Civil 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 maximum tensile stress at the section X -X shown in the figure below is
Answer : Option A
Explaination / Solution:
No Explaination.
Q3. 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]
Q4. The stepped cantilever is subjected to moments, M as shown in the figure below.
The vertical deflection at the free end (neglecting the self weight) is
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. 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
Q6. The degree of static indeterminacy of the rigid frame having two internal hinges
as shown in the figure below, is
Answer : Option D
Explaination / Solution:
No Explaination.
Q7. 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).
Q8. The members EJ and IJ of a steel truss shown in the figure below, are subjected
to a temperature rise to 30o C. The coefficient of thermal expansion of steel is
0.000012 per oC per unit length. The displacement (mm) of joint E relative to
joint H along the direction HE of the truss, is
Answer : Option C
Explaination / Solution:
No Explaination.
Q9. You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. You choose a coin at random and toss it, and it comes up heads. The probability that the other face is tails is
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. 
The span(s) to be loaded uniformly for maximum positive (upward) reaction at support P, as shown in the figure below, is (are)
Answer : Option D
Explaination / Solution:
No Explaination.
