Engineering Mathematics - Online Test
Q1. 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)
Q2. 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:
Q3. 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:
Q4. 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
Q5. 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
Q6. 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:
Q7. 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
Q8. The n-bit fixed-point representation of an unsigned real number real X uses f bits for the
fraction part. Let i = n –f. The range of decimal values for X in this representation is
Answer : Option D
Explaination / Solution:
i = n – f . f
Max value = 111.....1 (i times).111........1 (f times)
Q9. Consider the first-order logic sentence F: ∀z (∃yR(x,y)). Assuming non-empty logical
domains, which of the sentences below are implied by F?
I. ∃y (∃xR(x,y)) II. ∃y (∀xR(x,y))
III. ∀y (∃xR(x,y)) IV. ¬∃x (∀y¬R(x,y))
Answer : Option B
Explaination / Solution:
Q10. Consider the following functions from positive integers to real numbers:
The CORRECT arrangement of the above functions in increasing order of asymptotic
complexity is:
Answer : Option B
Explaination / Solution:
No Explaination.
