# Gate/GATE ECE Mcq Sample Test,Sample questions

## 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`

1.1/3

2.1/2

3.2/3

4.3/4

Posted Date:-2022-03-15 10:56:32

## Question: ``` One of the parts (A, B, C, D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT? I requested that he should be given the driving test today instead of tomorrow. ```

1. requested that

2.should be given

3.the driving test

Posted Date:-2022-03-15 11:25:39

## Question: ``` The electric field of a uniform plane electromagnetic wave in free space, along the positive x direction, is given by . The frequency and polarization of the wave, respectively, are ```

1. 1.2 GHz and left circular

2.4 Hz and left circular

3.1.2 GHz and right circular

4.4 Hz and right circular

Posted Date:-2022-03-15 10:37:42

## Question: ``` The output Y of a 2-bit comparator is logic 1 whenever the 2-bit input A is greater than the 2-bit input B. The number of combinations for which the output is logic 1, is ```

1.4

2.6

3.8

4.10

Posted Date:-2022-03-15 10:39:10

## Question: `A and B are friends. They decide to meet between 1 PM and 2 PM on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is`

1.1/4

2.1/16

3.7/16

4.9/16

Posted Date:-2022-03-15 11:51:47

## 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 ```

1.7/80

2.63/80

3. 9/10

4.1/10

Posted Date:-2022-03-15 10:57:53

## Question: `A BPSK scheme operating over an AWGN channel with noise power spectral density of N0 / 2 , uses equiprobable signals s1(t) = âˆš2E/T sin(wc t) and s2(t) = -âˆš2E/T sin(wc t) over the symbol interval (0, T). If the local oscillator in a coherent receiver is ahead in phase by 45o with respect to the received signal, the probability of error in the resulting system is`

1. Q(âˆš2E/N0)

2.Q(âˆšE/N0)

3. Q(âˆšE/2N0)

4.Q(âˆšE/4N0)

Posted Date:-2022-03-15 10:52:24

## 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 ÃŽÂµ and decreases that of the second by ÃŽÂµ . After encoding, the entropy of the source`

1.increases

2.remains the same

3. increases only if N = 2

4.decreases

Posted Date:-2022-03-15 10:44:13

## Question: ```A system with transfer function G(s) = [(s2 + 9)(s + 2)] / [(s + 1)(s + 3)(s + 4)] is excited by sin(w t) . The steady-state output of the system is zero at```

Posted Date:-2022-03-15 10:46:59

## Question: ```A transmission line with a characteristic impedance of 100 Ã¢â€žÂ¦ is used to match a 50 Ã¢â€žÂ¦ section to a 200 Ã¢â€žÂ¦ section. If the matching is to be done both at 429 MHz and 1 GHz, the length of the transmission line can be approximately ```

1.82.5 cm

2.1.05 m

3.1.58 m

4.1.75 m

Posted Date:-2022-03-15 10:53:31

## Question: ```An infinitely long uniform solid wire of radius a carries a uniform dc current of density j. The magnetic field at a distance r from the center of the wire is proportional to```

1.r for r < a and 1/r2 for r > a

2.0 for r < a and 1/r for r > a

3.r for r < a and 1/r for r > a

4.0 for r < a and 1/r2 for r > a

Posted Date:-2022-03-15 11:00:41

## Question: ```If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 = ```

1.2.23

2.4.33

3.11.37

4.27.64

Posted Date:-2022-03-15 11:04:40

## Question: ```If x = âˆš-1 , then the value of xx is ```

1.e-Ãâ‚¬/2

2.eÃâ‚¬/2

3.x

4.1

Posted Date:-2022-03-15 10:50:29

## Question: ```If x[n] = (1/3)|n| - (1/ 2)n u[n], then the region of convergence (ROC) of its Z-transform in the Z-plane will be ```

1.1/3 < |z| < 3

2.1/3 < |z| < 1/2

3.1/2 < |z| < 3

4.1/3 < |z|

Posted Date:-2022-03-15 10:46:02

## 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 inter-symbol interference, the maximum possible signaling rate in symbols per second is ```

1.1720

2.2625

3.4000

4.5250

Posted Date:-2022-03-15 10:36:57

## Question: ```Let y[n] denote the convolution of h[n] and g[n], where h[n] = (1/2)n u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals ```

