Electrical Engineering - Online Test
Q1. Which one of the following statements is TRUE about every n × n matrix with only real
eigenvalues?
Answer : Option A
Explaination / Solution:
If the trace of the matrix is positive and the determinant of the matrix is negative then atleast
one of its eigen values is negative.
Since determinant = product of eigen values.
Q2. Consider a hash table with 100 slots. Collisions are resolved using chaining. Assuming
simple uniform hashing, what is the probability that the first 3 slots are unfilled after the first
3 insertions?
Answer : Option A
Explaination / Solution:
Q3. With respect to the numerical evaluation of the definite integral, 
where a and b
are given, which of the following statements is/are TRUE?
where a and b
are given, which of the following statements is/are TRUE?(I) The value of K obtained using the trapezoidal rule is always greater than or equal to the
exact value of the definite integral.
(II) The value of K obtained using the Simpson’s rule is always equal to the exact value of
the definite integral.
Answer : Option C
Explaination / Solution:
Q4. The value of the integral given below is 
Answer : Option A
Explaination / Solution:
Q5. 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.
Q6. 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
Q7. 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)
Q8. 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:
Q9. 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:
Q10. 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
