GATE Electronics and Communication Test Online

1. The aircraft _______ take off as soon as its flight plan was filed.

2. A continuous, linear time-invariant filter has an impulse response h(t) described by
h(t) =     3 for 0 ≤ t ≤ 3
0    otherwise

3. Let X be a real valued random variable with E[X] and E[X²] denoting the mean values of X and X², respectively. The relation which always holds true is:

4. A 230 V rms source supplies power to two loads connected in parallel. The first load draws 10 kW at 0.8 leading power factor and the second one draws 10 kVA at 0.8 lagging power factor. The complex power delivered by the source is:

5. In the equivalent circuit shown in the figure, if i_in is the input current and R_F is very large, the type of feedback is:

6. A Y network has resistances of 10Ω each in two of its arms, while the third arm has a resistance of 11Ω. In the equivalent Δ-network, the lowest value (in Ω) among the three resistance is _______.

7. Let X₁, X₂ and X₃ be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probablity P{X₁ is the largest} is ________.

8. The volume under the surface z(x, y) = x + y and above the triangle in the x - y plane defined by [0 ≤ x ≤ 12] is _________.

9. Consider a random process X(t) = √2 sin (2πt+φ), where the random phase φ is uniformly distributed in the interval [0, 2π]. The auto correlation E[X(t₁) X(t₂) is

10. For matrices of same dimensions M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?

11. The Taylor series expansion of 3 sin x + 2 cos x is:

12. The exports and imports (in crores and र) of a country from 2000 to 2007 are given in the following bar chart. If the trade deficit is defined as excess of imports over exports, in which year is the trade deficit 1/5th of the exports?

13. If fixed positive charges are present in the gate oxide of an n- channel enhancement type MOSEFT, it will lead to:

14. Consider the feedback system shown in the figure. The Nyquist plot of G(s) is also shown. Which one of the following conclusions is correct?

15. The capacity of Binary Symmetric Channel (BSC) with cross-over probability 0.5 is ________.

16. For the following feedback system G(s) = 1/(s + 1)(s + 2). The 2% settling time of the step response is required to be less than 2 seconds.

Which if the following compensators C(s) achieves this?

17. A train that is 280 meters long, travelling at a uniform speed, crosses a platform in 60 seconds and passes a man standing on the platform in 20 seconds. What is the length of the platform in meters?

18. A real (4 x 4) matrix A satisfies the equation A²  = I, where I is the (4 x 4) identity matrix. The positive eigen value of A is ______

19. The statistics of runs scored in a series by four batsmen are provided in the following table. Who is the most consistent batsman of these four?

20. If the figure, assume that the forward voltage drops on the PN diode D₁ and Schottky diode D₂ are 0.7 V and 0.3 V, respectively. If ON denotes conducting state of the diode and OFF denotes non-conducting state of the diode, then in the circuit,

21. In a code-division multiple access (CDMA) system with N = 8 chips, the maximum number of users who can be assigned mutually orthogonal signature sequences is _____________.

22. Find the amplifier shown in the figure, the BJT parameters are V_BE = 0.7 V, β = 200, and thermal voltage V_T = 25 mV. The voltage gain (v_o/v_i) of the amplifier is _________.

23. Find the odd one from the following group:
W,E,K,O   I,Q,W,A    F,N,T,X     N,V,D,B

24. For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance Z₁ of the first section to the input impedance Z₂

25. A system is described by the following differential equation, where u(t) is the input to the system and y(t) in the output of the system.    y(t) + 5 y(t) = u(t)         When y(0) = 1 and u(t) is a unit step function, y(t) is

26. In the voltage regulator circuit shown in the figure, the op-amp is ideal. The BJT has V = 0.7 V_BE and β = 100, and the zener voltage is 4.7 V. For a regulated output of 9 V, the value of R (in Ω) is ________.

27. C is a closed path in the z-plane given by |z| = 3. The value of the integral C (z² - z + 4j / z + 2j) dz is:

28. Five JK flip-flops are cascaded to form the circuit shown in figure. Clock pulses at a frequency of 1 MHz are applied as shown. The frequency (in kHz) of the waveform at Q₃ is ___________.

29. Consider two real valued signals, x(t) band-limited to [- 500 Hz, 500 Hz] and y (t) band-limited to [-1 kHz, 1 kHz]. For z (t) = x(t) . y(t), the Nyquist sampling frequency (in KHz) is ________.

30. When the optical power incident on a photodiode is 10 μW and the responsivity is 0.8 A/W, the photocurrent generated (in μA) is:

31. A discrete- time single x [n] = sin (π²n), n being an integer, is

32. Many ancient cultures attributed disease to supernatural causes. However, modern science has largely helped ______ such nations.

33. What is the next number in the series?
12   35    81     173   357   _____

34. A BJT is biased in forward active mode. Assume V_BE = 0.7 V, kT/q = 25 mVand reverse saturation current I_s =10^-13 A. The transconductance of the BJT (in mA/V) is _________.

35. In the circuit shown, the op-amp has finite input impedance, infinite voltage gain and zero input offset voltage. The output voltage. The output voltage V_out is

36. Read the sentences:
All women are entrepreneurs.
Some women are doctors.
Which of the following conclusions can be logically inferred from the above sentences?

37. Consider a discrete time periodic signal x[n] = sin (πn/5). Let a_k be the complex Fourier series coefficient of x[n]. The coefficient[a_k] are non-zero when k = Bm ± 1, where m is any integer. The value of B is __________.

38. In a hosing society, half of the families have a single child per family, while the remaining half have two children per family. The probability that a child picked at random, has a sibling is _________.

39. A good current buffer has:

40. In the circuit shown in the figure, the value of capacitor C (in mF) needed to have critically damped response i(t) is ________.