Mechanical Engineering - Online Test
Q1. The value of the integral given below is 
Answer : Option A
Explaination / Solution:
Q2. Consider the set of all functions f : {0,1,...,2014} → {0,1...,2014} such that f (f (i)) = i for 0 ≤ i ≤ 2014. Consider the following statements.
P. For each such function it must be the case that for every i, f(i) = i,
Q. For each such function it must be the case that for some i,f(i) = i,
R. Each such function must be onto.
Which one of the following is CORRECT?
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. Let δ denote the minimum degree of a vertex in a graph. For all planar graphs on n vertices
with δ ≥3, which one of the following is TRUE?
Answer : Option A
Explaination / Solution:
We know that v + r = e+2 ⇒ e=n+r-2......(1)
Where V= n (number of vertices); r = number of faces and
e = number of edges
Given, δ ≥ 3 then 3n ≤
2e
Number of faces is atleast (n/2) + 2
Q4. The CORECT formula for the sentence, “not all rainy days are cold” is
Answer : Option D
Explaination / Solution:
Given statement is
(Since p→q ≡~ p∨q and let r(d) be rainy day, c(d) be cold day)
Q5. Consider a function f(x) = 1-|x| on -1≤ x ≤ 1. The value of x at which the function attains a
maximum, and the maximum value of the function are.
Answer : Option C
Explaination / Solution:
Q6. Four branches of a company are located at M.N.O and P. M is north of N at a distance of
4km: P is south of O at a distance of 2 km: N is southeast of O by 1 km. What is the distance
between M and P in km?
Answer : Option A
Explaination / Solution:
Q7. Let f(x) = x-(1/3) and A denote the area of the region bounded by f(x) and the X-axis, when x
varies from – 1 to 1. Which of the following statements is/are TRUE?
(I) f iscontinuous in [-1,1]
(II) f isnot bounded in [-1,1]
(III) A is nonzero and finite
Answer : Option C
Explaination / Solution:
Since
f(0) ® ¥
f is not bounced in [-1,1] and hence f is not continuous in [-1,1]
Statement II & III are true
Q8. A shaving set company sells 4 different types of razors, Elegance, Smooth, Soft and
Executive. 
Elegance sells at Rs. 48, Smooth at Rs. 63, Soft at Rs. 78 and Executive at Rs. 173 per piece.
The table below shows the numbers of each razor sold in each quarter of a year.
Which product contributes the greatest fraction to the revenue of the company in that year?
Answer : Option B
Explaination / Solution:
Total income from Elegance=48(27300+25222+28976+21012) = 4920480
Total income from Smooth=63(20009+19392+22429+18229 = 5043717
Total income from Soft=78(17602+18445+19544+16595) =5630508
Total income from Executive=173(9999+8942+10234+10109) =6796132
Q9. Let an be the number of n-bit strings that do NOT contain two consecutive 1s. Which one of
the following is the recurrence relation for an?
Answer : Option B
Explaination / Solution:
Q10. Let c1 ........cn be scalars, not all zero, such that 
where ai are column vectors in
Rn . Consider the set of linear equations Ax = b where A = [a1 ........an] and 
The set of equations has
where ai are column vectors in
Rn . Consider the set of linear equations Ax = b where A = [a1 ........an] and The set of equations has
Answer : Option C
Explaination / Solution:
Since the scalars are not all zero
∴ The column vectors ai for i = 1,2...,n are linearly dependent
