Q. 1 Q. 25 carry one mark each.

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1 Q. Q. 5 carry one mark each. Q. Consider a system of linear equations: x y 3z =, x 3y 4z =, and x 4y 6 z = k. The value of k for which the system has infinitely many solutions is. Q. A function 3 = is defined in the closed interval [, ] f ( x) x x open interval (, ) for which the mean value theorem is satisfied, is. The value of x, in the (A) (B) 3 (C) 3 (D) / Q.3 Suppose and B are two independent events with probabilities () 0 and () 0. Let and be their complements. Which one of the following statements is FALSE? (A) ( ) =()() (C) ( ) =() () (B) ( ) =() (D) =() Q.4 Let z = x iy be a complex variable. Consider that contour integration is performed along the unit circle in anticlockwise direction. Which one of the following statements is NOT TUE? z (A) The residue of z at z = is / (B) = 0 (C) = (D) z (complex conjugate of z ) is an analytical function Q.5 4 The value of p such that the vector is an eigenvector of the matrix is Q.6 In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is. EC /3

2 Q.7 In the network shown in the figure, all resistors are identical with = 300 Ω. The resistance ab (in Ω) of the network is. a = 300 Ω ab b Q.8 In the given circuit, the values of V and Vrespectively are 4Ω Ι Ι V 5A 4Ω 4Ω - - V (A) 5 V, 5 V (B) 0 V, 30 V (C) 5 V, 35 V (D) 0 V, 0 V Q.9 A region of negative differential resistance is observed in the current voltage characteristics of a silicon PN junction if (A) both the P-region and the N-region are heavily doped (B) the N-region is heavily doped compared to the P-region (C) the P-region is heavily doped compared to the N-region (D) an intrinsic silicon region is inserted between the P-region and the N-region Q.0 A silicon sample is uniformly doped with donor type impurities with a concentration of 0 6 /cm 3. The electron and hole mobilities in the sample are 00 cm /V-s and 400 cm /V-s respectively. Assume complete ionization of impurities. The charge of an electron is C. The resistivity of the sample (in Ω-cm) is. EC /3

3 Q. For the circuit with ideal diodes shown in the figure, the shape of the output ( ) for the given sine wave input ( ) will be 0 0.5T T v in v out (A) (B) 0 0.5T T 0 0.5T T (C) (D) 0 0.5T T 0 0.5T T Q. In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output voltage (in volts) is. kω 0V kω V O - Q.3 In the circuit shown, the switch SW is thrown from position A to position B at time t = 0. The energy (in μj) taken from the 3 V source to charge the 0. μf capacitor from 0 V to 3 V is 3 V 0 Ω SW B A t = 0 0. μf (A) 0.3 (B) 0.45 (C) 0.9 (D) 3 EC 3/3

4 Q.4 In an 8085 microprocessor, the shift registers which store the result of an addition and the overflow bit are, respectively (A) B and F (B) A and F (C) H and F (D) A and C Q.5 A 6 Kb (=6,384 bit) memory array is designed as a square with an aspect ratio of one (number of rows is equal to the number of columns). The minimum number of address lines needed for the row decoder is. Q.6 Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 000 are 0 V and V respectively. The analog value (in Volts) corresponding to the digital signal is. Q.7 The result of the convolution ( ) ( ) is (A) ( ) (B) ( ) (C) ( ) (D) ( ) Q.8 The waveform of a periodic signal x() t is shown in the figure. x(t) t -3 A signal gt () is defined by t gt () = x. The average power of gt () is. Q.9 Negative feedback in a closed-loop control system DOES NOT (A) reduce the overall gain (B) reduce bandwidth (C) improve disturbance rejection (D) reduce sensitivity to parameter variation Q.0 A unity negative feedback system has the open-loop transfer function () = ()(3). The value of the gain K (>0) at which the root locus crosses the imaginary axis is. Q. The polar plot of the transfer function () = 0() 0 for 0 ω < will be in the (A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant EC 4/3

5 Q. A sinusoidal signal of khz frequency is applied to a delta modulator. The sampling rate and step-size Δ of the delta modulator are 0,000 samples per second and 0. V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in Volts) is (A) π (C) π (B) π (D) π Q.3 Consider the signal st () = mt ()cos( π ft) ˆ c mt ()sin( π ft c ) where mt ˆ () denotes the Hilbert transform of mt () and the bandwidth of mt () is very small compared to f c. The signal st () is a (A) high-pass signal (B) low-pass signal (C) band-pass signal (D) double sideband suppressed carrier signal Q.4 Consider a straight, infinitely long, current carrying conductor lying on the z-axis. Which one of the following plots (in linear scale) qualitatively represents the dependence of H φ on r, where H φ is the magnitude of the azimuthal component of magnetic field outside the conductor and r is the radial distance from the conductor? (A) (B) H φ H φ (C) r (D) r H φ H φ r r Q.5 The electric field component of a plane wave traveling in a lossless dielectric medium is given by r 8 z Ezt (,) = aˆ y cos0 t V/m. The wavelength (in m) for the wave is. EC 5/3

