Engineering Mathematics - Online Test

Q1. Consider the differential equation  Which of the following is a solution to this differential equation for x > 0?
Answer : Option C
Explaination / Solution:



Q2. The state transition matrix for the system
 is 
Answer : Option C
Explaination / Solution:



Q3. To evaluate the double integral  we make the substitution  The integral will reduce to
Answer : Option B
Explaination / Solution:



Q4. The minimum value of the function f(x) = x3 - 3x2 - 24x + 100  in the interval [-3. 3] is
Answer : Option B
Explaination / Solution:



Q5. Consider a function f(x) = 1 - |x| on -1 ≤ x ≤ 1. The value of x at which the function attains a maximum, and the maximum value of function are:
Answer : Option C
Explaination / Solution:



Q6. Given f (z) = g(z) + h(z), where f, g, h are complex valued functions of a complex variable z. Which one of the following statements is TRUE?
Answer : Option B
Explaination / Solution:



g(z) and h(z) are differentiable then f(z) = g(z) + h(z) is differentiable.

Q7. The Laplace transform of  The Laplace transform of  is
Answer : Option B
Explaination / Solution:



Q8. We have a set of 3 linear equations in 3 unknowns. means X and Y are equivalent statements and  means X and Y are not equivalent statements.
P: There is a unique solution.
Q: The equations are linearly independent.
R: All eigenvalues of the coefficient matrix are nonzero. 
S: The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?  
Answer : Option A
Explaination / Solution:
No Explaination.


Q9. Two coins R and S are tossed. The 4 joint events HRHS, TTS,HTS,THS have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE? 
Answer : Option D
Explaination / Solution:



Q10. The z-Transform of a sequence x[n] is given as X(z) = 2z+4-4/z+3z2. If y[n] is the first difference of x[n], then Y(z) is given by 
Answer : Option A
Explaination / Solution:

y(n) is first difference of x(n) So
g(n)=x(n)-x(n-1)