GATE Electronics online test paper 3
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Question 1 of 15
The phase margin in degrees of
G(s) = 10 / [(s + .1)(s+1)(s+10) ]
calculated using the asymptotic Bode plot isCorrect
Question 2 of 15
Let X be a real-valued random variable with E[X] and E[X*X] denoting the mean values of X and X*X, respectively. The relation which always holds true isCorrect
Question 3 of 15
A fair coin is tossed repeatedly until a ‘Head’ appears for the first time. Let L be the number of tosses to get this first ‘Head’. The entropy H(L) in bits isCorrect
Question 4 of 15
For a parallel plate transmission line, let v be the speed of propagation and Z be the characteristic impedance. Neglecting fringe effects, a reduction of the spacing between the plates by a factor of two results inCorrect
Question 5 of 15
The second moment of a Poisson-distributed random variable is 2. The mean of the random variable isCorrect
Question 6 of 15
Given the following statements about a function f: R→R, select the right option:
P: If f(x) is continuous at x=x0, then it is also differentiable at x=x0
Q: If f(x) is continuous at x=x0, then it may not be differentiable at x=x0.
R: If f(x) is differentiable at x=x0, then it is also continuous at x=x0.Correct
Question 7 of 15
A continuous-time function x(t) is periodic with period T. The function is sampled uniformly with a sampling period Ts. In which one of the following cases is the sampled signal periodic?Correct
Question 8 of 15
A continuous-time sinusoid of frequency 33 Hz is multiplied with a periodic Dirac impulse train of frequency 46 Hz. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of 23 Hz. The fundamental frequency (in Hz) of the output isCorrect
Question 9 of 15
Consider the following statements for a metal oxide semiconductor field effect transistor (MOSFET):
P: As channel length reduces, OFF-state current increases.
Q: As channel length reduces, output resistance increases.
R: As channel length reduces, threshold voltage remains constant.
S: As channel length reduces, ON current increases.
Which of the above statements are INCORRECT?Correct
Question 10 of 15
Match the inferences X, Y, and Z, about a system, to the corresponding properties of the elements of first column in Routh’s Table of the system characteristic equation.
X: The system is stable …
Y: The system is unstable …
Z: The test breaks down …
P: … when all elements are positive
Q: … when any one element is zero
R: … when there is a change in sign of coefficientsCorrect
Question 11 of 15
A closed-loop control system is stable if the Nyquist plot of the corresponding open-loop transfer functionCorrect
Question 12 of 15
Consider binary data transmission at a rate of 56 kbps using baseband binary pulse amplitude modulation (PAM) that is designed to have a raised-cosine spectrum. The transmission bandwidth (in kHz) required for a roll-off factor of 0.25 isCorrect
Question 13 of 15
A superheterodyne receiver operates in the frequency range of 58 MHz − 68 MHz. The intermediate frequency Fi and local oscillator frequency Fl are chosen such that Fi≤Fl. It is required that the image frequencies fall outside the 58MHz − 68 MHz band. The minimum required Fi(in MHz) isCorrect
Question 14 of 15
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal s(t) = 5 cos 1600*pi*t+ 20 cos 1800*pi*t+ 5 cos 2000*pi*t. The value of the modulation index isCorrect
Question 15 of 15
Concentric spherical shells of radii 2 m, 4 m, and 8 m carry uniform surface charge densities of 20nC/m2,-4nC/m2 and Ps respectively.The value of Ps (nC/m2) required to ensure that the electric flux density D = 0 at radius 10m is (note number after m should be read as meter square)Correct