Civil Engineering - Online Test
Q1. 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
Q2. 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)
Q3. 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:
Q4. 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.
Q5. The value of 
Answer : Option C
Explaination / Solution:
Q6. Let u and v be two vectors in R2 whose Euclidean norms satisfy ||u|| = 2 ||v||. What is the value
of α such that w = u + αv bisects the angle between u and v ?
Answer : Option A
Explaination / Solution:
Q7. Let p, q, and r be propositions and the expression (p → q) → r be a contradiction. Then, the
expression (r → p) → q is
Answer : Option D
Explaination / Solution:
(p →q) → r is contradiction only when
And now for the above combination, the expression (r → p) → q is always true when q is
true. When q is false in the above combination (third one) (r → p) → q will be false.
Q8. Let A be n × n real valued square symmetric matrix of rank 2 with 
Consider
the following statements.
Consider
the following statements. (I) One eigen value must be in [-5, 5]
(II) The eigen value with the largest magnitude must be strictly greater than 5.
Which of the above statements about eigen values of A is/are necessarily CORRECT?
Answer : Option B
Explaination / Solution:
∴One eigen value must be in [−5,5] and largest eigen value magnitude is not greater than 5
∴ (II) is false
Q9. A contour line joins locations having the same height above the mean sea level. The following
is a contour plot of a geographical region. Contour lines are shown at 25m intervals in this
plot. If in a flood, the water level rises to 525m, which of villages P,Q, R, S,T get submerged
?
Answer : Option C
Explaination / Solution:
The given contour is a hill station, the peak point of this hill station is P, it is under a contour
of 550 . At floods, the water level is 525m. So the village of R, S and T are under a contour of
500. Therefore these villages are submerged.
Q10. The expression ((x + y) - |x - y|)/2 is equal to
Answer : Option B
Explaination / Solution:
