Mechanical Engineering - Online Test
Q1. Fine the solution of d2y/dx2 which passes through the origin and the point (In 2,3/4),
Answer : Option C
Explaination / Solution:
Q2. Consider the function f(x) = |x| in the interval -1 ≤ x ≤ 1. At the point x = 0,f(x) is
Answer : Option C
Explaination / Solution:
f(x) = |x| –1 ≤ x ≤ 1
at x = 0
∴ It is continuous.
∴It is not differentiable.
Q3. 
Answer : Option B
Explaination / Solution:
Q4. The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is
Answer : Option A
Explaination / Solution:
Q5. For the spherical surface x2 + y2 + z2 = 1, the unit outward normal vector at the point (1/√2, 1/√2, 0)is given by
Answer : Option A
Explaination / Solution:
To find the direction of normal, take the gradient i.e.
8 unit vector will become
Q6. At x = 0, the function f(x) = x3 + 1 has
Answer : Option D
Explaination / Solution:
So, x = 0 is point of inflexion
Q7. For the matrix 
ONE of the normalized Eigen vectors is given as
ONE of the normalized Eigen vectors is given as
Answer : Option B
Explaination / Solution:
To find eigenvector, first find Eigen-values by solving equation
So for λ = 2, the eigenvector 15
Normalized Eigen Vector
Q8. The inverse Laplace transform of the function F(s) = 1/(s(S+1)) is given by
Answer : Option D
Explaination / Solution:
No Explaination.
Q9. +2y + z = 4
2x + y + 2z = 5
x - y + z = 1
The system of algebraic equation given above has
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. 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.
