Electrical Engineering - Online Test
Q1. A container originally contains 10 litres of pure spirit. From this container 1 litre
of spirit is replaced with 1 litre of water. Subsequently, 1 litre of the mixture is
again replaced with 1 litre of water and this process is repeated one more time.
How much spirit is now left in the container?
Answer : Option D
Explaination / Solution:
Q2. Consider a random variable X that takes values + 1 and -1 with probability 0.5 each. The
values of the cumulative distribution function F(x) at x = -1 and +1 are
Answer : Option C
Explaination / Solution:
The cumulative distribution function
F(x) = P(X ≤ x)
F(-1) = P(X ≤ -1) = P(X = -1) = 0.5
F(+1) = P(X ≤ +1) = P(X = -1) + P(X = +1) = 0.5 + 0.5 = 1
Q3. Let A be the 2 x 2 matrix with elements a11 = a12 = a21= + 1 and a22 =-1. Then the eigen values
of the matrix A19 are
Answer : Option D
Explaination / Solution:
Characteristic equation of A is |A - λI| = 0 where λ is the eigen value
Q4. Consider the function f(x) = sin(x) in the interval x ∈ [π/4, 7π/4]. The number and location
(s) of the local minima of this function are
Answer : Option B
Explaination / Solution:
Sin x has a maximum value of 1 at , π/2 and a minimum value of –1 at 3π/2 and at all angles
conterminal with them.
The graph of f(x) = sin x is
In the int erval [π/4, 7π/4], it has one local minimum at x = 3π/2
Q5. How many onto (or surjective) functions are there from an n-element (n ≥ 2) set to a 2-
element set?
Answer : Option C
Explaination / Solution:
Total number of functions is 2n , out of which there will be exactly two functions where all
elements map to exactly one element, so total number of onto functions is 2n -2
Q6. Suppose a fair six-sided die is rolled once. If the value on the die is 1, 2, or 3, the die is rolled
a second time. What is the probability that the sum total of values that turn up is at least 6?
Answer : Option B
Explaination / Solution:
Required probability = 1/6 × 2/6 + 1/6 × 3/6 + 1/6 × 4/6 + 1/6 = 15/36 = 5/12
Q7. The bisection method is applied to compute a zero of the function f(x) = x4 - x3 - x2 – 4 in the
interval [1,9]. The method converges to a solution after ______ iterations.
Answer : Option B
Explaination / Solution:
Q8. Which of the following graph is isomorphic to
Answer : Option B
Explaination / Solution:
The graph in option (A) has a 3 length cycle whereas the original graph does not have a 3
length cycle
The graph in option (C) has vertex with degree 3 whereas the original graph does not have a
vertex with degree 3
The graph in option (D) has a 4 length cycle whereas the original graph does not have a 4
length cycle
Q9. An automobile plant contracted to buy shock absorbers from two suppliers X and Y. X supplies
60% and Y supplies 40% of the shock absorbers. All shock absorbers are subjected to a quality test.
The ones that pass the quality test are considered reliable Of X's shock absorbers, 96% are reliable.
Of Y's shock absorbers, 72% are reliable.
The probability that a randomly chosen shock absorber, which is found to be reliable, is made by
Y is
Answer : Option B
Explaination / Solution:
x y
Supply 60% 40%
Reliable 96% 72%
Overall 0.576 0.288
P(x) = 0.288/(0.576 + 0.288) = 0.334
Q10. A political party orders an arch for the entrance to the ground in which the annual convention is
being held. The profile of the arch follows the equation y = 2x − 0.1x2 where y is the height of
the arch in meters. The maximum possible height of the arch is
Answer : Option B
Explaination / Solution:
x = 10
y = 20 - 10 = 10m
