Mechanical Engineering - Online Test
Q1. 
A source emits bit 0 with probability 1/3 and bit 1 with probability 2/3. The emitted bits are communicated to the receiver. The receiver decides for either 0 or 1 based on the received value R. It is given that the conditional density functions of R are as
The minimum decision error probability is
Answer : Option D
Explaination / Solution:
Given the conditional density function of R as
Decision error probability that receiver decides 0 for a transmitted bit 1 is
fR/1 (r =
0) = 1/6
Again, the decision error probability that receiver decides 1 for a transmitted bit 0 is
fR/0 (r = 1) = 1/4
Hence, the minimum decision error probability is
fR/1 (r = 0) = 1/6
Q2. The natural frequency of a spring-mass system on earth is ωn. The natural
frequency of this system on the moon (gmoon = gearth/ 6) is
Answer : Option A
Explaination / Solution:
No Explaination.
Q3. A moist air sample has dry bulb temperature of 30ºC and specific humidity of
11.5g water vapour per kg dry air. Assume molecular weight of air as 28.93. If
the saturation vapour pressure of water at 30ºC is 4.24kPa and the total pressure
is 90kPa, then the relative humidity (in %) of air sample is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. Two sequences [a, b, c] and [A, B, C ] are related as.
If another sequence [p, q , r ] is derived as,
then the relationship between the sequences [p, q , r ] and [a, b, c] is
Answer : Option C
Explaination / Solution:
Given relation is
Comparing it with the DFT concept of taking fourier transform by matrix form. We may calculate that here we are taking the 3 order DFT of [a b c]T whose
transformed output is [A B C]T . So,
Again, we consider the equation (1),
Since, the relation between cube roots of unity is given as
So, we solve the matrix equation as
Again, we consider the equation (2),
In above equation, we apply elementary row operation as
Hence, we can conclude that
[p q r] =[c a b]
Q5. Tooth interference in an external involute spur gear pair can be reduced by
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. In a steam power plant operating on the Rankine cycle, steam enters the turbine at
4MPa, 350ºC and exits at a pressure of 15kPa. Then it enters the condenser and exits as
saturated water. Next, a pump feeds back the water to the boiler. The adiabatic
efficiency of the turbine is 90%. The thermodynamic states of water and steam are
given in the table.
h is specific enthalpy, s is specific entropy and v the specific volume; subscripts f and g
denote saturated liquid state and saturated vapour state.
The net work output (kJ kg-1) of the cycle is
Answer : Option C
Explaination / Solution:
No Explaination.
Q7. The solution of the differential equation 
is
is
Answer : Option B
Explaination / Solution:
We have the differential equation,
Given equation is linear constant coefficient differential equation. Let
Q8. For the stability of a floating body, under the influence of gravity alone, which of
the following is TRUE?
Answer : Option B
Explaination / Solution:
No Explaination.
Q9. In a steam power plant operating on the Rankine cycle, steam enters the turbine at
4MPa, 350ºC and exits at a pressure of 15kPa. Then it enters the condenser and exits as
saturated water. Next, a pump feeds back the water to the boiler. The adiabatic
efficiency of the turbine is 90%. The thermodynamic states of water and steam are
given in the table.
h is specific enthalpy, s is specific entropy and v the specific volume; subscripts f and g
denote saturated liquid state and saturated vapour state.
Heat supplied (kJ kg-1) to the cycle is
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. Which one of the following graphs describes the function 
Answer : Option B
Explaination / Solution:
This condition is satisfied by the graph shown in option (B).
