GATE Electronics online test paper 1
by Esha Upadhyay · Published · Updated
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Question 1 of 17
1. Question
In a baseband communications link, frequencies upto 3500 Hz are used for signaling. Using a raised cosine pulse with 75% excess bandwidth and for no intersymbol interference, the maximum possible signaling rate in symbols per second is
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Question 2 of 17
2. Question
The output Y of a 2bit comparator is logic 1 whenever the 2bit input A is greater than the 2bit input B. The number of combinations for which the output is logic 1, is
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Question 3 of 17
3. Question
The average power delivered to an impedance (4 – j3) ohm by a current 5cos(100 pi t + 100) A is in W
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Question 4 of 17
4. Question
With initial condition x(1) = 0.5 , the solution of the differential equation,
t (dx/dt) + x = t is
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Question 5 of 17
5. Question
A source alphabet consists of N symbols with the probability of the first two symbols being the same. A source encoder increases the probability of the first symbol by a small amount a and decreases that of the second by a . After encoding, the entropy of the source
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Question 6 of 17
6. Question
The radiation pattern of an antenna in spherical coordinates is given by
F (theta ) = cos 4 theta where theta lies between 0 to 180 degree (take 4 as power of cos)
The directivity of the antenna is
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Question 7 of 17
7. Question
Two independent random variables X and Y are uniformly distributed in the interval [–1, 1]. The probability that max[X, Y] is less than 1 2 is
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Question 8 of 17
8. Question
A transmission line with a characteristic impedance of 100 ohm is used to match a 50 ohm section to a 200 ohm section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately
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Question 9 of 17
9. Question
The Fourier transform of a signal h(t) is H( jw) = (2cosw)(sin2w) /w . The value of h(0) is
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Question 10 of 17
10. Question
A fair coin is tossed till a head appears for the first time. The probability that the number of required tosses is odd, is
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Question 11 of 17
11. Question
A binary symmetric channel (BSC) has a transition probability of 1/8. If the binary transmit symbol X is such that P(X=0) = 9/10, then the probability of error for an optimum receiver will be
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Question 12 of 17
12. Question
Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2) to the power (n) u[n] n and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals
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Question 13 of 17
13. Question
The maximum value of f(x) = x3 – 9×2 + 24x + 5 in the interval [1, 6] is (read number after x as power for example x3 is cube of x)
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Question 14 of 17
14. Question
For matrices of same dimension M, N and scalar c, which one of these properties DOES NOT ALWAYS hold?
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Question 15 of 17
15. Question
In a housing 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
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Question 16 of 17
16. Question
A real (4 × 4) matrix satisfies the equation A2 = I (read 2 after A as sqaure of A), where is the (4 × 4) identity matrix. The positive eigen value of A is
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Question 17 of 17
17. Question
Let X1, X2, and X3 be independent and identically distributed random variables with the uniform distribution on [0, 1]. The probability P{X1 is the largest} is
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