Q3.An examination consists of two papers, Paper 1 and Paper 2. The probability of failing in Paper 1 is 0.3 and that in Paper 2 is 0.2. Given that a student has failed in Paper 2, the probability of failing in Paper 1 is 0.6. The probability of a student failing in both the papers is
Q5.The equation x − x + x − = is to be solved using the Newton - Raphson method. If x = is taken as the initial approximation of the solution, then next approximation using this method will be
Q7.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
Q8.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 AExplaination / 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
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?
Answer : Option CExplaination / 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.