Mechanical Engineering - Online Test
Q1. Let M4 = I, (where I denotes the identity matrix) and M ≠ I, M2 ≠ I and M3 ≠ I. Then, for any
natural number k, M-1 equals:
Answer : Option C
Explaination / Solution:
D is not correct
Q2. Given the following statements about a function
f : R⟶R, select the right option
P: If f(x) is continuous at x = x0, then it is also differentiable at x = x0.
Q: If f(x) is continuous at x = x0, then it may not be differentiable at x = x0.
R: If f(x) is differentiable at x = x0, then it is also continuous at x = x0.
Answer : Option B
Explaination / Solution:
We know that every differentiable function is continuous but converse need not be True
Q3. Which one of the following is a property of the solutions to the Laplace equation: Δ2f = 0?
Answer : Option A
Explaination / Solution:
No Explaination.
Q4. Consider the plot of f(x) versus x as shown below.
Suppose 
Which one of the following is a graph of F(x)?
Which one of the following is a graph of F(x)?
Answer : Option C
Explaination / Solution:
Since the integration of an odd function is even in this logic A and B cannot be the answer as they are odd functions.
However both C and D are even functions but the integration of a linear curve has to be parabolic in nature and it cannot be a constant function. Based on this Option C is correct.
Q5. Consider a two-port network with the transmission matrix: 
If the network is
reciprocal, then
If the network is
reciprocal, then
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. The Laplace transform of the causal periodic square wave of period T shown in the figure
below is 
Answer : Option B
Explaination / Solution:
Q7. Let U and V be two independent zero mean Gaussain random variables of variances 1/4 and 1/9 respectively. The probability 
is
is
Answer : Option B
Explaination / Solution:
No Explaination.
Q8. Let A be an m × n matrix and B an n × m matrix. It is given that determinant (Im + AB) = determinant (In + BA), where Ik is the k × k identity
matrix. Using the above property, the determinant of the matrix given below is
Answer : Option B
Explaination / Solution:
Consider the given matrix be
From the given property
Q9. A system described by the differential equation 
Let
x(t) be a rectangular pulse given by
Let
x(t) be a rectangular pulse given byAssuming that y(0) = 0 and dy/dt = 0 at t = 0, the Laplace transform of y(t) is
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. A system described by a linear, constant coefficient, ordinary, first order
differential equation has an exact solution given by y(t) for t > 0, when the
forcing function is x(t) and the initial condition is y(0). If one wishes to modify
the system so that the solution becomes -2y(t) for t > 0, we need to
Answer : Option D
Explaination / Solution:
No Explaination.
