This is the Uncategorized Multiples Choice Questions Part 6 of the Series in Engineering Mathematics. 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 Part VI of the Series

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

251. Water is poured at the rate of 8 cu ft/min into a conical shaped tank, 20 ft. deep and 10 ft. diameter at the top. If the tank has a leak in the bottom and the water level is rising at the rate of 1 inch/min, when the water is 16 ft. deep, how fast is the water leaking?

- a. 2.96 cu ft/min
- b. 4.28 cu ft/min
- c. 3.81 cu ft/min
- d. 5.79 cu ft/min

252. An airplane is flying at a constant speed at an altitude of 10000 ft. on a line that will take it directly over an observer on the ground. At a given instant the observer notes that the angle of elevation of the airplane is Ï€/3 radians and is increasing at the rate of 1/60 rad/sec. Find the speed of the airplane.

- a. -222.22 ft/sec
- b. -232.44 ft/sec
- c. -332.22 ft/sec
- d. -432.12 ft/sec

253. A horizontal trough is 16 m long and its ends are isosceles trapezoids with an altitude of 4 m lower base of 4 m and an upper base of 6 m. If the water level is decreasing at the rate of 25 cm/min, when the water is 3 m deep, at what rate is water being drawn from the trough?

- a. 20 cu m/min
- b. 22 cu m/min
- c. 25 cu m/min
- d. 30 cu m/min

254. The sides of an equilateral triangle is increasing at rate of 10 cm/min. What is the length of the sides if the area is increasing at the rate of 69.82 sq cm/min?

- a. 5 cm
- b. 8 cm
- c. 10 cm
- d. 15 cm

255. The two adjacent sides of a triangle are 6m and 8m respectively. If the included angle is changing at the rate of 3 rad/min, at what rate is the area of a triangle changing if the included angle is 30 degrees?

- a. 55.23 sq m
- b. 62.35 sq m
- c. 65.76 sq m
- d. 70.32 sq m

256. Water is pouring into a swimming pool. After t hours, there are t+√t gallons in the pool. At what rate is the water pouring into the pool when t = 9 hours?

- a. 7/6 gph
- b. 1/6 gph
- c. 3/2 gph
- d. ½ gph

257. A point on the rim of a flywheel of radius cm, has a vertical velocity of 50 cm/sec at a point P, 4 cm above the x-axis. What is the angular velocity of the wheel?

- a. 14.35 rad/sec
- b. 16.67 rad/sec
- c. 19.95 rad/sec
- d. 10.22 rad/sec

258. A spherical balloon is filled with air at the rate of 2 cu cm/min. Compute the time rate of change of the surface are of the balloon at the instant when its volume is 32Ï€/3 cu cm.

- a. 2 cu cm/min
- b. 3 cu cm/min
- c. 4 cu cm/min
- c. 5 cu cm/min

259. The coordinate (x,y) in ft of a moving particle P are given by x = cos(t) – 1 and y = 2sin(t) + 1, where t is the time in seconds. At what extreme rates in fps is P moving along the curve?

- a. 2 and 0.5
- b. 3 and 2
- c. 2 and 1
- d. 3 and 1

260. A bomber plane is flying horizontally at a velocity of 440 m/s and drops a bomb to a target h meters below the plane. At the instant the bomb was dropped, the angle of depression of the target is 45 degrees and is increasing at the rate of 0.05 rad/sec. Determine the value of h.

- a. 2040 m
- b. 3500 m
- c. 4400 m
- d. 6704 m

261. Glycerine is flowing into a conical vessel 18cm deep and 10 cm across the top at the rate of 4 cu cm per min. The deep of glyerine is h cm. If the rate which the surface is rising is 0.1146 cm/min, find the value of h.

- a. 12 cm
- b. 16 cm
- c. 20 cm
- d. 25 cm

262. Helium is escaping from a spherical balloon at the rate of 2 cu cm/min. When the surface area is shrinking at the rate of sq cm/min, find the radius of the spherical balloon.

- a. 12 cm
- b. 16 cm
- c. 20 cm
- d. 25 cm

263. Water is running into hemispherical bowl having a radius of 10 cm at a constant rate of 3 cu cm/min. When the water is h cm deep, the water level is rising at the rate of 0.0149 cm/min. What is the value of h?

- a. 2 cm
- b. 4 cm
- c. 5 cm
- d. 6 cm

264. A train, starting noon, travels north at 40 mph. Another train starting from the same pint at 2 pm travels east at 50mph. How fast are the two trains separating at 3 pm?

- a. 34.15 mph
- b. 46.51 mph
- c. 56.15 mph
- d. 98.65 mph

265. An automobile is traveling at 30 fps towards north is approaching an intersection. When the automobile is 120 ft. from the intersection, a truck traveling at 40 fps towards east is 60 ft. from the same intersection. The automobile and the truck are on the roads that are at right angles to each other. How fast are they separating after 6 sec?

- a. 23.74 fps
- b. 47.83 fps
- c. 56.47 fps
- d. 87.34 fps

266. A train, starting noon, travels north at 40 mph. Another train starting from the same point at 2 pm travels east at 50 mph. How fast are the trains separating after a long time?

- a. 46 mph
- b. 53 mph
- c. 64 mph
- d. 69 mph

267. At noon a car drives from A towards the east at 60mph. Another car starts from B towards A at 30 mph. B has a direction and distance of N 30 degrees east and 42 m respectively from A. Find the time when the cars will be nearest each other.

- a. 23 min after noon
- b. 24 min after noon
- c. 25 min after noon
- d. 26 min after noon

268. A ferris wheel 15 m in diameter makes 1 rev every 2 min. If the center of the wheel is 9m above the ground, how many fast is a passenger in the wheel moving vertically when he is 12.5 above the ground?

- a. 20.84 m/min
- b. 22.34 m/min
- c. 24.08 m/min
- d. 25.67 m/min

269. A bomber plane, flying horizontally 3.2 km above the ground is sighting on at a target on the ground directly ahead. The angle between the line of sight and the pad of the plane is changing at the rate of 5/12 rad/min. When the angle is 30 degrees, what is the speed of the plane in mph?

- a. 200
- b. 260
- c. 220
- d. 240

270. Two railroad tracks are perpendicular to each other. At 12 pm there is a train at each track was approaching the crossing at 50kph, one being 100 km the other 150 km away from the crossing. How fast in kph is the distance between the two trains changing at 4 pm?

- a. 67.08 kph
- b. 68.08 kph
- c. 69.08 kph
- d. 70.08 kph

271. a ball is thrown vertically upward and its distance from the ground is given as S = 104t – 16t^2. Find the maximum height to which the ball will rise if S is expressed in meters and t in seconds.

- a. 169 m
- b. 179 m
- c. 187 m
- d. 190 m

272. If f(x) = ax^3 + bx^2 + cx, determine the value of a so that the graph will have a point of inflection at (1,-1) and so that the slope of the inflection tangent there will be -3.

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

273. If f(x) = ax^3 + bx^2, determine the values of a and b so that the graph will have a point of inflection at (2,16).

- a. -1, 6
- b. -2, 5
- c. -1, 7
- d. -2, 8

274. Under what condition is the inflection point of y = ax^3 + bx^2 + cx + d on the y-axis?

- a. b=0
- b. b=1
- c. b=3
- d. b=4

275. Find the equation of the curve whose slope is 4x – 5 and passing through (3,1).

- a. 2x^2 – 5x – 2
- b. 5x^2 – 9x - 1
- c. 5x^2 + 7x – 2
- d. 2x^2 – 8x + 5

276. The point (3,2) is on a curve and at any point (x,y) on the curve the tangent line has a slope equal to 2x – 3. Find the equation of the curve.

- a. y = x^2 – 3x – 4
- b. y = x^2 – 3x + 2
- c. y = x^2 + 8x + 5
- d. y = x^3 + 3x – 3

277. If m is the slope of the tangent line to the curve y = x^2 – 2x^2 + x at the point (x,y), find the instantaneous rate of change of the slope m per unit change in x at the point (2,2).

- a. 8
- b. 9
- c. 10
- d. 11

278. Suppose the daily profit from the production and sale of x units of a product is given by P = 180x – (x^2)/1000 – 2000. At what rate is the profit changing when the number of units produced and sold is 100 and is increasing at 10 units per day?

- a. P989
- b. P1798
- c. P1932
- d. P2942

279. The population of a city was found to be given by P = 40500e^(0.03t) where t is the number of years after 1990. At what rate is the population expected to be growing in 2000?

