This is the Multiples Choice Questions in Engineering Mathematics Part 4 of the Series. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize each and every questions compiled here taken from various sources including past Board Exam Questions, Engineering Mathematics Books, Journals and other Engineering Mathematics References. In the actual board, you have to answer 100 items in Engineering Mathematics within 5 hours. You have to get at least 70% to pass the subject. Engineering Mathematics is 20% of the total 100% Board Rating along with Electronic Systems and Technologies (30%), General Engineering and Applied Sciences (20%) and Electronics Engineering (30%).

### The Series

Following is the list of multiple choice questions in this brand new series:

**Engineering Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART 2**

**MCQs from Number 101 – 150**Answer key:

**PART 3**

**MCQs from Number 151 – 200**Answer key:

**PART 4**

**MCQs from Number 201 – 250**Answer key:

**PART 5**

**MCQs from Number 251 – 300**Answer key:

**PART 6**

**MCQs from Number 301 – 350**Answer key:

**PART 7**

**MCQs from Number 351 – 400**Answer key:

**PART 8**

**MCQs from Number 401 – 450**Answer key:

**PART 9**

**MCQs from Number 451 – 500**Answer key:

**PART 10**

### Continue Practice Exam Test Questions Part IV of the Series

**Choose the letter of the best answer in each questions.**

151. Find two numbers whose sum is 36 if the product of one by the square of the other is a maximum.

- a. 12, 24
- b. 13, 23
- c. 20, 16
- d. 11, 25

152. Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of 108 cu in. in square inches.

- a. 123.5
- b. 127.5
- c. 125.5
- d. 129.5

153. A buyer is to take a plot of land fronting street, the plot is to be rectangular and three times its frontage added to twice its depth is to be 96 meters. What is the greatest number of sq m be may take?

- a. 298 sq m
- b. 352 sq m
- c. 384 sq m
- d. 443 sq m

154. A company has determined that the marginal cost function for the production of a particular cost function for the production of a particular commodity is given as y” = 125 + 10x – (x^2)/9 where y is the cost of producing x units of the commodity. If the fixed cost is 250 pesos, what is the cost of producing 15 units?

- a. 200
- b. 225
- c. 250
- d. 300

155. A pig weighing 300lb gains 8 pounds per day and cost 6 pesos per day to maintain. The market price for the pig is seven pesos and fifty centavos per pound but is decreasing 10 centavos per day. When should the pig be sold?

- a. 10 days
- b. 15 days
- c. 18 days
- d. 20 days

156. It costs a bus company P125 to run a bus on a certain tour, plus P15 per passenger. The capacity of the bus is 20 persons and the company charges P35 per ticket if the bus is full. For each empty seat, however, the company increases the ticket price by P2.0. For maximum profit how many empty seats would the company like to see?

- a. 3
- b. 4
- c. 5
- d. 6

157. A book publisher prints the pages of a certain book with 0.5 inch margins on the top, bottom and one side and a one inch margin on the other side to allow for the binding. Find the dimensions of the page that will maximize the printed area of the page if the area of the entire page is 96 sq inches.

- a. 7 inches
- b. 8 inches
- c. 9 inches
- d. 10 inches

158. The cost of manufacturing an engine parts is P300 and the number which can be sold varies inversely as the fourth power of the selling price. Find the selling price which will yield the greatest total net profit.

- a. 350
- b. 375
- c. 400
- d. 450

159. The price of the product in a competitive market is P300. If the cost per unit of producing the product is 160 + x where x is the number of units produced per month, how many units should the firm produce and sell to maximize its profit?

- a. 80
- b. 70
- c. 60
- d. 50

160. If the cost per unit of producing a product by ABC company is 10 + 2x and if the price on the competitive market is P50, what is the maximum daily profit that the company can expect of this product?

- a. 200
- b. 300
- c. 400
- d. 600

161. An entrepreneur starts new companies and sells them when their growth is maximized. Suppose the annual profit for a new company is given by P(x) = 22 – x/2 – 18/(x + 1) where P is in thousand of pesos and x is the number of years after the company is formed. If the entrepreneur wants to sell the company before profit begins to decline, after how many years would the company be sold?

- a. 4
- b. 5
- c. 6
- d. 7

162. The profit function for a product is P(x) = 5600x + 85x^2 – x^3 – x – 200000. How many items will produce a maximum profit?

- a. 80
- b. 70
- c. 60
- d. 40

163. The following statistics of a manufacturing company shows the corresponding values for manufacturing x units.

Production cost = 60x + 10000 pesos

Selling price/unit = 200 – 0.02x pesos

How many units must be produced for max profit?

