltage V T =6mV. k k 5V 5k V p 5V V out Q Q Q Q The output voltage V out (in volts) is. (. to.) KCL at node a Vo Vi Vx.7 5 V V 4V.8 C i x V 5V.8 o x V S I 5k V x a k V o X T VS VT Now, V V I e e s s V V x T V n V Vx V V T Vx.789V From equation (i) S S T n Vo 5.789.8.45V k ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 4
EC GATE-7-PAPER-II www.gateforum.com 5. The state diagram of a finite state machine (FSM) designed to detect an overlapping sequence of three bits is shown in the figure. The FSM has an input In and an output Out. The initial state of the FSM is S. In Out In Out In Out S In Out S In Out In Out In Out S S In Out If the input sequence is, starting with the left-most bit, then the number times Out will be is. (4 to 4) From the state diagram, let us obtain the transition of states and out when IN channel. Initial state is So, the input sea is When IN then S S, with out Next IN then S Sz with out IN then S S with out n IN then S S with out IN, then S S with out IN, then S S with out IN, then S S with out IN, then S S with out IN, then S S with out IN, then S S with out u IN, then S S with out IN, then S S with out IN, then S S with out IN, then S S with out The ticketed mark now corresponding to output =. So output will be 4 times. 5. Standard air filled rectangular waveguides of dimensions a =.9 cm and b=. cm are designed for radar applications. It is desired that these waveguides operate only in the dominatnt TE mode but not higher than 95% of the next higher cutoff frequency. The range of the allowable operating frequency f is. (A) 8.9 GHz f. GHz (C) 6.55 GHz f. GHz (B) (B) 8.9 GHz f.45 GHz (D).64 GHz f.4 GHz ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 5
Cut off frequency of TE is EC GATE-7-PAPER-II www.gateforum.com a Since, b next higher mode is TE f C TE c.ghz a f.95..45ghz f 8 c c a.9 8 65.5 Hz 5. For a particular intensity of incident light on a silicon pn junction solar cell, the photocurrent density (J L ) is.5 ma/cm and the open-circuit voltage (V oc ) is.45 V. consider thermal voltage (V T ) to be 5mV. If the intensity of the incident light is increased by times, assuming that the temperature remains unchanged. V oc (in volts) will be. (.5 to.54) JL.5 JS.6 A cm V.45 OC V.5 T e e Now if the intensity of the light is increased by times it means their photocurrent will also increased by times. KT J L Voc n q JS.5.6.56 Volt. 5 n 54. In the circuit shown, transistors Q and Q are biased at a collector current of.6ma. Assuming that transistor current gains are sufficiently large to assume collector current equal to emitter current and thermal voltage of 6 mv, the magnitude of voltage gain V /V s in the mid-band frequency range is (up to second decimal place). 5V k V O Q V S Q R B 5V (49. to 5.) a.c equivalent circuit for the given figure ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 6
EC GATE-7-PAPER-II www.gateforum.com g C m VT 6 m E AV 5 gmr E V I.6 m R C k; R E ; g A 5 m g R V S ~ R C R E k g m 55. Two n-channel MOSFETs, T and T, are identical in all respects except that the width of T is double that of T. Both the transistors are biased in the saturation region of operation, but the gate overdrive voltage (V GS -V TH ) of T is double that of T, where V GS and V TH are the gate to source voltage and threshold voltage of the transistors, respectively. If the drain current and transconductance of T are I D and g m respectively, the corresponding values of these two parameters for T are (A) 8I D and g m (B) 8I D and 4g m (C) 4I D and 4g m (D) 4I D and g m (B) Drain current in saturation is I D W ncox VGS VTH L For transistor T ID I I and g g C V V V L D D m m n ox Gs TH GS For transistor T W W W V V V V V V GS Th GS Th GS Th W ID ncox VGS VTH 8ID L I W g C V V 4g D m n ox Gs Th m VGS L General Aptitude Q. No. - 5 Carry One Mark Each. The ninth and the tenth of this month are Monday and Tuesday. (A) figuratively (B) retrospectively (C) respectively (D) rightfully (C). 5 students are taking one or more courses out of Chemistry, Physics, and Mathematics. Registration records indicate course enrolment as follows: Chemistry (9). Physics (86). ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 7
EC GATE-7-PAPER-II www.gateforum.com Mathematics (95). Chemistry and Physics (8), Chemistry and Mathematics (7), and Physics and Mathematics (6). How many students are taking all subjects? (A) 7 (B) 4 (C) 47 (D) 5 (D) Given A x 8... A y 6... A x 7... And x x A x 9...(4) x A y y 86...(5) x A y z 95... 6 x x x y y z A 5...(7) x y x 6 A...(8) 4 5 6 A 6 A x y z 8 A 6 A x y z 8 From 8 A 76 5 x x y A 8 From 7 A 76 5 6 A A 8 86 A 8 A 5 Alternate method nc 9, np 86, nm 95, nc P 8; np C M. 5 9 86 95 8 7 6 np C m np C m 5 447 5. n C M 7, P M 6 n P C M n C n P n M n C P n C m n P M C9 P86 y x x A x y z M 95. It is to read this year s textbook the last year s. (A) easier, than (B) most easy, than (C) easier, from (D) easiest, from (A) 4. Fatima starts from point P, goes North for km, and then East for 4km to reach point Q. She then turns to face point P and goes 5km in that direction. She then goes North for 6km. How far is she from point P, and in which direction should she go to reach point P? (A) 8km, East (B) km, North (C) 6km, East (D) km, North (A) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 8
EC GATE-7-PAPER-II www.gateforum.com The required distance FP x 6 64 x 8, East 4 km Q F 'x ' km P 5 km 6 km 5 km O 5. A rule states that in order to drink beer one must be over 8 years old. In a bar, there are 4 people. P is 6 years old, Q is 5 years old, R is drinking milkshake and S is drinking beer. What must be checked to ensure that the rule is being followed? (A) Only P s drink (C) Only S s age (B) (B) Only P s drink and S s age For rules to be followed, we need to check P's drink and S's age. (D) Only P s drink, Q s drink and S s age Q. No. 6- Carry Two Marks Each 6. Each of P, Q, R, S, W, X, Y and Z has been married at most once. X and Y are married and have two children P and Q. Z is the grandfather of the daughter S of P. Z and W are married and are parents of R. Which one of the following must necessarily be FALSE? (A) X is the mother-in-law of R (C) P is a son of X and Y (D) (B) P and R are not married to each other (D) Q cannot be married to R 7. The number of -digit numbers such that the digit is never to the immediate right of is (A) 78 (B) 79 (C) 88 (D) 89 (C) Total no. of digit no s = 9 = 9 The no. of -digit numbers in which is to the immediate right of = 9 choices 9 choices 9 choices The no. of -digit no s such that the digit is never to immediate right of is 9 9 88 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India 9
Alternate method EC GATE-7-PAPER-II www.gateforum.com Total no. of digit numbers are 9 9 9. Numbers with digit is to the immediate right of are x x 9 9 So, no. of digit numbers such that the digit is never to the immediate right of are = 9-9= 88 8. A contour line joins locations having the same height above the mean sea level. The following is a contour plot of a geographical region. Contour lines are shown at 5m intervals in this plot. 45 45 Q R P 575 55 S 55 575 T 5 475 5 Which of the following is the steepest path leaving from P? (A) P to Q (B) P to R (C) P to S (D) P to T (B) Closer lines represents steepest path Alternate method km The steepest path will be the path which is deepest from sea level. So, P to R is the steepest path. 9. men and 5 women can build a bridge in weeks. 9men and 5 women will take weeks to build the same bridge. How many men will be needed to build the bridge in one week? (A) (B) (C) 6 (D) 9 (C) Given Men + 5 Women can build a bridge in weeks. And 9 Men + 5 Women will take weeks to build the same bridge To complete in a week; there are 4 Men + W required in the first equation and 7 Men + 75 Women required in the second equation. 4 M + W = 7M + 75W 6M W 5 ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India
EC GATE-7-PAPER-II www.gateforum.com The no. of men required to build the bridge in one week 6M 4M 6 Men 5 Alternate method Let a man can build the bridge in x weeks and a woman can build the bridge in y weeks. 5 So, x y 9 5 x y Byequations i and ii ;weget x 6; y A man build the bridge6 weeks Required men 6 tobuildina week.. If you are looking for a history of India, or for an account of the rise and fall of the British Raj, or for the reason of the cleaving of the subcontinent into two mutually antagonistic parts and the effects this mutilation will have in the respective section, and ultimately on Asia, you will not find it in these pages; for though I have spent a lifetime in the country, I lived too near the seat of events, and was too intimately associated with the actors, to get the perspective needed for the impartial recording of these matters. Which of the following statements best reflects the author s opinion? (A) An intimate association does not allow for the necessary perspective. (B) Matters are recorded with an impartial perspective. (C) An intimate association offers an impartial perspective. (D) Actors are typically associated with the impartial recording of matters. (A) ICP Intensive Classroom Program egate-live Internet Based Classes DLP TarGATE-All India Test Series Leaders in GATE Preparations 65+ Centers across India