6 Q. 6 Q. 55 carry two marks each. Q.6 The solution of the differential equation d y dy y = 0 with y(0) = y (0) = is dt dt (A) ( te ) t (B) ( te ) (C) ( te ) (D) ( te ) t Q.7 A vector is given by =. Which one of the following statements is TUE? (A) is solenoidal, but not irrotational (B) is irrotational, but not solenoidal (C) is neither solenoidal nor irrotational (D) is both solenoidal and irrotational Q.8 Which one of the following graphs describes the function f(x) = (x x)? (A) (B) (C) (D) Q.9 The maximum area (in square units) of a rectangle whose vertices lie on the ellipse. x 4y = is Q.30 The damping ratio of a series LC circuit can be expressed as (A) C L L (B) C (C) C L (D) L C EC 6/3

7 Q.3 In the circuit shown, switch SW is closed at t = 0. Assuming zero initial conditions, the value of v c (t) (in Volts) at t = sec is. t = 0 3 Ω SW 0 V Ω 5 F 6 v c (t) Q.3 In the given circuit, the maximum power (in Watts) that can be transferred to the load L is. Ω 4 0 V rms jω L Q.33 The built-in potential of an abrupt p-n junction is 0.75 V. If its junction capacitance (C J ) at a reverse bias (V ) of.5 V is 5 pf, the value of C J (in pf) when V = 7.5 V is. Q.34 A MOSFET in saturation has a drain current of ma for V DS = 0.5 V. If the channel length modulation coefficient is 0.05 V -, the output resistance (in kω) of the MOSFET is. Q.35 For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are 0 7 cm -3 and 0 5 cm -3, respectively. The lifetimes of electrons in P region and holes in N region are both 00 µs. The electron and hole diffusion coefficients are 49 cm /s and 36 cm /s, respectively. Assume kt/q = 6 mv, the intrinsic carrier concentration is 0 0 cm -3, and q = C. When a forward voltage of 08 mv is applied across the diode, the hole current density (in na/cm ) injected from P region to N region is. Q.36 The Boolean expression F(X,Y,Z) = X Y Z X Y ZX Y Z X Y Z converted into the canonical product of sum (POS) form is (A) (XYZ)(XYZ)(XYZ)(XYZ) (C) (XYZ)(XYZ)(XYZ)(XYZ) (B) (XYZ)(XYZ)(XYZ)(XYZ) (D) (XYZ)(XYZ)(XYZ)(XYZ) EC 7/3

8 Q.37 All the logic gates shown in the figure have a propagation delay of 0 ns. Let A = C = 0 and B = until time t = 0. At t = 0, all the inputs flip (i.e., A = C = and B = 0) and remain in that state. For t > 0, output Z = for a duration (in ns) of. Q.38 A 3-input majority gate is defined by the logic function M ( abc,, ) = ab bc ca. Which one of the following gates is represented by the function M ( M( a, b, c), M( a, b, c), c )? (A) 3-input NAND gate (C) 3-input NO gate (B) 3-input XO gate (D) 3-input XNO gate Q.39 For the NMOSFET in the circuit shown, the threshold voltage is, where > 0. The source voltage is varied from 0 to. Neglecting the channel length modulation, the drain current as a function of is represented by V DD V SS (A) (B) I D I D V SS V SS V DD V th V th (C) (D) I D I D V DD - V th V SS V DD V th V SS EC 8/3

9 Q.40 In the circuit shown, assume that the opamp is ideal. The bridge output voltage V 0 (in mv) for δ = 0.05 is. 50 (δ) Ω 50 (-δ) Ω 00 Ω V V 0 50 (-δ) Ω 50 (δ) Ω 00 Ω 50 Ω Q.4 The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are v out C C (A) and = C (C) and = C (B) C and = 4 (D) C and = 4 Q.4 In the circuit shown, I = 80 ma and I = 4 ma. Transistors T and T are identical. Assume that the thermal voltage V T is 6 mv at 7 o C. At 50 o C, the value of the voltage V = V V (in mv) is. V S I V V I V T T EC 9/3

