Civil Engineering - Online Test
Q1. Consider the differential equation 
with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
with the boundary conditions of y(0) = 0 and y(1) = 1. The complete solution of the differential equation is
Answer : Option A
Explaination / Solution:
No Explaination.
Q2. A box contains 4 red balls and 6 black balls. Three balls are selected randomly from the box one
after another, without replacement. The probability that the selected set contains one red ball and
two black balls is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. Let X be a nominal variable with mean 1 and variance 4. The probability P(X < 0) is
Answer : Option B
Explaination / Solution:
which is greater than zero and less than 0.5
Q4. Choose the CORRECT set of functions, which are linearly dependent.
Answer : Option C
Explaination / Solution:
No Explaination.
Q5. The following surface integral is to be evaluated over a sphere for the given
steady velocity vector field, F = xi + yj + zk defined with respect to a Cartesian
coordinate system having i, j, and k as unit base vectors.
Where S is the sphere, x2 + y2 + z2 = 1 and n is the outward unit normal vector to
the sphere. The value of the surface integral is
Answer : Option A
Explaination / Solution:
Q6. The function f(t) satisfies the differential equation 
and the auxiliary
conditions,
The Laplace transform of f(t) is given by
and the auxiliary
conditions, The Laplace transform of f(t) is given by
Answer : Option C
Explaination / Solution:
Q7. A linear programming problem is shown below:
Maximize 3x + 7y
3x + 7y ≤ 10
Subject to 4x + 6y ≤ 8
x, y ≥ 0
It has
Answer : Option B
Explaination / Solution:
Q8. The probability that a student knows the correct answer to a multiple choice
question is 2/3. If the student does not know the answer, then the student
guesses the answer. The probability of the guessed answer being correct is 1/4. Given that the student has answered the question correctly, the conditional
probability that the student known the correct answer is
Answer : Option D
Explaination / Solution:
A = The student answer the question correctly 
E1 = Student knows the correct answer
E2 = Student guesses the correct answer
Q9. The solution to the differential equation 
where k is a constant,
subjected to the boundary conditions u(0)=0 and u(L)=U, is
where k is a constant,
subjected to the boundary conditions u(0)=0 and u(L)=U, is
Answer : Option B
Explaination / Solution:
Q10. The value of the definite integral 
Answer : Option C
Explaination / Solution:
