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# MCQ in Engineering Mathematics Part 5 | Math Board Exam

This is the Multiples Choice Questions in Engineering Mathematics Part 5 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 5 of the Series

Choose the letter of the best answer in each questions.

201. An airplane, flying horizontally at an altitude of 1 km, passes directly over an observer. If the constant speed of the plane is 240 kph, how fast is its distance from the observer increasing 30 seconds later?

a. 137.78 kph

b. 214.66 kph

c. 256.34 kph

d. 324.57 kph

Solution:

202. A metal disk expands during heating. If its radius increases at the rate of 20 mm per second, how fast is the area of one of its faces increasing when its radius is 8.1 meters?

a. 0.846 sq m per sec

b. 1.018 sq m per sec

c. 1.337 sq m per sec

d. 1.632 sq m per sec

Solution:

203. The structural steel work of a new office building is finished. Across the street 20 m from the ground floor of the freight elevator shaft in the building, a spectator is standing and watching the freight elevator ascend at a constant rate of 5 meters per second. How fast is the angle of elevation of the spectatorโs line of sight to the elevator increasing 6 seconds after his line of sight passes the horizontal?

a. 1/10

b. 1/12

c. 1/13

d. 1/15

Solution:

204. A boy rides a bicycle along the Quezon Bridge at a rate of 6 m/s. 24 m directly below the bridge and running at right angles to it is a highway along which an automobile is traveling at the rate of 80 m/s. How far is the distance between the boy and the automobile changing when the boy is 6m, past the point directly over the path of the automobile and the automobile is 8m past the point directly under the path of the boy?

a. 20 m/s

b. 26 m/s

c. 28 m/s

d. 30 m/s

Solution:

205. A point moves on the parabola y2 = 8 in such a way that the rate of change of the ordinate is always 5 units per sec. How fast is the abscissa changing when the ordinate is 4?

a. 3

b. 4

c. 5

d. 7

Solution:

206. An air traffic controller spots two planes at the same altitude converging on a point as they fly at right angles to one another. One plane is 150 miles from the point and is moving at 450 mph. The other plane is 200 miles from the point and has the speed of 600 mph. How much time does the traffic controller have to get one of the planes on a different flight path?

a. 15 min

b. 20 min

c. 25 min

d. 30 min

Solution:

207. An LRT train 6 m above the ground crosses a street at a speed of 9 m/s, at the instant that a car approaching at a speed of 4 m/s is 12 m up the street. Find the rate of the LRT train and the car are separating one second later.

a. 3.64 m/s

b. 4.34 m/s

c. 6.43 m/s

d. 4.63 m/s

Solution:

208. A street light is 8 m from a wall and 4 m from a point along the path leading to the shadow of the man 1.8 m tall shortening along the wall when he is 3 m from the wall. The man walks towards the wall at the rate of 0.6 m/s.

a. -1.018 m/s

b. -0.027 m/s

c. -0.192 m/s

d. -0.826 m/s

Solution:

209. A mercury light hangs 12 ft above the island at the center of Ayala Avenue which is 24 ft wide. A cigarette vendor 5 ft tall walks along the curb of the street at a speed of 420 fpm. How fast is the tip of the shadow of the cigarette vendor moving at the same instant?

a. 10 fps

b. 12 fps

c. 14 fps

d. 15 fps

Solution:

210. The sides of an equilateral triangle are increasing at the rate of 10 m/s. What is the length of the sides at the instant when the area is increasing 100 sq m/sec?

a. 15/โ3

b. 20/โ3

c. 22/โ3

d. 25/โ3

Solution:

211. Water is the flowing into a conical vessel 15 cm deep and having a radius of 3.75 cm across the top. If the rate at which water is rising is 2 cm/s, how fast is the water flowing into the conical vessel when the depth of water is 4 cm?

a. 1.5 cu m/min

b. 2.5 cu m/min

c. 4 cu m/min

d. 6.28 cu m/min

Solution:

212. Two sides of a triangle are 5 and 8 units respectively. If the included angle is changing at the rate of one radian pr second, at what rate is the third side changing when the included angle is 60 degrees?

a. 3.87 units/sec

b. 4.24 units/sec

c. 4.95 units/sec

d. 5.55 units/sec

Solution:

213. The two adjacent sides of a triangle are 5 and 8 meters respectively. If the included angle is changing at the rate of 2 rad/sec, at what rate is the area of the triangle changing if the included angle is 60 degrees?

a. 15 sq m/sec

b. 20 sq m/sec

c. 23 sq m/sec

d. 25 sq m/sec

Solution:

214. A triangular trough is 12 m long, 2 m wide at the top and 2 m deep. If water flows in at the rate of 12 cu m per min, find how fast the surface is rising when the water is 1 m deep.

a. 1

b. 2

c. 3

d. 4

Solution:

215. A man starts from a point on a circular track of radius 100 m and walks along the circumference at the rate of 40 m/min. An observer is stationed at a point on the track directly opposite the starting point and collinear with the center of the circular track. How fast is the manโs distance form the observer changing after one minute?

a. -6.48 m/min

b. -7.95 m/min

c. 8.62 m/min

d. 9.82 m/min

Solution:

216. A plane 3000 ft from the earth is flying east at the rate of 120 mph. It passes directly over a car also going east at 60 mph. How fast are they separating when the distance between them is 5000 ft?

a. 63.7 ft/sec

b. 70.4 ft/sec

c. 76.2 ft/sec

d. 84.3 ft/sec

Solution:

217. A horseman gallops along the straight shore of a sea at the rate of 30 mph. A battleship anchored 3 miles offshore keeps searchlight trained on him as he moved along. Find the rate of rotation of the light when the horseman is 2 miles down the beach?

Solution:

218. Find the point in the parabola y2 = 4x at which the rate of change of the ordinate and abscissa are equal.

a. (1,2)

b. (-1,4)

c. (2,1)

d. (4,4)

Solution:

219. Water flows into a vertical cylindrical tank, at the rate of 1/5 cu ft/sec. The water surface is rising at the rate of 0.425 ft/min. What is the diameter of the tank?

a. 4 ft

b. 6 ft

c. 8 ft

d. 10 ft

Solution:

220. The radius of a sphere is changing at a rate of 2 cm/sec. Find the rate of change of the surface area when the radius is 6 cm.

a. 68ฯ sq cm/sec

b. 78ฯ sq cm/sec

c. 84ฯ sq cm/sec

d. 96ฯ sq cm/sec

Solution:

221. The radius of a circle is increasing at the rate of 2 cm/min. Find the rate of change of the area when r = 6 cm.

a. 18 ฯ sq cm/sec

b. 24 ฯ sq cm/sec

c. 30 ฯ sq cm/sec

d. 36 ฯ sq cm/sec

Solution:

222. All edges of a cube are expanding at the rate of 3 cm/sec. How fast is the volume changing when each edge is 10 cm long?

a. 900 cu cm/sec

b. 800 cu cm/sec

c. 600 cu cm/sec

d. 400 cu cm/sec

Solution:

223. A spherical balloon is inflated with gas at the rate of 20 cu m/min. How fast is the radius of the balloon changing at the instant the radius is 2 cm?

a. 0.388

b. 0.398

c. 0.422

d. 0.498

Solution:

224. The base radius of a cone is changing at a rate of 3 cm/sec. Find the rate of change of its volume when the radius is 4 cm and its altitude is 6cm.

a. 18 ฯ cu cm/sec

b. 24 ฯ cu cm/sec

c. 36 ฯ cu cm/sec

d. 48 ฯ cu cm/sec

Solution:

225. The edge of cube is changing at a rate of 2 cm/min. Find the rate of change of its diagonal when each edge is 10 cm long.

a. 2.128 cm/min

b. 3.464 cm/min

c. 5.343 cm/min

d. 6.283 cm/min

Solution:

226. The radius of a circle is changing at a rate of 4 cm/sec. Determine the rate of change of the circumference when the radius is 6 cm.

