ADVANCED ENGINEERING MATHEMATICS FOR EE
1. Find the volume of the parallelepiped whose edges are represented
by the vectors 𝑎⃗ = −3𝑖̂ + 7𝑗̂ + 5𝑘̂, 𝑏⃗⃗ = −5𝑖̂ + 7𝑗̂ − 3𝑘̂ , and 𝑐⃗ = 7𝑖̂ − 5𝑗̂ − 3𝑘̂.
A. 375
B. 264*
C. 250
D. None of these
2. The coefficient of x^2 in the expansion of e^(2x) about 0 is
A. 2
C. 6
B. 4*
D. 8
3. The coefficient of x in the Maclaurin’s series expansion of
e^(sinx) is equal to.
A. 2
C. 3
B. 1*
D. 0
4. Determine the inverse Laplace transform of: I(s) = 100 / [s^2 [s^2
+ 100]
A. i(t) = t – cos 10t
C. i(t) = t – 0.1sin10t*
B. i(t) = t2 – 0.1sin10t
D. i(t) = t2 – cos10t
5. Determine the area of the quadrilateral having (8, - 2), (5, 6),
(4, 1), (-7, 4), consecutive vertices.
A. 25
C. 33
B. 15
D. 22*
6. Find the area of parallelogram having diagonals A = 3i + j - 2k
and B = i – 3j + 4k.
A. 8.66 units^2*
C. 7.29 units^2
B. 9.65 units^2
D. 7.07 units^2
7. Find the angle between Vector A and Vector B if A = 3𝑎𝑥 + 4𝑎𝑦 + 𝑎𝑧 and
B = 2𝑎𝑦 − 5𝑎𝑧 .
A. 73.83 deg
C. 73.38 deg
B. 83.73 deg*
D. 38.73 deg
8. The magnitude of a given vector with end points (4, – 4, 0) and (–
2, – 2, 0) must be
A. 6
C. 4
B. 5√2
D. 2√10*
9.
is Maclaurin’s series of what function?
A. cos (x)
B. e^(x^2)
C. cos (x^2)
D. sin (x^2)*
10.
Find the area of the region enclosed by the triangle with
vertices (1, 1), (3, 2), and (2, 4).
A. 7/2
C. 1/2
B. 5/2*
D. 3/2
ADVANCED ENGINEERING MATHEMATICS FOR EE
11.
Evaluate ln (2 + j3).
A. 1.34 + j0.32
B. 2.54 + j0.866
C. 2.23 + j0.21
D. 1.28 + j0.98*
12.
In the case of a periodic function possessing half-wave
symmetry, which Fourier coefficient is zero?
A. 𝑎𝑛
C. 𝑏𝑛*
B. 𝑎0
D. none of the above
13.
Which of the following are even functions?
A. t + t^2
C. e^(t^2)
B. (t^2)cost*
D. (t^3)cost
14.
A.
B.
C.
D.
Find the Laplace transform of 𝑓 𝑡 = 3𝑒 ^(−0.5𝑡 ) sin 3𝑡 sinh 7𝑡 .
3
3
−
2
2
(𝑠−6.5) +9
4.5
−
(𝑠−6.5)2 +9
4
−
(𝑠−6.5)2 +9
4.5
−
(𝑠−6.5)2 +9
(𝑠+6.5) +9
4.5
(𝑠+6.5)2 +9
4
(𝑠+6.5)2 +9
4.5
*
(𝑠+7.5)2 +9
15.
If the Fourier coefficient
zero, then it must possess ____
A. even
B. even quarter-wave
ba of a periodic function is
symmetry.
C. odd
D. either A or B*