Engineering Mathematics - Online Test
Q1. The following simultaneous equations x + y + z = 3, x + 2y + 3z = 4, and x + 4y + kz = 6 will NOT have a unique solution for k equal to
Answer : Option D
Explaination / Solution:
No Explaination.
Q2. 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.
Q3. 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.
Q4. 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.
Q5. 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.
Q6. The partial differential equation 
is a
is a
Answer : Option D
Explaination / Solution:
No Explaination.
Q7. The eigen values of symmetric matrix are all
Answer : Option C
Explaination / Solution:
No Explaination.
Q8. 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.
Q9. If a function is continuous at a point,
Answer : Option D
Explaination / Solution:
No Explaination.
Q10. Divergence of the vector field 
Answer : Option C
Explaination / Solution:
