EC GATE 2013 - Online Test

Q1.
In a MOSFET operating in the saturation region, the channel length modulation effect causes
Answer : Option D
Explaination / Solution:

In a MOSFET operating in the saturation region, the channel length modulation effect causes a decrease in output resistance.

Q2. The maximum value of ᶿ until which the approximation sin ᶿ=ᶿ holds to within 10% error is 
Answer : Option B
Explaination / Solution:

Here, as we know
  
but for 10% error, we can check option (B) first

so, the error is more than 10%. Hence, for error less than 10%, ᶿ = 18º can have the approximation


Q3.
The bit rate of a digital communication system is R kbits/s. The modulation used is 32-QAM. The minimum bandwidth required for ISI free transmission is
Answer : Option B
Explaination / Solution:

In ideal Nyquist Channel, bandwidth required for ISI (Inter Symbol reference) free transmission is
 
Here, the used modulation is 32 - QAM (Quantum Amplitude modulation
 


Q4.
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid
Answer : Option A
Explaination / Solution:

Given, the maximum frequency of the band-limited signal
fm = 5 kHz
According to the Nyquist sampling theorem, the sampling frequency must be greater than the Nyquist frequency which is given as 

So, the sampling frequency fs must satisfy

only the option (A) does’nt satisfy the condition therefore, 5K HZ is not a valid sampling frequency.


Q5. In the summer of 2012, in New Delhi, the mean temperature of Monday to Wednesday was 41°C and of Tuesday to Thursday was 43 °C. If the temperature on Thursday was 15% higher than that of Monday, then the temperature in °C on Thursday was
Answer : Option C
Explaination / Solution:
No Explaination.


Q6. A car travels 8 km in the first quarter of an hour, 6 km in the second quarter and 16 km in the third quarter. The average speed of the car in km per hour over the entire journey is
Answer : Option C
Explaination / Solution:
No Explaination.


Q7. Find the sum to n terms of the series 10+84+734+......
Answer : Option D
Explaination / Solution:
No Explaination.


Q8. The set of values of p for which the roots of the equation 3x2 + 2x + p(p – 1) = 0  are of opposite sign is
Answer : Option B
Explaination / Solution:
No Explaination.


Q9. What is the chance that a leap year, selected at random, will contain 53 Sundays?
Answer : Option A
Explaination / Solution:

In a leap year, there are 366 days So, 52 weeks will have 52 saturdays and for remaining two days (366 - 52 × 7 = 2) We can have the following combinations
Saturday, Sunday
Sunday, Monday
Monday, Tuesday
Tuesday, Wednesday
Wednesday, Thursday
Thursday, Friday
Friday, Saturday
Out of these seven possibilities, only two consist a saturday. Therefore, the probability of saturday is given as
P = 2/7

Q10. The return loss of a device is found to be 20 dB. The voltage standing wave ratio (VSWR) and magnitude of reflection coefficient are respectively
Answer : Option A
Explaination / Solution: