Mechanical Engineering - Online Test
Q1. Let 
The Region of Convergence (ROC) of the z -transform of x[n].
The Region of Convergence (ROC) of the z -transform of x[n].
Answer : Option C
Explaination / Solution:
Given the discrete signal,
So, the z -transform of signal is obtained as
The above series converges, if
Combining the two inequalities, we get
(1/9) < |z| < (1/3)
This is the ROC of the z -transform
Q2. For the configuration shown, the angular velocity of link AB is 10 rad/s
counterclockwise. The magnitude of the relative sliding velocity (in ms-1) of slider
B with respect to rigid link CD is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. The inlet angle of runner blades of a Francis turbine is 90o. The blades are so
shaped that the tangential component of velocity at blade outlet is zero. The flow
velocity remains constant throughout the blade passage and is equal to half of the
blade velocity at runner inlet. The blade efficiency of the runner is
Answer : Option C
Explaination / Solution:
No Explaination.
Q4. A system is described by the following differential equation, where u(t) is the input to the system and y(t) is the output of the system
y(t) + 5y(t) = u(t)
when y(t) = 1 and u(t) is a unit step function, y(t) is
Answer : Option A
Explaination / Solution:
Given the differential equation of the system
y(t) + 5y(t) = u(t)
Applying Laplace transform both the sides,
We obtain the constants A and B as
Substituting there values in equation (1), we get
Taking inverse Laplace transform, we get
Q5. Two pipes of inner diameter 100 mm and outer diameter 110 mm each are joined
by flash-butt welding using 30 V power supply. At the interference, 1 mm of
material melts from each pipe which has a resistance of 42.4Ω. If the unit melt
energy is 64.4 MJm-3, then time required for welding (in s) is
Answer : Option C
Explaination / Solution:
No Explaination.
Q6. The temperature distribution within the thermal boundary layer over a heated
isothermal flat plate is given by 
where
Tw and
T∞ are
the temperature of plate and free stream respectively, and
y is the normal
distance measured from the plate. The local Nusselt number based on the thermal
boundary layer thickness δt is given by
where
Tw and
T∞ are
the temperature of plate and free stream respectively, and
y is the normal
distance measured from the plate. The local Nusselt number based on the thermal
boundary layer thickness δt is given by
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. Consider the state space model of a system, as given below
The system is
Answer : Option B
Explaination / Solution:
Given the state-space model of system
In standard form, we define the state space model as
[X] = A[X] + Bu
y = C[X] + Du
Comparing it to the given space model, we have the matrix
So, we obtain the controllability matrix as
Therefore, the rank of matrix CM is
Rank (CM) = 2 < 3 (order of system)
Hence, the system is uncontrollable
Again, we obtain the observability matrix as
Therefore, the rank of observability matrix is
Rank (OM) = 3 = order of system
Hence, the system is observable.
Q8. A massless beam has a loading pattern as shown in the figure. The beam is of
rectangular cross-section with a width of 30mm and height of 100mm.
The maximum bending moment occurs at
Answer : Option C
Explaination / Solution:
No Explaination.
Q9. In a counter flow heat exchanger, hot fluid enters at 60oC and cold fluid leaves
at 30oC. Mass flow rate of the fluid is 1 kg/s and that of the cold fluid is 2 kg/s.
Specific heat of the hot fluid is 10 kJ/kgK and that of the cold fluid is 5 kJ/kgK.
The Log Mean Temperature Difference (LMTD) for the heat exchanger in oC is
Answer : Option B
Explaination / Solution:
No Explaination.
Q10. A discrete random variable X takes values from 1 to 5 with probabilities as shown in the table. A student calculates the mean X as 3.5 and her teacher calculates the variance of X as 1.5. Which of the following statements is true ?
Answer : Option B
Explaination / Solution:
