Mathematics - Online Test
Q1. If Log (P) = (1/2)Log (Q) = (1/3) Log (R), then which of the following options is
TRUE?
Answer : Option B
Explaination / Solution:
Q2. P, Q, R and S are four types of dangerous microbes recently found in a human
habitat. The area of each circle with its diameter printed in brackets represents
the growth of a single microbe surviving human immunity system within 24 hours
of entering the body. The danger to human beings varies proportionately with the
toxicity, potency and growth attributed to a microbe shown in the figure
below 
A pharmaceutical company is contemplating the development of a vaccine
against the most dangerous microbe. Which microbe should the company target
in its first attempt?
Answer : Option D
Explaination / Solution:
By observation of the table, we can say S
Q3. The variable cost (V) of manufacturing a product varies according to the equation
V= 4q, where q is the quantity produced. The fixed cost (F) of production of same
product reduces with q according to the equation F = 100/q. How many units
should be produced to minimize the total cost (V+F)?
Answer : Option A
Explaination / Solution:
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the
minimum cost.
Q4. 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:
Q5. 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
Q6. 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
Q7. 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
Q8. 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
Q9. 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
Q10. 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:
