Engineering Mathematics - Online Test

Q1. For the function ex , the linear approximation around x = 2 is
Answer : Option A
Explaination / Solution:


Neglecting higher powers

Q2. Consider the function f (x) = x − x − . The maximum value of f (x) in the closed interval [− 4, 4] is
Answer : Option A
Explaination / Solution:

We have
                                    f (x) = x − x +


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
Answer : Option C
Explaination / Solution:



Q4. The solution of the differential equation  under the boundary conditions
(i) y = y1 at x = 0 and
(ii) y = y2 at x = , where k, y1 and y2 are constants, is
Answer : Option D
Explaination / Solution:




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
Answer : Option B
Explaination / Solution:



Q6. If the semi-circular control D of radius 2 is as shown in the figure, then the value of the integral  is

Answer : Option A
Explaination / Solution:



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
Answer : Option B
Explaination / Solution:



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 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

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 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. The system of linear equations 4x + 2y = 7 2x + y = 6 has
Answer : Option B
Explaination / Solution: