Mathematics - Online Test
Q1. A box of oranges is inspected by examining three randomly selected oranges drawn without replacement. If all the three oranges are good, the box is approved for sale, otherwise, it is rejected. Find the probability that a box containing 15 oranges out of which 12 are good and 3 are bad ones will be approved for sale.
Answer : Option D
Explaination / Solution:
Total oranges = 15., Good Oranges = 12. Therefore , Required Probability =.
Q2. The trigonometric Fourier series for the waveform f (t) shown below contains
Answer : Option C
Explaination / Solution:
For a function x(t) trigonometric fourier series is
For an even function x(t),Bn = 0
Since given function is even function so coefficient Bn = 0, only cosine and constant
terms are present in its fourier series representation.
Constant term :
Constant term is negative.
Q3. If f : N ××N →→N is such that f (m, n) = m + n where N is the set of natural number, then which of the following is true ?
Answer : Option B
Explaination / Solution:
No Explaination.
Q4.
Given that the events A and B are such that P(A) =, P (A ∪ B) = and P(B) = p. Find p if A and B are mutually exclusive
Answer : Option A
Explaination / Solution:
Since A and B are mutually exclusive events.,
Q5. A function n(x) satisfied the differential equation 
where L is a constant. The boundary conditions are :n(0) = K and n(∞) = 0. The solution to this equation is
where L is a constant. The boundary conditions are :n(0) = K and n(∞) = 0. The solution to this equation is
Answer : Option D
Explaination / Solution:
Given differential equation
Q6. The function sin is periodic with period
Answer : Option A
Explaination / Solution:
No Explaination.
Q7.
Given that the events A and B are such that P(A) =, P (A ∪ B) = and P(B) = p. Find p if they independent.
Answer : Option D
Explaination / Solution:
Q8. Consider the z -transform 
The inverse z -transform x[n] is
The inverse z -transform x[n] is
Answer : Option A
Explaination / Solution:
Q9.
If A = [a, b], B = [c,d], C = [d, e] then {(a, c), (a, d), (a,e), (b,c), (b, d), (b, e)} is equal to
Answer : Option C
Explaination / Solution:
No Explaination.
Q10. Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4. Find P(A ∩ B)
Answer : Option B
Explaination / Solution:
Let A and B be independent events with P (A) = 0.3 and P(B) = 0.4