- a. 3300
- b. 3500
- c. 3800
- d. 4000

164. The cost per unit of production is expressed as (4 + 3x) and the selling price on the competitive market is P100 per unit. What maximum daily profit that the company can expect of this product?

- a. P657
- b. P678
- c. P768
- d. P876

165. A certain unit produced by the company can be sold for 400 – 0.02x pesos where x is the number of units manufactured. What would be the corresponding price per unit in order to have a max revenue?

- a. P150
- b. P180
- c. P200
- d. P220

166. Given the cost equation of a certain product as follows C = 50t^2 – 200t + 10000 where t is in years. Find the maximum cost from the year 1995 to 2002.

- a. P6,400
- b. P7,200
- c. P9,800
- d. P10,600

167. The total cost of production a shipment of a certain product is C = 5000x + 125000/x where x is the number of machines used in the production. How many machines will minimize the total cost?

- a. 5
- b. 10
- c. 15
- d. 20

168. The demand x for a product is x = 10000 – 100P where P is the market price in pesos per unit. The expenditure for the two product is E = Px. What market price will the expenditure be the greatest?

- a. 50
- b. 60
- c. 70
- d. 100

169. Analysis of daily output of a factory shows that the hourly number of units y produced after t hours of production is y = 70t + (t^2)/2 – t^3. After how many hours will the hourly number of units be maximized?

- a. 5
- b. 6
- c. 7
- d. 8

170. An inferior product with large advertising budget sells well when it is introduced, but sales fall as people discontinue use of the product. If the weekly sales are given by S = 200t/(t + 1)^2 where S is in millions of pesos and t in weeks. After how many weeks will the sales be maximized?

- a. 1
- b. 2
- c. 3
- d. 4

171. In the coming presidential election of 1998, it is estimated that the proportions P of votes that recognizes a certain presidentiables name t months after the campaign is given by P = [7.2t/(t^2 + 16)] + 0.20. After how many months is the proportional maximized?

- a. 3
- b. 4
- c. 5
- d. 6

172. A car manufacturer estimates that the cost of production of x cars of a certain model is C = 20x – 0.01x^2 – 800. How many cars should be produced for a minimum cost?

- a. 900
- b. 1000
- c. 1100
- d. 1200

173. Analysis of daily output of a factory shows that the hourly number of units y produced after t hours of production is y = 70t + (t^2)/2 – t^3. After how many hours will the hourly number of units be maximized and what would be the maximum hourly output?

- a. 3hrs, 223.6
- b. 4hrs, 273.6
- c. 5hrs, 237.5
- d. 6hrs, 243.5

174. A time study showed that on average, the productivity of a worker after t hours on the job can be modeled by the expression P = 27 + 6t – t^3 where P is the number of units produced per hour. What is the maximum productivity expected?

- a. 34
- b. 36
- c. 40
- d. 44

175. The sum of two numbers is equal to S. Find the minimum sum of the cube of the two numbers/

- a. (S^3)/4
- b. S/4
- c. (S^2)/4
- d. (S^3)/5

176. Given the cost equation of a certain product as follows: C = 50t^2 – 200t + 10000 where t is in years. Find the maximum cost from year 1995 to 2002.

- a. P9000
- b. P9800
- c. P8500
- d. P7300

177. A manufacturer determines that the profit derived from selling x units of a certain item is given by P = 0.003x^2 + 10x. Find the marginal profit for a production of 50 units.

- a. P10.30
- b. P12.60
- c. P15.40
- d. P17.30

178. The total cost of production spare parts of computers is given as C = 4000x – 100x^2 + x^3 where x is the number of units of spare parts produced so that the average cost will be minimum?

- a. 4
- b. 10
- c. 20
- d. 50

179. A viaduct is traversed by a truck running at 15mph at the same time that another truck traveling at a speed of 30mph on the street 22ft below and at right angle to the viaduct, approached the point directly below the viaduct from a distance of 55ft. Find the nearest distance between the trucks.

- a. 29 ft
- b. 33 ft
- c. 39 ft
- d. 44 ft

180. A sector is cut out of a circular disk of radius √3 and the remaining part of the disk I bent up so that the two edges join and a cone is formed. What is the largest volume for the cone?

- a. 2π/3
- b. π/3
- c. 3π/4
- d. π/4

181. Four squares are cut out of a rectangular cardboard 50 cm by 80 cm. in dimension and the remaining piece is folded into a closed, rectangular box with two extra flaps trucked in. What is the largest possible volume for such a box?

- a. 6000
- b. 7000
- c. 8000
- d. 9000

182. An isosceles triangle with equal sides of 20 cm has these sides at a variable equal angle with the base. Determine the max area of the triangle.

