# MCQ in Engineering Mathematics Part 6 | ECE Board Exam

(Last Updated On: January 10, 2021) This is the Multiples Choice Questions in Engineering Mathematics Part 6 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%).

#### Continue Practice Exam Test Questions Part 6 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

View Answer:

Answer: Option C

Solution:

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 π/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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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 32π/3 cu cm.

a. 2 cu cm/min

b. 3 cu cm/min

c. 4 cu cm/min

c. 5 cu cm/min

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option A

Solution:

271. a ball is thrown vertically upward and its distance from the ground is given as S = 104t – 16t2. 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

View Answer:

Answer: Option A

Solution:

272. If f(x) = ax3 + bx2 + 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

View Answer:

Answer: Option A

Solution:

273. If f(x) = ax3 + bx2, 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

View Answer:

Answer: Option A

Solution:

274. Under what condition is the inflection point of y = ax3 + bx2 + cx + d on the y-axis?

a. b = 0

b. b = 1

c. b = 3

d. b = 4

View Answer:

Answer: Option A

Solution:

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

a. 2x2 – 5x – 2

b. 5x2 – 9x – 1

c. 5x2 + 7x – 2

d. 2x2 – 8x + 5

View Answer:

Answer: Option A

Solution:

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 = x2 – 3x – 4

b. y = x2 – 3x + 2

c. y = x2 + 8x + 5

d. y = x3 + 3x – 3

View Answer:

Answer: Option B

Solution:

277. If m is the slope of the tangent line to the curve y = x2 – 2x + 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

View Answer:

Answer: Option A

Solution:

278. Suppose the daily profit from the production and sale of x units of a product is given by P = 180x – (x2)/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

View Answer:

Answer: Option B

Solution:

279. The population of a city was found to be given by P = 40500e0.03t  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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option B

Solution:

281. What is the area bounded by the curve x2 = -9y and the line y + 1 = 0.

a. 6

b. 5

c. 4

d. 3

View Answer:

Answer: Option C

Solution:

282. What is the area bounded by the curve y2 = x and the line x – 4 = 0?

a. 10

b. 32/3

c. 31/3

d. 11

View Answer:

Answer: Option B

Solution:

283. What is the area bounded by the curve y2 = 4x and x2 = 4y.

a. 6

b. 7.333

c. 6.666

d. 5.333

View Answer:

Answer: Option D

Solution:

284. Find the area bounded by the curve y = 9 – x2 and the x-axis.

a. 25 sq units

b. 36 sq units

c. 18 sq units

d. 30 sq units

View Answer:

Answer: Option A

Solution:

285. Find the area bounded by the curve y2 = 9x and its latus rectum.

a. 10.5

b. 13.5

c. 11.5

d. 12.5

View Answer:

Answer: Option B

Solution:

286. Find the area bounded by the curve 5y2 = 164x and the curve y2 = 8x – 24.

a. 30

b. 20

c. 16

d. 19

View Answer:

Answer: Option C

Solution:

287. Find the area bounded by the curve y2 = 4x and the line 2x + y = 4.

a. 10

b. 9

c. 7

d. 4

View Answer:

Answer: Option B

Solution:

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

View Answer:

Answer: Option A

Solution:

289. By integration, determine the area bounded by the curves y = 6x – x2 and y = x2 – 2x.

a. 17.78 sq units

b. 21.33 sq units

c. 25.60 sq units

d. 30.72 sq units

View Answer:

Answer: Option B

Solution:

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

a. π/2

b. 2

c. 4

d. 0

View Answer:

Answer: Option C

Solution:

291. What is the area between y = 0, y = 3x2, x = 0 and x = 2?

a. 6

b. 8

c. 12

d. 24

View Answer:

Answer: Option B

Solution:

292. Determine the tangent to the curve 3y2 = x3 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

View Answer:

Answer: Option C

Solution:

293. Find the areas bounded by the curve y = 8 – x3 and the x-axis.

a. 12 sq units

b. 13 sq units

c. 10 sq units

d. 15 sq units

View Answer:

Answer: Option A

Solution:

294. Find the area in the first quadrant bounded by the parabola, y2 = 4x and the line x = 3 and x=1.

a. 9.535

b. 5.595

c. 5.955

d. 9.955

View Answer:

Answer: Option B

Solution:

295. Find the area (in sq units) bounded by the parabola x2 – 2y = 0 and x2 = –2y + 8.

a. 11.7

b. 4.7

c. 9.7

d. 10.7

View Answer:

Answer: Option D

Solution:

296. In x years from now, one investment plan will be generating profit at the rate of R1(x)= 50 + x2 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. 10 yrs, P1360.25

b. 12 yrs, P1450.25

c. 14 yrs, P15640.25

d. 15 yrs, P1687.50

View Answer:

Answer: Option D

Solution:

297. An industrial machine generates revenue at the rate R(x) = 5000 – 20x2 pesos per yr and results in cost that accumulates at the rate of C(x) = 2000 + 10x2 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. 10 yrs, P20000

b. 12 yrs, P25000

c. 15 yrs, P30000

d. 14 yrs, P35000

View Answer:

Answer: Option A

Solution:

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

a. 3

b. 4

c. 5

d. 7

View Answer:

Answer: Option B

Solution:

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

a. 0

b. 1

c. 2

d. 3

View Answer:

Answer: Option B

Solution:

300. Find the area bounded by the curve y = 8 – x3, x = 0, y = 0.

a. 11

b. 12

c. 13

d. 15

View Answer:

Answer: Option B

Solution:

### Online Question and Answer in Engineering Mathematics Series

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

MCQ in Engineering Mathematics
PART 1: MCQ from Number 1 – 50                                 Answer key: PART 1
PART 2: MCQ from Number 51 – 100                             Answer key: PART 2
PART 3: MCQ from Number 101 – 150                            Answer key: PART 3
PART 4: MCQ from Number 151 – 200                            Answer key: PART 4
PART 5: MCQ from Number 201 – 250                            Answer key: PART 5
PART 6: MCQ from Number 251 – 300                            Answer key: PART 6
PART 7: MCQ from Number 301 – 350                             Answer key: PART 7
PART 8: MCQ from Number 351 – 400                             Answer key: PART 8
PART 9: MCQ from Number 401 – 450                             Answer key: PART 9
PART 10: MCQ from Number 451 – 500                           Answer key: PART 10

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