Mechanical Engineering - Online Test
Q1. 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 magnitude of bending stress (in MPa) is given by
Answer : Option B
Explaination / Solution:
No Explaination.
Q2. The average heat transfer co-efficient on a thin hot vertical plate suspended in still
air can be determined from observations of the change in plate temperature with
time as it cools. Assume the plate temperature to be uniform at any instant of
time and radiation heat exchange with the surroundings negligible. The ambient
temperature is 25oC, the plat has a total surface area of 0.1m2 and a mass of
4 kg. The specific heat of the plate material is 2.5 kJ/kgK. The convective heat
transfer co-efficient in W/m2K, at the instant when the plate temperature is
225oC and the change in plate temperature with time dT/dt = -0.02 K/s, is
Answer : Option D
Explaination / Solution:
No Explaination.
Q3. Let X be a real-valued random variable with E[X] and E[X2] denoting the
mean values of X and X2 , respectively. The relation which always holds true is
Answer : Option B
Explaination / Solution:
No Explaination.
Q4. In a shear cutting operation, a sheet of 5mm thickness is cut along a length of 200mm.
The cutting blade is 400mm long and zero-shear (S=0) is provided on the edge. The
ultimate shear strength of the sheet is 100MPa and penetration to thickness ratio is 0.2.
Neglect friction.
Assuming force vs displacement curve to be rectangular, the work done (in J) is
Answer : Option A
Explaination / Solution:
No Explaination.
Q5. The stroke and bore of a four stroke spark ignition engine are 250 mm and
200 mmrespectively. The clearance volume is 0.001 m3. If the specific heat ratio γ = 1.4, the air-standard cycle efficiency of the engine is
Answer : Option C
Explaination / Solution:
No Explaination.
Q6. Consider a random process 
where the random
phase 
is uniformly distributed in the interval [0, 2π]. The auto-correlation E[X(t1) X(t2)] is
where the random
phase is uniformly distributed in the interval [0, 2π]. The auto-correlation E[X(t1) X(t2)] is
Answer : Option D
Explaination / Solution:
We have the random process
Where random phase ϕ is uniformly distributed in the interval [0, 2π]. So, we
obtain the probability density function as
fϕ(ϕ)= 1/2π
Therefore, the auto-correlation is given as
Using the trigonometric relation,
Q7. In a shear cutting operation, a sheet of 5mm thickness is cut along a length of 200mm.
The cutting blade is 400mm long and zero-shear (S=0) is provided on the edge. The
ultimate shear strength of the sheet is 100MPa and penetration to thickness ratio is 0.2.
Neglect friction.
A shear of 20mm (S=20mm) is now provided on the blade. Assuming force vs
displacement curve to be trapezoidal, the maximum force (in kN) exerted is
Answer : Option D
Explaination / Solution:
No Explaination.
Q8. A building has to be maintained at 21oC (dry bulb) and 14.5oC (wet bulb).
The dew point temperature under these conditions is 10.17oC. The outside
temperature is
-23oC (dry bulb) and the internal and external surface heat
transfer coefficients are 8 W/m2K and 23 W/m2K respectively. If the building
wall has a thermal conductivity of 1.2 W/m K, the minimum thickness (in m) of
the wall required to prevent condensation is
Answer : Option B
Explaination / Solution:
No Explaination.
Q9.
The minimum eigen value of the following matrix is
Answer : Option A
Explaination / Solution:
For, a given matrix [A] the eigen value is calculated as 
where 
gives the eigen values of matrix. Here, the minimum eigen value among the given options is 
We check the characteristic equation of matrix for this eigen value
where gives the eigen values of matrix. Here, the minimum eigen value among the given options is We check the characteristic equation of matrix for this eigen value= 3(60 - 49h- 5(25 - 14)+ 2)35 - 24h
= 33 - 55 + 22
= 0
Hence, it satisfied the characteristic equation and so, the minimum eigen value is
Q10. In a simply-supported beam loaded as shown below, the maximum bending
moment in Nm is
Answer : Option B
Explaination / Solution:
No Explaination.
