EC GATE 2010 - Online Test
Q1. Suppose that the modulating signal is 
and the carrier signal is 
, which one of the following is a conventional AM signal without over-modulation
and the carrier signal is , which one of the following is a conventional AM signal without over-modulation
Answer : Option C
Explaination / Solution:
No Explaination.
Q2. If 137 + 276 = 435 how much is 731 + 672 ?
Answer : Option C
Explaination / Solution:
Since 7 + 6 = 13 but unit digit is 5 so base may be 8 as 5 is the remainder when 13 is divided by 8. Let us check.
1378 7318
2768 6728
435 1632
Thus here base is 8. Now
Q3. Consider an angle modulated signal 
The average power of x(t) is
The average power of x(t) is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. 5 skilled workers can build a wall in 20 days; 8 semi-killed worker can build a wall in 25 days; 10 unskilled workers can build a wall in 30 days. If a team has 2 killed, 6 semi-killed and 5 unskilled workers, how long will it take to build the wall
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. If the scattering matrix [S ] of a two port network is 
then the network is
then the network is
Answer : Option C
Explaination / Solution:
Q6. Given digits 2, 2, 3, 3, 4, 4, 4 how many distinct 4 digit numbers greater than 3000 can be formed
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. A transmission line has a characteristic impedance of 50 Ω and a resistance of 0.1Ω/m . If the line is distortion less, the attenuation constant(in Np/m) is
Answer : Option D
Explaination / Solution:
For distortion less transmission line characteristics impedance
Q8. Hari(H), Gita(G), Irfan(I) and Saira(S) are sibilings (i.e. brothers and sisters). All were born on Ist January. The age difference between any two successive siblings (that is born one after another) is less than 3 years. Given the following facts:
(i) Hari’s age + Gita’s age > Irfan’s age + Saira’s age
(ii) The age difference between Gita and Saira is 1 year. However, Gita is not the oldest and Saira is not the youngest
(iii) There are not twins.
In what order were they born (oldest first)
Answer : Option B
Explaination / Solution:
Let H , G, S and I be ages of Hari, Gita, Saira and Irfan respectively.
Now from statement (1) we have H + G > I + S
Form statement (2) we get that G - S = 1 or S - G = 1
As G can’t be oldest and S can’t be youngest thus either GS or SG possible.
From statement (3) we get that there are no twins
(A) HSIG : There is I between S and G which is not possible
(B) SGHI : SG order is also here and S > G > H > I andG + H > S + I which is possible.
(C) IGSH : This gives I > G and S > H and adding these both inequalities we have I + S > H + G which is not possible.
(D) IHSG : This gives I > H and S > G and adding these both inequalities we have I + S > H + G which is not possible.
Q9. The Nyquist sampling rate for the signal 
is given by
is given by
Answer : Option C
Explaination / Solution:
S(t) = sinc(500t) sinc(700t)
S(f ) is convolution of two signals whose spectrum covers f1 = 250 Hz and f2 = 350 Hz. So convolution extends
f = 25 + 350 = 600 Hz
Nyquist sampling rate
N = 2f = 2#600 = 1200 Hz
Q10. X(t) is a stationary process with the power spectral density Sx(f)>0, for all f . The process is passed through a system shown below
Let Sy (f ) be the power spectral density of Y(t). Which one of the following statements is correct
Answer : Option D
Explaination / Solution:
