Exam Set A.docx

GARCIA COLLEGE OF TECHNOLOGY Kalibo, Aklan Electrical Engineering Department EE 320E (ADVANCED EE MATHEMATICS) FINAL EXAM

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SET A Directions: Encircle the letter of the correct answer. Strictly no erasures. Each item weighs two (2) points. 1. Find the inverse Laplace transform of 1 / [s(s2 + 4)]. a. ¼ (1 – cos 2t) c. ¼ (1 – sin 2t) b. ¼ (1 – cosh 2t) d. ¼ (1 – sinh 2t)

10. Find the product of 11 + 2i and its conjugate. a. 125 c. 130 b. 120 d. 115

3 2. If 𝐴 = ( −2 AATBC.

11. If A = 2(cos 20 + i sin 20) and B = 3(cos 40 + i sin 40), the product AB is ___. a. 6(cos 20 + i sin 20) c. 6(cos 60 + i sin 60) b. sq. rt. of 6(cos 20 + i sin 20) d. sq. rt. of 6(cos 60 + isin 60)

a. (

1 4

2 2 ),𝐵 = ( −2 3

−86 ) 144

−1 −1 ) and 𝐶 = ( ). Find 4 2

c. (

96 b. ( ) −102

86 ) −144

12. If 𝑖 = √−1 and n is a positive integer, which of the following statements is FALSE? a. i4n = 1 c. i4n + 1 = -i 4n + 2 b. i = -1 d. in + 4 = in

−96 d. ( ) 102

3. Find the value of y in (3x + 4yi)(6 – 7i) = 3 + 5i. a. 1/20 c. 1/10 b. 3/20 d. 1/5 2 −2 4. 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝐷 = | 1 −1

5 −3 3 −6

a. -2 b. -3

−3 2 −2 4

𝑤 13. Let: 𝐴 = ( 𝑦 that 2A = 3B – 2C. a. -4 b. -2

−2 −5 2| 3

5. The curl of u = x2i + y2j + z2k at the point (1, 1, 1) is ___. a. 2i + 2j + 2k c. 0 b. i + j + k d. 6 6. Find the Laplace transform of e-2t sin 4t. a. (s – 4) / (s2 + 4s + 20) c. 4 / (s2 + 4s + 20) 2 b. (s + 2) / (s + 4s + 20) d. (2s) / (s2 + 4s + 20)

a. (

−7 29

4 7

7 29

−4 7

b. (

1 4

−2 5

0 ) −36 0 ) −36

3 3 ) and 𝐵 = ( 6 −7 c. (

0 1

2 ). Find 2A – 3B. 8

−7 29

−4 7

0 ) −36

−7 29

−4 7

0 ) −36

d. (

2 ). Find x such −3

c. -5 d. -10

15. Evaluate inverse Laplace of 2s / (s2 + 1)2. a. t sin t c. cos 25t b. sin 2t d. e2t sin t 16. Determine the value of sin h (0.942 + j0.429). a. 0.99 + j0.614 c. 0.919 + j0.416 b. 0.99 + j0.416 d. 0.919 + j0.614 𝑥 17. Solve for z: ( 𝑦

c. -1 + j1 d. -1 + j2

8. Find the unit vector (i.e., the direction vector) associated with the vector 18i + 3j + 29k. a. 0.525i + 0.088j + 0.846k c. 0.892i + 0.178j + 0.416k b. 1.342i + 0.868j + 2.437k d. 6i + j + 9.677k 9. Given: 𝐴 = (

1 −2 )&𝐶=( 6 7

14. Given the points A(3, 4, 5), B(4, -8, 9) and C(3, 5, -8). Find the area of the triangle ABC. a. 72.46 c. 76.28 b. 74.81 d. 70.89

c. -1 d. -4

7. Simplify: j3217 – j427 + j18. a. 1 + j2 b. 1 + j1

𝑥 5 𝑧 ) , 𝐵 = (4

a. 2 b. -1

−1 4 )( 3 −1

𝑤 9 )=( 𝑧 1

8 ) −3

c. 1 d. -2

18. Solve the inverse Laplace transform of (3s + 16) / (s2 – s – 6). a. 3e3t – 4e-2t c. 5e2t – 2e-3t 3t -2t b. 4e – 3e d. 5e3t – 2e-2t

1/3

3 19. Given the matrix (0 2 matrix. a. -5 b. -4

2 −1 0

1 −1), solve the co-factor A21 of the 2 c. -3 d. -6

1 32. 𝐼𝑓 𝐴 = [ 1

20. Find the Laplace transform of t2e3t. a. 2s / (s – 3)3 c. 2 / (s – 3)3 3 b. s / (s – 3) d. (s + 2) / (s – 3)3

a. -6 b. -7

2 2

5 3 ] 𝑎𝑛𝑑 𝐵 = [6 9 4

a. 29 b. 53

6 𝑥 −40 )( ) = ( ). Find y. 5 𝑦 −41

1 21. Given: ( −3

31. Simplify the expression: A x B  C, given A = 3i + 2j; B = 2i + 3j + k; C = 5i + 2k a. 60 c. 180 b. 20 d. 100

1 0], the (2, 1) entry of AB is 7 c. 33 d. 64

33. Determine cosh (0.0454 + j0.357). a. 0.937 + j0.0246 c. 0.937 + j0.0158 b. 0.891 + j0.0158 d. 0.891 + j0.0246

c. -5 d. -4

22. Find the unit vector (i.e., the direction vector) associated with the vector 18i + 3j + 29k. a. 0.521i + 0.088j + 0.846k c. 0.892i + 0.178j + 0.416k b. 1.342i + 0.866j + 2.437k d. 6i + j + 9.667k