10 Q.43 Two sequences [ abcand,, ] [,, ] ABC are related as, A a π j 3 B W3 W 3 b = where W3 = e. 4 C W3 W 3 c If another sequence [ p, qr, ] is derived as, p 0 0 A/3 q W3 W 3 0 W3 0 B/3 =, 4 4 r W3 W W 3 C/3 then the relationship between the sequences [ p, qr, ] and [ abc,, ] is (A) [ p, qr, ] = [ bac,, ] (B) [ p, qr, ] = [ bca,, ] (C) [ p, qr, ] = [ cab,, ] (D) [ p, qr, ] = [ cba,, ] Q.44 For the discrete-time system shown in the figure, the poles of the system transfer function are located at X[n] Y[n] (A), 3 (B),3 (C), (D), Q.45 The pole-zero diagram of a causal and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity 4. The impulse response of the system is h[]. If h[0] =, we can conclude Im(z) e(z) -0.5 (A) h[] is real for all (B) h[] is purely imaginary for all (C) h[] is real for only even (D) h[] is purely imaginary for only odd EC 0/3

11 Q.46 The open-loop transfer function of a plant in a unity feedback configuration is given as Ks ( 4) Gs () =. The value of the gain K ( > 0) for which j lies on the root locus is ( s 8)( s 9). Q.47 A lead compensator network includes a parallel combination of and C in the feed-forward path. If s the transfer function of the compensator is Gc () s =, the value of C is. s 4 Q.48 K I A plant transfer function is given as Gs () = KP. When the plant operates in a s s( s ) unity feedback configuration, the condition for the stability of the closed loop system is KI (A) K P > > 0 (B) KI > KP > 0 (C) K I < K P (D) K I > K P Q.49 The input X to the Binary Symmetric Channel (BSC) shown in the figure is with probability 0.8. The cross-over probability is /7. If the received bit Y = 0, the conditional probability that was transmitted is. P[X = 0] = 0. X Y 6/7 0 0 /7 /7 P[X = ] = 0.8 6/7 Q.50 The transmitted signal in a GSM system is of 00 khz bandwidth and 8 users share a common bandwidth using TDMA. If at a given time users are talking in a cell, the total bandwidth of the signal received by the base station of the cell will be at least (in khz). EC /3

12 Q.5 In the system shown in Figure (a), m(t) is a low-pass signal with bandwidth W Hz. The frequency response of the band-pass filter H( f ) is shown in Figure (b). If it is desired that the output signal () = 0(), the maximum value of (in Hz) should be strictly less than. x(t) = m(t) cos(400πt) Amplifier y(t) = 0x (t) x (t) H( f ) Band-pass filter z(t) (a) H( f ) (b) f (Hz) Q.5 A source emits bit 0 with probability 3 and bit with probability. The emitted bits are 3 communicated to the receiver. The receiver decides for either 0 or based on the received value. It is given that the conditional density functions of are as f 0, 3 x,, x 5, () r = 4 and f() r = 6 0, otherwise, 0, otherwise. The minimum decision error probability is (A) 0 (B) / (C) /9 (D) /6 Q.53 The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression (,,, ) =0. cos(5) cos(30.3 ) cos( 0 ) (/) The cross-sectional dimensions of the waveguide are given as = 0.08 and = The mode of propagation inside the waveguide is (A) TM (B) TM (C) TE (D) TE Q.54 The electric field intensity of a plane wave traveling in free space is given by the following expression (, ) = 4 cos( ) (V/m) In this field, consider a square area 0 cm x 0 cm on a plane =. The total time-averaged power (in mw) passing through the square area is. EC /3

13 Q.55 Consider a uniform plane wave with amplitude (E 0 ) of 0 V/m and. GHz frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity (ε r ) and permeability (μ r ) as shown in the figure. Air η = 0πΩ Dielectric μ r = j ε r = j 0 cm E =? E 0 = 0 V/m Freq =. GHz The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 0 cm inside the dielectric region is. END OF THE QUESTION PAPE EC 3/3

Answer Key. Electronics Engineering GATE Forenoon Session 31st Jan, Write us at Phone: ,

Answer Key. Electronics Engineering GATE Forenoon Session 31st Jan, Write us at Phone: , Answer Key of Electronics Engineering GATE-2015 Forenoon Session 31st Jan, 2015 Write us at info@madeeasy.in Phone: 011-45124612, 9958995830 www.madeeasy.in Page 1 Section - I (General Aptitude) Q.1 Choose