**Q1. Consider a system of linear equations :**

** x – 2y + 3z = –1,**

** x – 3y + 4z = 1, and**

** –2x + 4y – 6z = k.**

**The value of k for which the system has infinitely many solutions is _______.**

**Solution: Key = 2**

**Q2. A function f(x) = 1 – x ^{2} + x^{3}= is defined in the closed interval [–1, 1]. The value of x, in the open interval (–1, 1) for which the mean value theorem is satisfied, is**

**(A) –1/2 (B) –1/3 (C) 1/3 (D) 1/2**

**Solution: (B)**

**Q3. Suppose A and B are two independent events with probabilities P(A) ≠ 0 and P(B) ≠ 0. Let be their complements. Which one of the following statements is FALSE? **

**(A) P(A ∩ B) = P(A) P(B) (B) P(A|B) = P(A)**

**(C) P(A ∪ B) = P(A) + P(B) (D) **

**Solution: (C)**

**Q4. 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 is NOT TRUE?**

**(A) The residue of at z = 1 is 1/2 (B) **

**(C) (D) **

**Solution: (D)**

**Q5. The value of p such that the vector is an eigenvector of the matrix is**

**Solution: Key = 16.5 to 17.5**

**Q6. In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ______ **

**Solution: Key = 24 to 26**

**Q7. In the network shown in the figure, all resistors are identical with R = 300 Ω. The resistance R _{ab} (in Ω) of the network is ________.**

**Solution: Key = 99.5 to 100.5**

**Q8. In the given circuit, the values of V _{1} and V_{2} respectively are**

**(A) 5 V, 25 V (B) 10 V, 30 V (C) 15 V, 35 V (D) 0 V, 20 V**

**Solution: (A)**

**Q9. A region of negative differential resistance is observed in the current voltage characteristics of 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**

**Solution: (A)**

**Q10. A silicon sample is uniformly doped with donor type impurities with a concentration of 10 ^{16}/cm^{3}. The electron and hole mobilities int eh sample are 1200 cm^{2}/V-s respectively. Assume complete ionization of impurities. The charge of an electron is 1.6 × 10^{−19} C. The resistivity of the sample (in Ω –cm) is _______.**

**Solution: Key = 0.50 to 0.54**

**Q11. For the circuit with ideal diodes shown in the figure, the shape of the output (v _{out}) for the given sin wave input (v_{in}) will be**

**(A) (B) (C) (D) **

**Solution: (C)**

**Q12. In the circuit shown below, the Zener diode is ideal and the Zener voltage is 6 V. The output voltage V _{0}(in volts) is _________.**

**Solution: Key = 5**

**Q13. 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 0.1 μF capacitor from 0V to 3 V is**

**(A) 0.3 (B) 0.45 (C) 0.9 (D) 3**

**Solution: (C)**

**Q14. 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**

**Solution: (B)**

**Q15. A 16 Kb (=16,384 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 _______.**

**Solution: Key = 7**

**Q16. Consider a four bit D to A converter. The analog value corresponding to digital signals of values 0000 and 0001 are 0V and 0.0625 V respectively. The analog value (in Volts) corresponding to the digital signal 1111 is ________. **

**Solution: Key = 0.93 to 0.94**

**Q17. The result of the convolution x(–t) ∗ δ(–t – t _{0}) is**

**(A) (B) (C) (D) **

**Solution: (D)**

**Q18. The waveform of a periodic signal x(t) is shown in the figure.**

**A signal g(t) is defined by The average power of g(t) is _______**

**Solution: Key = 2**

**Q19. 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**

**Solution: (B)**

**Q20. A unit negative feedback system as the open-loop transfer function The value of the gain K(>0) at which the root locus crosses the imaginary axis is __________.**

**Solution: Key = 12**

**Q21. The polar plot of the transfer function for 0 ≤ ω < ∞ will be in the**

**(A) first quadrant (B) second quadrant (C) third quadrant (D) fourth quadrant**

**Solution: (A)**

**Q22. A sinusoidal signal of 2 kHz frequency is applied to a delta modulator. The sampling rate and step-size ∆ of the delta modulator are 20,000 samples per second and 0.1 V, respectively. To prevent slope overload, the maximum amplitude of the sinusoidal signal (in volts) is**

