Mathematics - Online Test
Q1. Which of the following functions is not one-one ?
Answer : Option B
Explaination / Solution:
No Explaination.
Q2. If the semi-circular control D of radius 2 is as shown in the figure, then the
value of the integral 
is
is
Answer : Option A
Explaination / Solution:
Q3. A 5-point sequence x n is given as x - 3 = 1, x - = 1, x - 1 = , x = 5 and x 1 = 1. Let X(ei𝜔) denoted the discrete-time Fourier transform of x n.
The value of 
is
is
Answer : Option B
Explaination / Solution:
Q4. A digit is selected at random from either of the two sets { 1, 2, 3, 4, 5, 6, 7, 8, 9} and {1, 2, 3, 4, 5, 6, 7, 8, 9{. What is the chance that the sum of the digits selected is 10 ?
Answer : Option D
Explaination / Solution:
No Explaination.
Q5.
If f (x) = then f (1) is equal to
Answer : Option D
Explaination / Solution:
No Explaination.
Q6. An input to a 6-level quantizer has the probability density function f(x) as shown
in the figure. Decision boundaries of the quantizer are chosen so as to maximize the
entropy of the quantizer output. It is given that 3 consecutive decision boundaries
are' −1'. '0 ' and '1'.
The values of a and b are
Answer : Option A
Explaination / Solution:
Area under the pdf curve must be unity
2a + 4a + 4b = 1
2a + 8b = 1.................................................(1)
For maximum entropy three region must by equivaprobable thus
2a = 4b = 4b...............................................(2)
From (1) and (2) we get
b = 1/12 and a = 1/6
Q7. If two squares are chosen at random on a chess board, the probability that they have a side common is
Answer : Option A
Explaination / Solution:
No Explaination.
Q8. The domain of the real-valued function is
Answer : Option C
Explaination / Solution:
No Explaination.
Q9. All the four entries of the 2 × 2 matrix 
are nonzero, and one of its
eigenvalue is zero. Which of the following statements is true?
are nonzero, and one of its
eigenvalue is zero. Which of the following statements is true?
Answer : Option C
Explaination / Solution:
The product of Eigen value is equal to the determinant of the matrix. Since one
of the Eigen value is zero, the product of Eigen value is zero, thus determinant
of the matrix is zero.
Q10. A coin tail on both sides is tossed twice. The probability of getting ‘a head’ is
Answer : Option D
Explaination / Solution:
No Explaination.