- a. 1640
- b. 1893
- c. 2120
- d. 2930

280. A bridge is h meters above a river which lies perpendicular to the bridge. A motorboat going 3 m/s passes under the bridge at the same instant that a man walking 2 m/s reaches that point simultaneously. If the distance between them is changing, at the rate of 2.647 m/s after 3 seconds, find the value of h.

- a. 8
- b. 10
- c. 12
- d. 14

281. What is the area bounded by the curve x^2 = -9y and the line y + 1 = 0.

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

282. What is the area bounded by the curve y^2 = x and the line x – 4 = 0?

- a. 10
- b. 32/3
- c. 31/3
- d. 11

283. What is the area bounded by the curve y^2 = 4x and x^2 = 4y.

- a. 6
- b. 7.333
- c. 6.666
- d. 5.333

284. Find the area bounded by the curve y = 9 – x^2 and the x-axis.

- a. 25 sq units
- b. 36 sq units
- c. 18 sq units
- d. 30 sq units

285. Find the area bounded by the curve y^2 = 9x and its latus rectum.

- a. 10.5
- b. 13.5
- c. 11.5
- d. 12.5

286. Find the area bounded by the curve 5y^2 = 164x and the curve y^2 = 8x – 24.

- a. 30
- b. 20
- c. 16
- d. 19

287. Find the area bounded by the curve y^2 = 4x and the line 2x + y = 4.

- a. 10
- b. 9
- c. 7
- d. 4

288. Find the area bounded by the curve y = 1/x with and upper limit of y = 2 and a lower limit of y = 10.

- a. 1.61
- b. 1.81
- c. 2.61
- d. 2.81

289. By integration, determine the area bounded by the curves y = 6x – x^2 and y = x^2 – 2x.

- a. 17.78 sq units
- b. 21.33 sq units
- c. 25.60 sq units
- d. 30.72 sq units

290. What is the appropriate total area bounded by the curve y = sin x and y = 0 over the interval 0≤x≤2Ï€ (in radians).

- a. Ï€/2
- b. 2
- c. 4
- d. 0

291. What is the area between y = 0, y = 3x^2, x = 0 and x = 2?

- a. 6
- b. 8
- c. 12
- d. 24

292. Determine the tangent to the curve 3y^2 = x^3 at (3,3) and calculate the area of the triangle bounded by the tangent line, the x-axis and the line x = 3.

- a. 3.50 sq units
- b. 2.50 sq units
- c. 3.00 sq units
- d. 4.00 sq units

293. Find the areas bounded by the curve y = 8 – x^3 and the x-axis.

- a. 12 sq units
- b. 13 sq units
- c. 10 sq units
- d. 15 sq units

294. Find the area in the first quadrant bounded by the parabola, y^2 = 4x and the line x = 3 and x=1.

- a. 9.535
- b. 5.595
- c. 5.955
- d. 9.955

295. Find the area (in sq units) bounded by the parabola x^2 – 2y = 0 and x^2 = –2y + 8.

- a. 11.7
- b. 4.7
- c. 9.7
- d. 10.7

296. In x years from now, one investment plan will be generating profit at the rate of R1(x)= 50 + x^2 pesos per yr, while a second plan will be generating profit at the rate R2(x)= 200 + 5x pesos per yr. For how many yrs will the second plan be more profitable one? Compute also the net excess profit if the second plan would be used instead of the first.

- a. 10yrs, P1360.25
- b. 12yrs, P1450.25
- c. 14yrs, P15640.25
- d. 15yrs, P1687.50

297. An industrial machine generates revenue at the rate R(x) = 5000 – 20x^2 pesos per yr and results in cost that accumulates at the rate of C(x) = 2000 + 10x^2 pesos per yr. For how many yrs (x) is the use of this machine profitable? Compute also that net earnings generated by the machine at this period.

- a. 10yrs, P20000
- b. 12yrs, P25000
- c. 15yrs, P30000
- d. 14yrs, P35000

298. Find the area under one arch of the curve y = sin(x/2).

- a. 3
- b. 4
- c. 5
- d. 7

299. Find the area bounded by the curve y = arc sin x, x = 1 and y = Ï€/2 on the first quadrant.

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

300. Find the area bounded by the curve y = 8 – x^3, x = 0, y = 0.

- a. 11
- b. 12
- c. 13
- d. 15

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