This is the Multiples Choice Questions in Engineering Mathematics Part 3 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 III of the Series

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

101. Locate the point of inflection of the curve y = f(x) = (x^2)(e^x).

- a. -2 plus or minus (sqrt of 3)
- b. 2 plus or minus (sqrt of 2)
- c. -2 plus or minus (sqrt of 2)
- d. 2 plus or minus (sqrt of 3)

102. The daily sales in thousands of pesos of a product is given by S = (x^2 – x^3 + 6)/6 where x is the thousand of pesos spent on advertising. Find the point of diminishing returns for money spent on advertising.

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

103. y = x^3 – 3x . Find the maximum value of y.

- a. 2
- b. 1
- c. 0
- d. 3

104. Find the curvature of the parabola y^2 = 12x at (3,6).

- a. -√2/24
- b. √2/8
- c. 3√2
- d. 8√2/3

105. Locate the center of curvature of the parabola x^2 = 4y at point (2,2).

- a. (-2,6)
- b. (-3,6)
- c. (-2,4)
- d. (-3,7)

106. Compute the radius of curvature of the parabola x^2 = 4y at the point (4,4).

- a. 22.36
- b. 24.94
- c. 20.38
- d. 18.42

107. Find the radius of curvature of the curve y = 2x^3 + 3x^2 at (1,5).

- a. 97
- b. 90
- c. 101
- d. 87

108. Compute the radius of curvature of the curve x = 2y^3 – 3y^2 at (4,2).

- a. -97.15
- b. -99.38
- c. -95.11
- d. -84.62

109. Find the radius of curvature of a parabola y^2 – 4x = 0 at point (4,4).

- a. 22.36
- b. 25.78
- c. 20.33
- d. 15.42

110. Find the radius of curvature of the curve x = y^3 at point (1,1).

- a. -1.76
- b. -1.24
- c. 2.19
- d. 2.89

111. A cylindrical boiler is to have a volume of 1340 cu ft. The cost of the metal sheets to make the boiler should be minimum. What should be its diameter in feet?

- a. 7.08
- b. 11.95
- c. 8.08
- d. 10.95

112. A rectangular corral is to be built with a required area. If an existing fence is to be used as one of the sides, determine the relation of the width and the length which would cost the least.

- a. width=twice the length
- b. width=1/2 length
- c. width=length
- d. width=3 times the length

113. Find the two numbers whose sum is 20, if the product of one by the cube of the other is to be minimum.

- a. 5 and 15
- b. 10 and 10
- c. 4 and 16
- d. 8 and 12

114. The sum of two numbers is 12. Find the minimum value of the sum of their cubes.

- a. 432
- b. 644
- c. 346
- d. 244

115. A printed page must contain 60 sq m of printed material. There are to be margins of 5 cm on either side and margins of 3 cm on top and bottom. How long should the printed lines be in order to minimize the amount of paper used?

- a. 10
- b. 18
- c. 12
- d. 15

116. a school sponsored trip will cost each students 15 pesos if not more than 150 students make the trip, however the cost per student will reduced by 5 centavos for each student in excess of 150. How many students should make the trip in order for the school to receive the largest group income?

- a. 225
- b. 250
- c. 200
- d. 195

117. A rectangular box with square base and open at the top is to have a capacity of 16823 cu. cm. Find the height of the box that requires minimum amount of materials required.

- a. 16.14 cm
- b. 14.12 cm
- c. 12.13 cm
- d. 10.36 cm

118. A closed cylindrical tank has a capacity of 576.56 cu m. Find the minimum surface area of the tank.

- a. 383.40 cu m
- b. 412.60 cu m
- c. 516.32 cu m
- d. 218.60 cu m

119. A wall 2.245 m high is x meters away from a building. The shortest ladder that can reach the building with one end resting on the ground outside the wall is 6m. What is the value of x?

- a. 2 m
- b. 2.6 m
- c. 3.0 m
- d. 4.0 m

120. With only 381.7 sq m of materials, a closed cylindrical tank of maximum volume is to be the height of the tank, in m?

- a. 9 m
- b. 7 m
- c. 11 m
- d. 13 m

121. If the hypotenuse of a right triangle is known, what is the ratio of the base and the altitude of the right triangle when its are is maximum?

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

122. The stiffness of a rectangular beam is proportional to the breadth and the cube of the depth. Find the shape of the stiffest beam that can be cut from a log of given size.

- a. depth=√3 breadth
- b. depth=breadth
- c. depth=√2 breadth
- d. depth=2√2 breadth

123. What is the maximum length of the perimeter if the hypotenuse of a right triangle is 5m long?

- a. 12.08 m
- b. 15.09 m
- c. 20.09 m
- d. 8.99 m

124. An open top rectangular tank with square s bases is to have a volume of 10 cu m. The material fir its bottom is to cost 15 cents per sq m and that for the sides 6 cents per sq m. Find the most economical dimensions for the tank.

- a. 2 x 2 x 2.5
- b. 2 x 5 x 2.5
- c. 2 x 3 x 2.5
- d. 2 x 4 x 2.5

125. A trapezoidal gutter is to be made from a strip of metal 22 m wide by bending up the sides. If the base is 14 m, what width across the top gives the greatest carrying capacity?

- a. 16
- b. 22
- c. 10
- d. 27

126. Divide the number 60 into two pats so that the product P of one part and the square of the other is maximum. Find the smallest part.

- a. 20
- b. 22
- c. 10
- d. 27

127. The edges of a rectangular box are to be reinforced with a narrow metal strips. If the box will have a volume of 8 cu m, what would its dimensions be to require the least total length of strips?

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

128. A rectangular window surmounted by a right isosceles triangle has a perimeter equal to 54.14 m. Find the height of the rectangular window so that the window will admit the most light.

- a. 10
- b. 22
- c. 12
- d. 27

129. A normal window is in the shape of a rectangle surrounded by a semi-circle. If the perimeter of the window is 71.416, what is its radius and the height of the rectangular portion so that it will yield a window admitting the most light?

- a. 10
- b. 22
- c. 12
- d. 27

130. Find the radius of a right circular cone having a lateral area of 544.12 sq m to have a maximum volume.

- a. 10
- b. 20
- c. 17
- d. 19

131. A gutter with trapezoidal cross section is to be made from a long sheet of tin that is 15 cm wide by turning up one third of its width on each side. What width across the top that will give a maximum capacity?

- a. 10
- b. 20
- c. 15
- d. 13

132. A piece of plywood for a billboard has an area of 24 sq ft. The margins at the top and bottom are 9 inches and at the sides are 6 in. Determine the size of plywood for maximum dimensions of the painted area.

- a. 4 x 6
- b. 3 x 4
- c. 4 x 8
- d. 3 x 8

133. A manufacturer estimates that the cost of production of x units of a certain item is C = 40x – 0.02x^2 – 600. How many units should be produced for minimum cost?

- a. 1000 units
- b. 100 units
- c. 10 units
- d. 10000 units

134. If the sum of the two numbers is 4, find the minimum value of the um of their cubes.

- a. 16
- b. 18
- c. 10
- d. 32

135. If x units of a certain item are manufactured, each unit can be sold for 200 – 0.01x pesos. How many units can be manufactured for maximum revenue? What is the corresponding unit price?

- a. 10000, P100
- b. 10500, P300
- c. 20000, P200
- d. 15000, P400

136. A certain spare parts has a selling price of P150 if they would sell 8000 units per month. If for every P1.00 increase in selling price, 80 units less will be sold out pr month. If the production cost is P100 per unit, find the price per unit for maximum profit per month.

- a. P175
- b. P250
- c. P150
- d. P225

137. The highway department is planning to build a picnic area for motorist along a major highway. It is to be rectangular with an area of 5000 sq m is to be fenced off on the three sides not adjacent to the highway. What is the least amount of fencing that ill be needed to complete the job?

- a. 200 m
- b. 300 m
- c. 400 m
- d. 500 m

138. A rectangular lot has an area of 1600 sq m. Find the least amount of fence that could be used to enclose the area.

- a. 160 m
- b. 200 m
- c. 100 m
- d. 300 m

139. A student club on a college campus charges annual membership due of P10, less 5 centavos for each member over 60. How many members would give the club the most revenue from annual dues?

- a. 130 members
- b. 420 members
- c. 240 members
- d. 650 members

140. A company estimates that it can sell 1000 units per weak if it sets the unit price at P3.00, but that its weekly sales will rise by 100 units for each P0.10 decrease in price. Find the number of units sold each week and its unit price per max revenue.

- a. 2000, P2.00
- b. 1000, P3.00
- c. 2500, P2.50
- d. 1500, P1.50

141. In manufacturing and selling x units of a certain commodity, the selling price per unit is P = 5 – 0.002x and the production cost in pesos is C = 3 + 1.10x. Determine the production level that will produce the max profit and what would this profit be?

- a. 975, P1898.25
- b. 800, P1750.75
- c. 865, P1670.50
- d. 785, P1920.60

142. ABC company manufactures computer spare parts. With its present machines, it has an output of 500 units annually. With the addition of the new machines the company could boosts its yearly production to 750 units. If it produces x parts it can set a price of P = 200 – 0.15x pesos per unit and will have a total yearly cost of C = 6000 + 6x – 0.003x in pesos. What production level maximizes total yearly profit?

- a. 660 units
- b. 237 units
- c. 560 units
- d. 243 units

143. The fixed monthly cost for operating a manufacturing plant that makes transformers is P8000 and there are direct costs of P110 for each unit produced. The manufacturer estimates that 100 units per month can be sold if the unit price is P250 and that sales will in crease by 20 units for each P10 decrease in price. Compute the number of units that must be sold per month to maximize the profit. Compute the unit price.

- a. 190, P205
- b. 160, P185
- c. 170, P205
- d. 200, P220

144. The total cost of producing and marketing x units of a certain commodity is given as C = (80000x – 400x^2 + x^3)/40000. For what number x is the average cost a minimum?

- a. 200 units
- b. 100 units
- c. 300 units
- d. 400 units

145. A wall 2.245 m high is 2 m away from a bldg. Find the shortest ladder that can reach the building with one end resting on the ground outside the wall.

- a. 6 m
- b. 9 m
- c. 10 m
- d. 4 m

146. If the hypotenuse of a right triangle is known, what is the relation of the base and the altitude of the right triangle when its area is maximum?

- a. altitude=base
- b. altitude=√2 base
- c. altitude=√2 base
- d. altitude=2 base

147. The hypotenuse of a right triangle is 20 cm. What is the max possible area of the triangle in sq cm?

- a. 100
- b. 170
- c. 120
- d. 160

148. A rectangular field has an area of 10,000 sq m. What is the least amount of fencing meters to enclose it?

- a. 400
- b. 370
- c. 220
- d. 560

149. A monthly overhead of a manufacturer of a certain commodity is P6000 and the cost of material is P1.0 per unit. If not more than 4500 units are manufactured per month, labor cost is P0.40 per unit, but for each unit over 4500, the manufacturer must pay P0.60 for labor per unit. The manufacturer can sell 4000 units per month at P7.0 per unit and estimates that monthly sales will rise by 100 for each P0.10 reduction in price. Find the number of units that should be produced each month for maximum profit.

- a. 4700 units
- b. 2600 units
- c. 6800 units
- d. 9900 units

150. Find two numbers whose product is 100 and whose sum is minimum.

- a. 10, 10
- b. 12, 8
- c. 5, 15
- d. 9, 11

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