Electrical Engineering - Online Test
Q1. 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
Q2. 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:
Q3. 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
Q4. 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)
Q5. 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:
Q6. 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.
Q7. The value of 
Answer : Option C
Explaination / Solution:
Q8. 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:
Q9. 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.
Q10. 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
