Civil Engineering - Online Test
Q1. The eigen values of symmetric matrix are all
Answer : Option C
Explaination / Solution:
No Explaination.
Q2. Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a ≠ 0, b ≠ 0 with respective eigenvectors 
. If a ≠ b then x1y1 + x2y2 + x3y3 equals
. If a ≠ b then x1y1 + x2y2 + x3y3 equals
Answer : Option D
Explaination / Solution:
We know that the Eigen vectors corresponding to distinct Eigen values of real symmetric
matrix are orthogonal.
Q3. If a function is continuous at a point,
Answer : Option D
Explaination / Solution:
No Explaination.
Q4. Divergence of the vector field 
Answer : Option C
Explaination / Solution:
Q5. An analytic function of a complex variable z = x + iy is expressed as f(z) = w(x, y) + iv(x, y),
where i = √−1. If u(x, y) = x2 – y2, then expression for v(x, y) in terms of x, y and a general
constant c would be
Answer : Option C
Explaination / Solution:
Given f(z) = w(x, y) + iv(x, y), is analytic and x = x2 - y2
We know that if f(z) = µ+iv is analytic then C-R equations will be satisfied.
∂µ/∂x = ∂v/∂xy and ∂µ/∂y = -∂v/∂x
v = 2xy + c is correct answer
Q6. Consider two solutions x(t) = x1(t) and x(t) and x(t) = x2(t) of the differential equation 
The Wronskian 
The Wronskian
Answer : Option A
Explaination / Solution:
Given Differential equation is
Q7. A series expansion for the function sinθ is
Answer : Option B
Explaination / Solution:
Q8. What is 
equal to?
equal to?
Answer : Option D
Explaination / Solution:
Applying L’ Hospitals rule, we have 
Q9. Eigen values of a real symmetric matrix are always
Answer : Option C
Explaination / Solution:
Eigen values of a real symmetric matrix are always real
Q10. The product of two complex numbers 1 + i and 2-5i is
Answer : Option A
Explaination / Solution:
(1 + i)(2 -5i) = 2 - 5i + 2i + 5 = 7 - 3i
