Mathematics - Online Test
Q1. 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
Q2. 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
Q3. 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
Q4. Function f is known at the following points
The value of 
computed using the trapezoidal rule is
computed using the trapezoidal rule is
Answer : Option D
Explaination / Solution:
Q5. Which one of the following functions is continuous at x = 3 ?
Answer : Option A
Explaination / Solution:
f(x) is continuous at x 3
Q6. Which one of the following does NOT equal 
Answer : Option A
Explaination / Solution:
If matrix B is obtained from matrix A by replacing the 1th row by itself plus k times the mth row, for 1 ≠ m then det(B)=det(A). With this property given matrix is equal to the matrices
given in options (B),(C) and (D).
Q7. Suppose p is number of cars per minute passing through a certain road junction between 5
PM and 6PM, and p has a Poisson distribution with mean 3. What is the probability of
observing fewer than 3 cars during any given minute in this interval?
Answer : Option C
Explaination / Solution:
Q8. What is the logical translation of the following statement?
“None of my friends are perfect.”
Answer : Option D
Explaination / Solution:
“None of my friends are perfect”
Q9. Out of all the 2-digit integers between 1 and 100, a 2-digit number has to be selected at
random. What is the probability that the selected number is not divisible by 7?
Answer : Option D
Explaination / Solution:
The number of 2 digit multiples of 7 = 13
∴ Probability of choosing a number
Not divisible by 7 = (90-13)/90 = 77/90
Q10. Find the sum of the expression
Answer : Option B
Explaination / Solution:
The expression can be written as