1.0

2.1/2

3.1

4.3/2

Posted Date:-2022-03-15 10:58:59

## Question: `The average power delivered to an impedance (4 - j3) Ã¢â€žÂ¦ by a current 5cos(100Ãâ‚¬ t + 100) A is`

1.44.2 W

2.50 W

3.62.5 W

4.125 W

Posted Date:-2022-03-15 10:41:25

## Question: `The current ib through the base of a silicon npn transistor is 1 + 0.1 cos(10000 Ãâ‚¬ t) mA. At 300 K, the rÃâ‚¬ in the small signal model of the transistor is`

1.250 Ã¢â€žÂ¦

2.27.5 Ã¢â€žÂ¦

3.25 Ã¢â€žÂ¦

4.22.5 Ã¢â€žÂ¦

Posted Date:-2022-03-15 10:35:22

## Question: ```The Fourier transform of a signal h(t) is H(jw) = (2cosw)(sin2w) /w . The value of h(0) is ```

1.1/4

2.1/2

3.1

4.2

Posted Date:-2022-03-15 10:55:26

## Question: `The input x(t) and output y(t) of a system are related as y(t) = . The system is`

1.time-invariant and stable

2.stable and not time-invariant

3.time-invariant and not stable

4.not time-invariant and not stable

Posted Date:-2022-03-15 10:54:24

## Question: ```The maximum value of f(x) = x3 - 9x2 +24x + 5 in the interval [1, 6] is ```

1.21

2.25

3.41

4.46

Posted Date:-2022-03-15 10:59:37

## Question: `The power spectral density of a real process X(t) for positive frequencies is shown below. The values of E[X2(t)] and E[X(t)] , respectively, are`

1.6000/Ãâ‚¬, 0

2.6400/Ãâ‚¬, 0

3.6400/Ãâ‚¬, 20/(Ãâ‚¬ âˆš2)

4. 6000/Ãâ‚¬, 20/(Ãâ‚¬ âˆš2)

Posted Date:-2022-03-15 10:36:23

## Question: ```The radiation pattern of an antenna in spherical co-ordinates is given by F(ÃŽÂ¸) = cos4 ÃŽÂ¸; 0 Ã¢â€°Â¤ ÃŽÂ¸ Ã¢â€°Â¤ Ãâ‚¬ /2 The directivity of the antenna is```

1.10 dB

2.12.6 dB

3.11.5 dB

4.18 dB

Posted Date:-2022-03-15 10:45:12

## Question: `The source of a silicon (ni = 1010 per cm3) n-channel MOS transistor has an area of 1 sq ÃŽÂ¼m and a depth of 1 ÃŽÂ¼m. If the dopant density in the source is 1019/cm3, the number of holes in the source region with the above volume is approximately`

1.107

2.100

3.10

4.0

Posted Date:-2022-03-15 10:51:16

## Question: ```The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). Gc (s) is a lead compensator if ```

1. a =1, b = 2

2.a = 3, b = 2

3.a = "â€œ3, b = "â€œ1

4.a = 3, b = 1

Posted Date:-2022-03-15 11:02:33

## Question: ```The transfer function of a compensator is given as Gc (s) = (s + a)/(s + b). The phase of the above lead compensator is maximum at ```

Posted Date:-2022-03-15 11:03:25

## Question: `The unilateral Laplace transform of f(t) is 1/(s2 + s + 1). The unilateral Laplace transform of t f (t) is`

1.- s/(s2 + s + 1)2

2.- (2s + 1)/(s2 + s + 1)2

3. s/(s2 + s + 1)2

4.(2s + 1)/(s2 + s + 1)2

Posted Date:-2022-03-15 10:42:17

## Question: `Two independent random variables X and Y are uniformly distributed in the interval [â€œ1, 1]. The probability that max[X, Y] is less than 1 2 is`

1.3/4

2.9/16

3.1/4

4.2/3

Posted Date:-2022-03-15 10:49:16

## Question: ```With initial condition x(1) = 0.5 , the solution of the differential equation, t dx/dt + x = t is ```

1.x = t - 1/2

2. x = t2 - 1/2

3.x = t2/2

4.x = t/2

Posted Date:-2022-03-15 10:43:05

## More MCQS

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