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BATAAN PENINSULA STATE UNIVERSITY College of Engineering and Architecture MAIN Campus Department of Electrical Engineering EECE 513
–
COMPETENCY ENHANCEMENT 1 Group Assignment No. 4
INSTRUCTION
: Select the correct answer for each of the following TEST items. Mark only one answer for each item by encircling the corresponding letter of your choice.
STRICTLY NO ERASURES ALLOWED
MULTIPLE CHOICE
1.
A mass of 3 kg is attached to the end of a spring that is stretched 20 cm by a force of 15 N. It is set in motion with the initial position X
O
= 0 and initial velocity V
O
= -10m/s. Find the period of the resulting motion. A. pi/3 C. pi/4 B. 2pi/5 D. 3pi/2 2.
Find the equation of the line thru (4,1) perpendicular to the line 2x
–
3x + 4 = 0. A. 4x + 5y + 11 = 0 C. 3x + 2y
–
14 = 0 B. 6x
–
3y
–
21 = 0 D. 2x
–
3y + 5=0 3.
An isosceles right triangle has its perimeter 10.2426 ft. What is the area of the triangle? A. 2 ft
2
2 C. 3 ft
2
B. 4.5 ft
2
D. 4 ft
2
4.
Find the value of x in xy + xz = -8 xy + yz = 1 xz + yz = -3 A. ±1 C. ±3 B. ±2 D. ±4 5.
Find the 12
th
term of the harmonic progression 1, 1/3, 1/5…
A. 1/9 C. 1/23 B. 1/17 D. 1/21 6.
When the second derivative of the equation of a curve is positive, the curve at that point is concave in what direction? A. to the left C. to the right B. downward D. upward 7.
A cylindrical spar bouy 18 inches in diameter stands in fresh water with its axis vertical. When depressed lightly and released, the period of vibration is found to be 1.5 seconds. Find the weight of the bouy. A. 258 lbs C. 201 lbs B. 189 lbs D. 165 lbs 8.
The water in a 4ft x 2ft x 1ft rectangular water tank is discharged at a point 2ft above its surface level. Find the work required in lb.ft. A. 1,248 C. 1,380 B. 1,648 D. 1,050
M4
9.
The chemist needs to dilute 50% boric solution to a 10% solution. If he needs 25 liters of the 10% solution, how much of the 50% solution should be used? A. 4li C. 6li B. 7li D. 5li 10.
A drug for the relief of asthma can be purchased from 5 different manufacturers in liquid, tablet, or capsule form, all of which come in regular and extra strength. In how many different ways can a doctor prescribe the drug for a patient suffering from asthma? A. 21 C. 10 B. 30 D. 210 11.
What is the value of x in trigonometric substitution with an integrand involving (x
2
+a
2
)? A.asec
Ө
C.asinӨ
B.atanӨ
D.acosӨ
12.
The center of the suspension bridge forms a parabolic arc. The cable is suspended two support towers which are 800ft apart. The tops of the towers are 170ft. above the road and the lowest point of the cable is midway between the towers and 10ft. above the road, find the height of the cable at a distance 100ft from the tower. A. 90 C. 85.5 B. 100 D. 80 13.
A farmer estimates that if he digs his potatoes now he will have 120 bushels, which he can sell at $1.75 per bushels. If he expects his crop to increase 8 bushels per week, but the price to drop 5 cents per bushels per week, in how many weeks should he sell to realize the maximum amount for his crop? A. 10 weeks C. 15 weeks B. 20 weeks D. 18 weeks 14.
The number of newspaper distributed is given by C = 50t
2
–
200t + 1,000 where t is in years. Find the minimum number of copies distributed from 2000 to 2007. A. 300 C. 1,000 B. 800 D. 450 15.
Find the largest rectangle that can be inscribed in x
2
= -(y-26) and x
2
= y
–
2. A. 8cm x 8cm C. 4cm x 16cm B. 8cm x 32cm D. 4cm x 32cm 16.
A bicycle travels along a straight road. At t o’clock, it is (t squared)
miles from the end of the end of the road. Compute its average velocity in mi/hr from 1:00 to 4:00 A. 4 C. 5 B. 3 D. 2 17.
Determine the equation of the line through (3,4) which forms, with the positive x and positive y axes, the triangle with the least area. A. 4x + 5y = 32 C. 4x + 3y = 24 B. 3x + 4y =25 D. 2x + 3y = 18
18.