−1 9 34. 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝐷 = | 2 0

23. Find the inverse Laplace transform of 1 / (s2 + 2s). a. ½ (1 – e-2t) c. 2 – e-2t 2t b. ½ (1 + e ) d. 1 – e-2t

a. -44 b. -42

c. -46 d. -40

35. Simplify: i1996 + i2003 + i2010. a. 1 b. -1 – i

c. 1 + i d. – i

24. Solve the value of x which satisfies the following linear system. 3 7 𝑥 2 ( ) ( ) = ( ). 2 6 𝑦 4 a. 2 b. 4

a. (

2 −12

b. (

−4 2

2 4

−1 −1 ),𝐵 = ( 3 2

4 ) −14 6 ) −8

1 ), find BTAT. −4 c. (

2 4

d. (

−4 6

−12 ) −14 2 ) −8

28. What is the rationalized value of the complex number

6+2.5𝑖 ? 3+4𝑖

c. 28/25 – 33/50 i d. 50/51 – 34/25 i

29. Find the value of x so that 2i + 4j + 5k and i + xj – 2k are perpendicular. a. 1 c. 3 b. 2 d. 4 2 30. If 𝐴 = [ 4 2B – 4C.

−1 −1 ],𝐵 = [ 3 2

39. Find the adjoint matrix of matrix A if 𝐴 = (

1 1 ],𝐶 = [ −4 −2

0 a. [ −24

17 ] 5

c. [

0 b. [ −24

17 ] −5

d. [

4 −2

−3 ) 1

c. (

4 −3

−2 ) 1

d. (

b. (

c. -1 d. -i

a. 50/51 + 34/25 i b. 28/25 + 33/50 i

38. The divergence of the vector function, u = xyi + 2y 2j – yzk at the point (0, 1, 1) is ___. a. -4 c. 0 b. -1 d. 4

a. (

1−𝑖 10 (1+𝑖) .

a. 1 b. i

−1 3 1| −1

37. Determine the general value of ln (1 - j3)3. a. 0.693 + j12.522 c. 2.941 + j12.184 b. 1.047 + j15.439 d. 2.079 + j15.708

26. If A = 3<30, B = 3e–3i and C = 3 – 4i, find the absolute value of ABC. a. 45 c. 50 b. 60 d. 55 27. 𝑆𝑖𝑚𝑝𝑙𝑖𝑓𝑦:

1 −1 3 −2

36. Find the Laplace transform of (t sin t). a. 2 / (s2 +1)2 c. s / (s2 +1)2 2 2 b. 1 / (s +1) d. 2s / (s2 +1)2

c. -2 d. -4

25. If 𝐴 = (

−1 1 −2 3

0 24

−17 ] 5

0 24

17 ] −5

4 ] . Find 3A + −1

1 3

1 −2

−3 ) 4

3 −1

−4 ) 2

2 ). 4

40. Which of the following is a negative number? a. i25 c. i75 50 b. i d. i100 41. Evaluate: tanh-1 (j0.5). a. j0.785 b. j0.464 42. Find AAT where 𝐴 = ( a. (

−5 1

b. (

5 1

1 ) −26 1 ) 26

1 3

c. j0.927 d. j0.393 2 −1

0 ). 4 c. (

5 −1

−1 ) 26

1 26

5 ) 1

d. (

43. Find a unit vector perpendicular to the plane of the vectors A =3i – 2j + 4k and B = i + j – 2k. a. (2j + k) / 5 c. (j + 2k) / 5 b. (j + k) / 2 d. (j – k) / 2 2/3

44. Solve for b: (3 + bi) (a – 2i) = 13 + 0i. a. 4 c. 1 b. 3 d. 2 45. Find the area of a parallelogram with the sides identified by vectors from the origin, A = 3i + 4j and B = 8i. a. 40 c. 36 b. 32 d. 24 5 −1 46. 𝐸𝑣𝑎𝑙𝑢𝑎𝑡𝑒 𝐷 = | 8 2

1 1 6 2

5 −3 −2 2

1 −4 1| −3

a. -240 b. -220

c. -200 d. -250

47. Evaluate: tanh-1 (1 – j2). a. 0.1732 – j1.178 b. 1.4142 – j1.178

c. 0.1732 – j2.356 d. 1.4142 – j2.356

48. The Laplace transform of e-2t (3 cos 6t – 5 sin 6t). a. (3s – 30) / (s2 + 36) c. (3s – 24) / (s2 + 4s + 40) 2 b. (s – 5) / (s + 36) d. (3s – 5) / (s2 + 4s + 40) 49. If A = 40ej120, B = 20<-40, C = 26.46 + j0, solve for the magnitude of (A + B + C). a. 30.8 c. 35.4 b. 39.2 d. 33.7 50. Simplify: i1997 + i1999. a. 1 + i b. -1

c. 1 – i d. 0

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