Mechanical Engineering - Online Test
Q1. Let 
. Consider the set ܵ of all vectors 
such that a2 + b2 = 1 where 
Then ܵ is
. Consider the set ܵ of all vectors such that a2 + b2 = 1 where Then ܵ is
Answer : Option C
Explaination / Solution:
Q2. The spring constant of a helical compression spring DOES NOT
depend on
Answer : Option B
Explaination / Solution:
The spring constant (k) for the compression helical spring is given
by,
So, K is dependent on wire diameter, number of active coils, modulus
of rigidity, coil diameter, but does not depends on the martial
strength.
Q3. The figure below represents a triangle PQR with initial
coordinates of the vertices as P(1,3),Q(4,5) and R(5,3.5). The triangle
is rotated in the X-Y plane about the vertex P by angle θ in clockwise
direction. If sinθ= 0.6 and cosθ= 0.8, the new coordinates of the
vertex 𝑄 are
Answer : Option A
Explaination / Solution:
Since the triangle is rotated in CW direction, hence, for the new point
Q’ (x,y),
x > 4 and y < 5 __________(1)
and PQ = PQ’ or QR = Q’R’
Now we can get the answer easily by checking the option
Q4.
A hole is specified as 
The mating shaft has a clearance fit with
minimum clearance of 0.01 mm. The tolerance on the shaft is 0.04 mm. The
maximum clearance in mm between the hole and the shaft is
The mating shaft has a clearance fit with
minimum clearance of 0.01 mm. The tolerance on the shaft is 0.04 mm. The
maximum clearance in mm between the hole and the shaft is
Answer : Option C
Explaination / Solution:
Q5. 
Let the probability density function of a random variable, X, be given as:
where u(x) is the unit step function.
Then the value of 'a' and Prob {X ≤ 0}, respectively, are
Answer : Option A
Explaination / Solution:
Q6. A two-member truss PQR is supporting a load W. The axial
forces in members PQ and QR are respectively
Answer : Option B
Explaination / Solution:
FBD for the point Q is given by,
Q7. In order to have maximum power from a Pelton turbine, the bucket speed must be
Answer : Option B
Explaination / Solution:
Explanation:
Since, velocity of bucket = ½ times the velocity of jet.
Q8. In orthogonal turning of low carbon steel pipe with principal cutting edge angle
of 90o, the main cutting force is 1000 N and the feed force is 800 N. The shear
angle is 25o and orthogonal rake angle is zero. Employing Merchant’s theory, the
ratio of friction force to normal force acting on the cutting tool is
Answer : Option C
Explaination / Solution:
Q9. For a complex number z, 
is
is
Answer : Option D
Explaination / Solution:
Q10. In the gear train shown, gear 3 is carried on arm 5. Gear 3
meshes with gear 2 and gear 4. The number of teeth on gear 2, 3, and
4 are 60, 20, and 100, respectively. If gear 2 is fixed and gear 4
rotates with an angular velocity of 100 rpm in the counter clockwise
direction, the angular speed of arm 5 (in rpm) is
Answer : Option C
Explaination / Solution:
Given (taking CW as positive)