**(A) (B) (C) (D) **

**Solution: (A)**

**Q23. Consider the signal denotes the Hilbert transform of m(t) and the bandwidth of m(t) is very small compared of f _{c}. The single s(t) is a**

**(A) high-pas signal (B) low-pass signal **

**(C) band-pass signal (D) double sideband suppressed carrier signal**

**Solution: (C)**

**Q24. 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} or 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) **

**(C) (D) **

**Solution: (C)**

**Q25. The electric field component of a plane wave traveling in a lossless dielectric medium is given by The wavelength (in m) for the wave is ______**

**Solution: Key = 8.85 to 8.92**

**Q26. The solution of differential equation with y(0) = y′(0) = 1 is **

**(A) (B) (C) (D) **

**Solution: (B)**

**Q27. A vector is given by Which one of the following statements is TRUE?**

**(A) is solenoidal, but not irrotational**

**(B) is irrotational, but not solenoidal**

**(C) is neither solenoidal nor irrotational**

**(D) is both solenoidal and irrotational**

**Solution: (A)**

**Q28. Which one of the following graphs describes the function f(x) = e ^{−x} (x^{2} + x + 1)?**

**(A) (B) **

**(C) (D) **

**Solution: (B)**

**Q29. The maximum area (in square units) of a rectangle whose vertices lie on the ellipse x ^{2} + 4y^{2} = 1 is _________.**

**Solution: Key = 0.95 to 1.05**

**Q30. The damping ratio of a series RLC circuit can be expressed as**

**(A) (B) (C) (D) **

**Solution: (C)**

**Q31. 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 = 1 sec is ______.**

**Solution: Key = 2.48 to 2.58**

**Q32.In the given circuit, the maximum power (in Watts) that can be transferred to the load R _{L} is ________.**

**Solution: Key = 1.6 to 1.7**

**Q33. 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_{R}) of 1.25 V is 5 pF, the value of C_{J} (in pF) when V_{R} = 7.25 V is ________. **

**Solution: Key = 2.4 to 2.6**

**Q34. A MOSFET is saturation has a drain current of mA for V _{DS} = 0.5 V. If the channel length modulation coefficient is 0.05 V^{−1}, the output resistance (in kΩ) of the MOSFET is ________.**

**Solution: Key = 19 to 21**

**Q35. For a silicon diode with long P and N regions, the accepter and donor impurity concentrations are 1 × 10 ^{17} cm^{−}^{3} and 1 × 10^{15} cm^{−}^{3}, respectively. The lifetimes of electrons in P region and holes in N region are both 100 μs. The electron and hole diffusion coefficients are 49 cm^{2}/s and 36cm^{2}/s, respectively. Assume kT/q = 26 mV, the intrinsic carrier concentration is 1 × 10^{10} cm^{−}^{3}, and q = 1.6 × 10^{−}^{19} C. When a forward voltage of 208 mV is applied across the diode, the hole current density (in nA/cm^{2}) injected from P region to N region is __________**

**Solution: Key = 28 to 30**

**Q36. The Boolean expression converted into the canonical product of sum (POS) form is**

**(A) **

**(B) **

**(C) **

**(D) **

**Solution: (A)**

**Q37. All the logic gates shown in the figure have propagation delay of 20 ns. Let A = C = 0 and B = 1 until time t = 0. At t = 0, al the inputs flip (i.e., A = C = 1 and B = 0) and remain in that state. For t > 0, output Z = 1 for a duration (in ns) of**

**Solution: Key = 40**

**Q38. A 3-input majority gate is defined by the logic function M(a, b, c) = ab + bc + ca. Which one of the following gates is represented by the function **

**(A) 3-input NAND gate (B) 3-input XOR gate**

**(C) 3-input NOR gate (D) 3-input XNOR gate**

**Solution: (B)**

**Q39. For the NMOSFET in the circuit shown, the threshold voltage is V _{th}, where V_{th} > 0. The source voltage V_{SS} is varied from 0 to V_{DD}. Neglecting the channel length modulation, the drain current I_{D} as a function of V_{SS} is represented by**

