Mechanical Engineering - Online Test
Q1. Which one of the following statements is true for all real symmetric matrices?
Answer : Option A
Explaination / Solution:
Eigen values of a real symmetric matrix are all real
Q2. A hole is dimension 
mm. The corresponding shaft is of dimension 
mm. The resulting assembly has
mm. The corresponding shaft is of dimension mm. The resulting assembly has
Answer : Option C
Explaination / Solution:
No Explaination.
Q3. The ratios of the laminar hydrodynamic boundary layer thickness to thermal
boundary layer thickness of flows of two fluids P and Q on a flat plate are 1/2
and
2 respectively. The Reynolds number based on the plate length for both the flows
is 104. The Prandtl and Nusselt numbers for P are 1/8
and 35 respectively. The
Prandtl and Nusselt numbers for Q are respectively
Answer : Option A
Explaination / Solution:
Q4. A cubic casting of 50mm side undergoes volumetric solidification shrinkage and
volumetric solid contraction of 4% and 6% respectively. No. riser is used.
Assume uniform cooling in all directions. The side of the cube after solidification
and contraction is
Answer : Option A
Explaination / Solution:
Volumetric solidification shrinkage and volumetric solid contraction cause
decrease in dimensions.
Volume of cube = 503 = 125000 mm3
After considering both the allowances
V = 125000 × 0.96 × 0.94 = 112800mm3
Q5. Maximum of the real valued function f(x) = (x – 1)2/3 occurs at x equal to
Answer : Option C
Explaination / Solution:
Q6. A column has a rectangular cross-section of 10mm x 20mm and a length of 1m.
The slenderness ratio of the column is close to
Answer : Option B
Explaination / Solution:
No Explaination.
Q7. The crank radius of a single–cylinder I. C. engine is 60mm and the diameter of
the cylinder is 80mm. The swept volume of the cylinder in cm3 is
Answer : Option D
Explaination / Solution:
Stroke of the cylinder l = 2r = 2 × 60 = 120mm
Swept volume = (π/4)d2 × I = (π/4) × 802 × 120 = 603 cm3
Q8. The variable cost (V) of manufacturing a product varies according to the equation
V= 4q, where q is the quantity produced. The fixed cost (F) of production of same
product reduces with q according to the equation F = 100/q. How many units
should be produced to minimize the total cost (V+F)?
Answer : Option A
Explaination / Solution:
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the
minimum cost.
Q9. All the values of the multi-valued complex function
1i, where 
Answer : Option B
Explaination / Solution:
Q10. Match the following criteria of material failure, under biaxial stresses σ1 and σ2 and yield stress σy , with their corresponding graphic representations :
P. Maximum-normal-stress criterion L. 
Q. Maximum-distortion-energy criterion M. 
R. Maximum-shear–stress criterion N. 
Answer : Option C
Explaination / Solution:
No Explaination.