- a. 200 sq cm
- b. 250 sq cm
- c. 300 sq cm
- d. 280 sq cm

183. Formerly, for a package to go by parcel post, the sum of its length and girth could not exceed 120 cm. Find the dimensions of the rectangular package of greatest volume that could be sent.

- a. 20 x 40 x 10
- b. 20 x 20 x 20
- c. 40 x 20 x 30
- d. 20 x 20 x 40

184. The cross-section of a trough is an isosceles trapezoid. If the trough is made by bending up the sides of s strip of metal 12 cm wide, what would be the angle of inclination of the sides and the width across the bottom if the cross-sectional area is to be a maximum?

- a. 45 degrees
- b. 60 degrees
- c. 75 degrees
- d. 120 degrees

185. Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of 108 cu inches in square inches.

- a. 123.5
- b. 125.5
- c. 127.5
- d. 129.5

186. Compute the abscissa of the min point of the curve y = x^3 – 12x – 9.

- a. 2
- b. -2
- c. -1
- d. 1

187. What value of x does a maximum of y = x^3 – 3x occur?

- a. -1
- b. 1
- c. 2
- d. -2

188. Determine the point on the curve y^2 = 8x which is nearest to the external curve (4,2).

- a. (2,4)
- b. (4,3)
- c. (3,5)
- d. (6,8)

189. The LRT system runs from the Bonifacio Monument to Baclaran for a total distance of 15 km. The cost of electric energy consumed by a train per hour is directly proportional to the cube of its speed and is P250 per hour at 50 kph. Other expenses such as salaries, depreciation, overhead, etc. amounts to P1687.50 per hour. Find the most economical speed of the train in kph.

- a. 60
- b. 65
- c. 75
- d. 80

190. A businessman found out that his profit varies as the product of the amount spent for production and the square root of the amount spent for advertisement. If his total budget for these expenses is P1.5 million, how much must be allocated for advertisement to maximize his profit?

- a. 0.5M
- b. 0.7M
- c. 0.8M
- d. 1.0M

191. A steel girder 16 m long is moved on rollers along a passageway 8 m wide and into a corridor at right angles with the passageway. Neglecting the width of the girder, how wide must the corridor be?

- a. 1.4 m
- b. 1.8 m
- c. 2.8 m
- d. 3.6 m

192. A can manufacturer receives an order for milk cans having a capacity of 100 cu cm. Each can is made from a rectangular sheet of metal by rolling the sheet into a cylinder; the lids are stamped out from another rectangular sheet. What are the most economical proportions of the can?

- a. 2.53
- b. 2.55
- c. 2.59
- d. 3.67

193. A triangle has a variable sides x, y and z subject to the constraint that the perimeter P is fixed to 18 cm. What is the maximum possible area for the triangle?

- a. 14.03 sq cm
- b. 15.59 sq cm
- c. 17.15 sq cm
- d. 18.71 sq cm

194. Postal regulations require that a parcel post package shall be not greater than 600cm in the sum of its length and girth (perimeter of the cross-section). What is the volume in cu cm of the largest package allowed by the postal regulations if the package is to be rectangular in cu cm?

- a. 2 x 10^6
- b. 3 x 10^6
- c. 1.5 x 10^6
- d. 4 x 10^6

195. Divide 60 into 3 parts so that the product of the three parts will be a maximum, find the product.

- a. 4000
- b. 6000
- c. 8000
- d. 12000

196. Find the radius of the circle inscribe in a triangle having a max area of 173.205 sq cm.

- a. 2.19 cm
- b. 3.45 cm
- c. 4.96 cm
- d. 5.77 cm

197. The area of a circle inscribe in a triangle is equal to 113.10 sq cm. Find the max area of the triangle.

- a. 156. 59 sq cm
- b. 175.80 sq cm
- c. 186.98 sq cm
- d. 193. 49 sq cm

198. Find the perimeter of a triangle having a max area that is circumscribing a circle of radius 8 cm.

- a. 83.13 cm
- b. 84.96 cm
- c. 85.77 cm
- d. 92.19 cm

199. Suppose y is the number of workers in the labor force needed to produce x units of a certain commodity and x = 4y^2. If the production of the commodity this year is 25000 units and the production is increasing at the rate and the production is increasing at the rate of 18000 units per year, what is the current rate at which the labor force should be increased?

- a. 7
- b. 9
- c. 10
- d. 15

200. Sugar juice is filtering through a conical funnel 20 cm, deep and 12 cm across top, into a cylindrical container whose diameter is 10cm. When the depth of the juice in the funnel is 10 cm, determine the rate at which its level in the cylinder is rising.

- a. 0.15
- b. 0.45
- c. 0.75
- d. 1.25

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