**(A) (B) **

**(C) (D) **

**Solution: (A)**

**Q40. In the circuit shown, assume that the opamp is ideal. The bridge output voltage V _{0}(in mV) for δ = 0.05 is _______.**

**Solution: Key = 249 to 251**

**Q41. The circuit shown in the figure has an ideal opamp. The oscillation frequency and the condition to sustain the oscillations, respectively, are**

**(A) (B) **

**(C) (D) **

**Solution: (D)**

**Q42. In the circuit shown, I _{1} = 80 mA and I_{2} = 4 mA. Transistors, T_{1} and T_{2} are identical. Assume that the thermal voltage V_{T} is 26 mV at 27℃. At 50℃, ,the value of the voltage V_{12} = V_{1} – V_{2}(in mV) is _________.**

**Solution: Key = 83.5 to 84.0**

**Q43. Two sequences [a, b, c] and [A, B, C] are related as,**

**The another sequence [p, q, r] is derived as,**

**then the relationship between the sequences [p, q, r] and [a, b, c] is**

**(A) [p, q, r] = [b, a, c] (B) [p, q, r] = [b, c, a] (C) [p, q, r] = [c, a, b] (D) [p, q, r] = [c, b, a]**

**Solution: (C)**

**Q44. For the discrete-time system shown in the figure, the poles of the system transfer function are located at**

**(A) 2, 3 (B) 1/2, 3 (C) 1/2, 1/3 (D) 2, 1/3 **

**Solution: (C)**

**Q45. The pole-zero diagram of a casual 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[n]. If h[0] = 1, we can conclude**

**(A) h[n] is real for all n (B) h[n] is purely imaginary for all n**

**(C) h[n] is real for only even n (D) h[n] is purely imaginary for only odd n**

**Solution: (A)**

**Q46. The open-loop transfer function of a plant in a unity feedback configuration is given as The value of the gain K(>0) for which −1 + j2 lies on the root locus is _______.**

**Solution: Key = 25 to 26**

**Q47. A lead compensator network includes a parallel combination of R and C in the feed-forward path. If the transfer function of the compensator is the value of RC is ________. **

**Solution: Key = 0.5**

**Q48. A plant transfer function is given as When the plant operates in unity feedback configuration, the condition for the stability of the closed loop system is**

**(A) (B) (C) (D) **

**Solution: (A)**

**Q49. The input X to the Binary Symmetric Channel (BSC) shown in the figure is ‘1’ with probability 0.8. The cross-over probability is 1/7. If the received bit Y = 0, the conditional probability that ‘1’ was transmitted is ______.**

**Solution: Key = 0.39 to 0.41**

**Q50. The transmitted signal in a GSM system is of 200 khZ bandwidth and 8 users share a common bandwidth using TDMA. If at a given time 12 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) _________. **

**Solution: Key = 400**

**Q51. 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 z(t) = 10x (t), the maximum value of W (in Hz) should be strictly less than ________. **

**Solution: Key = 349 to 350**

**Q52. A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as s many as **

**The minimum decision error probability is**

**(A) 0 (B) 1/2 (C) 1/9 (D) 1/6**

**Solution: (D)**

**Q53.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**

** H _{z}(x, y, z, t) = 0.1 cos(25πx) cos(30.3 πy) cos(12π × 10^{9}t – βz ) (A/m)**

**The cross –sectional dimensions of the waveguide are given as a = 0.08 ma dn b = 0.033 m. The mode of propagation inside the waveguide is**

**(A) (B) (C) (D) **

**Solution: (C)**

**Q54. The electric field intensity of a plane wave traveling in free space is given by the following expression**

** E(x, t) = a _{y} 24π cos(ωt – k_{0}x) (V/m)**

**In this field, consider a square area 10 cm x 10 cm on a plane x + y = 1. The total time-averaged power (in mW) passing through the square area is**

**Solution: Key = 53 to 54**

**Q55. Consider a uniform plane wave with amplitude (E _{0}) of 10 V/m and 1.1 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.**

**The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of 10 cm inside the dielectric region is _______.**

**Solution: 0.08 to 0.12**