Mathematics - Online Test
Q1. The inner (dot) product of two vectors 
and 
is zero. The angle (degrees)
between the two vectors is
and is zero. The angle (degrees)
between the two vectors is
Answer : Option C
Explaination / Solution:
No Explaination.
Q2. If Log(P) = (1/2)Log(Q) = (1/3)Log(R), then which of the following options is
TRUE?
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. The probability that k number of vehicles arrive (i.e. cross a predefined line) in
time t is given as 
where λ is the average vehicle arrival rate. What
is the probability that the time headway is greater than or equal to time t1?
where λ is the average vehicle arrival rate. What
is the probability that the time headway is greater than or equal to time t1?
Answer : Option D
Explaination / Solution:
No Explaination.
Q4. For an analytic function, f(x + iy) = u(x,y) + iv(x,y), u is given by u = 3x2 - 3y2. The expression for v , considering K to be a constant is
Answer : Option D
Explaination / Solution:
No Explaination.
Q5. The partial differential equation 
is a
is a
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. The eigen values of symmetric matrix are all
Answer : Option C
Explaination / Solution:
No Explaination.
Q7. 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.
Q8. If a function is continuous at a point,
Answer : Option D
Explaination / Solution:
No Explaination.
Q9. Divergence of the vector field 
Answer : Option C
Explaination / Solution:
Q10. 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