At maximum point, the value of second derivative of the function is ________. A. infinite C. positive B. negative D. zero 19.
Simplify: (i raised to29) + (i raised to 21) + i. A. -1 C. -2i B. 3i D. i 20.
There are n couples at a party. Each man shakes hands with everyone else except his spouse. No hand shake take place between women. How many handshakes take place?(as a polynomial function of n) A. n!
–
1 C. (n
–
1)(n
–
2) B. n(n
–
1) D. (1/2)(3n
2
–
3n) 21.
Evaluate (1 + i)
10
A. -2i C. 32 B. 32i D. 2i 22.
A rectangular box with an open top is to be made from a piece of cardboard 60cm
2
by cutting equal squares from each corner and turning up the pertinent portions of the cardboard to form the sides. Determine by calculus the maximum volume of the box. A. 2, 500 cm
3
C. 9,000 cm
3
B. 4,000 cm
3
D. 16,000 cm
3
23.
The probability that a person recovers some heart attack is 0.9. Find the probability that 5 out of 7 heart attack patients will recover. A. 0.194 C. 0.124 B. 0.181 D. 0.168 24.
Evaluate the limit of sin x all over x as n approaches zero. A. 1 C. 0 B. infinity D. pi 25.
Find the volume generated by revolving the area bounded by y = x
3
, y= 8, x=0 about the y
–
axis. A. 64pi/7 C. 768pi/7 B. 512pi/5 D. 96pi/5 26.
What is the probability of getting a 7 or 11 when a pair of dice are thrown. A. 2/9 C. 1/6 B. 1/18 D. 3/8 27.
The orbit of
Halley’s comet around the sun is an ellipse with a the sun as
focus and eccentricity e = 0.967, the position where the comet is closest to the sun to the position where it is farthest from the sun is approximately 3.365 x 10
9
miles. Approximately how close the comet gets to the sun in million miles. A. 13 C. 56 B. 48 D. 23 28.
In the chemical processing of a certain mineral, the rate of change of the amount of mineral present varies as the amount of the mineral remaining. If after 8hrs, 100lbs of mineral have been reduced to 70 lbs, what quantity of the mineral will remain after 24hrs?
A. 53.2 C. 34.3 B. 43.4 D. 25.3 29.
Given n = 5 measurements 2, 1, 1, 3, 5 solve for the sample variants, s
2
? A. 1.6 C. 3 B. 2.4 D. 2.8 30.
From the relation y = 1/x, x is called the ________ of y. A. means C. surd B. inverse D. mutual 31.
A right triangle has a fixed hypotenuse of 30 cm. and the other 2 sides are allowed to vary. Determine the largest possible area of the triangle. A. 225 cm
2
C. 243 cm
2
B. 234 cm
2
D. 216 cm
2
32.
Find the perimeter of the largest rectangle that can be inscribed in x/400 + y/16 = 1. A. 400 C. 416 B. 41.6 D. 40 33.
Find the seventh and the eighth term of 1, 3, 6, 10. A. 18, 27 C. 21,28 B. 25,23 D. 28,36 34.
Marksman hits 75% of all his targets, what is the probability of hitting of exactly 4 of his next 10 shots? A. 0.01622 C. 0.004055 B. 0.4005 D. 0.001622 35.
Find the remainder when (x
12
+ 2) is divided by (x - ). A. 652 C. 231 B. 851 D. 731 36.
Change the equation y = x from rectangular to polar coordinates. A. theta equals pi/3 or 4pi/3 C. theta pi of pi/4 B. theta equals pi/4 or 5pi/4 D. theta equals 2pi or 3/4pi 37.
In a multiple-choice test consist of 5 questions each with 4 possible answers of which only 1 is correct, in how many ways can a student check off one answer to each question and get all the answers wrong? A. 720 C. 1024 B. 120 D. 243 38.
Cos law is A. a
2
= b
2
+ c
2
–
2abccosA C. b
2
= a
2
+ c
2
–
2accosA B. c
2
= a
2
+ b
2
–
2abcosA D. a
2
= b
2
+ c
2
–
2bcosA 39.
Find the Laplace Transform of sinhat. A. s/ (a
2
+ s
2
) C. a/(1
–
s
2
) B. a/(s
2
+ a
2
) D. a/(s
2
–
a
2
) 40.
Transform into intercept form: A. C.

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