a. 4 ฯ cm/sec

b. 6 ฯ cm/sec

c. 8 ฯ cm/sec

d. 10 ฯ cm/sec

Solution:

227. When a squares of side x are cut from the corners of a 12 cm square piece of cardboard, an open top box can be formed by folding up the sides. The volume of this box is given by V = x(12 โ 2x)2. Find the rate of change of volume when x = 1 cm.

a. 60

b. 40

c. 30

d. 20

Solution:

228. As x increases uniformly at the rate of 0.002 ft/sec, at what rate is expression (1 + x) to the third power increasing when x becomes 8 ft?

a. 0.300 cfs

b. 0.346 cfs

c. 0.430 cfs

d. 0.486 cfs

Solution:

229. A trough 10 m long has as it ends isosceles trapezoids, altitude 2 m, lower base, 2 m upper base 3 m. If water is let in at a rate of 3 cu m/min, how fast is the water level rising when the water is 1 m deep?

a. 0.12

b. 0.18

c.0.21

d. 0.28

Solution:

230. a launch whose deck is 7 m below the level of a wharf is being pulled toward the wharf by a rope attached to a ring on the deck. If a winch pulls in the rope at the rate of 15 m/min, how fast is the launch moving through the water when there are 25 m of rope out?

a. 14.525

b. -14.526

c. 15.148

d. -15.625

Solution:

231. An object is dropped freely from a bldg. having a height of 40 m. An observer at a horizontal distance of 30 m from a bldg is observing the object is it was dropped. Determine the rate at which the distance between the object and the observer is changing after 2sec.

a. -10.85

b. -11.025

c. 12.25

d. 14.85

Solution:

232. Car A moves due east at 30 kph at the same instant car B is moving S 30 deg E.with a speed of 30 kph. The distance from A to B is 30 km. Find how fast is the speed between them are separating after one hour.

a. 36 kph

b. 38 kph

c. 40 kph

d. 45 kph

Solution:

233. Water is flowing into a frustum of a cone at a rate of 100 liter/min. The upper radius of the frustum of a cone is 1.5 m while the lower radius is 1m and a height of 2 m. If the water rises at the rate of 0.04916 cm/sec, find the depth of water.

a. 10.3 cm

b. 13.6 cm

c. 15.5 cm

d. 18.9 cm

Solution:

234. Water is flowing into a conical vessel 18 cm deep and 10 cm across the top. If the rate at which the water surface is rising is 27.52 mm/sec, how fast is the water flowing into the conical vessel when the depth of water is 12 cm?

a. 9.6 cu cm/sec

b. 8.5 cu cm/sec

c. 7.4 cu cm/sec

d. 6.3 cu cm/sec

Solution:

235. Sand is falling off a conveyor onto a conical pile at the rate of 15 cu cm/min. The base of the cone is approximately twice the altitude. Find the height of the pile if the height of he pile is changing at the rate of 0.047746 cm/min.

a. 12 cm

b. 10 cm

c. 8 cm

d. 6 cm

Solution:

236. A company is increasing its production of a certain product at the rate of 100 units per month. The monthly demand function is given by P = 100 โ x/800. Find the rate of change of the revenue with respect to time in months when the monthly production is 4000.

a. P9000/month

b. P8000/month

c. P6000/month

d. P4000/month

Solution:

237. A machine is rolling a metal cylinder under pressure. The radius of the cylinder is decreasing at the rate of 0.05 cm/sec and the volume V is 128ฯ cu cm. At what rate is the length h changing when the radius is 2.5 cm?

a. 0.8192 cm/sec

b. 0.7652 cm/sec

c. 0.6178 cm/sec

d. 0.5214 cm/sec

Solution:

238. Two sides of a triangle are 15 cm and 20 cm long respectively. How fast is the third side increasing if the angle between the given sides is 60 degrees and is increasing at the rate of 2 deg/sec?

a. 0.05 cm/s

b. 1.20 cm/s

c. 2.70 cm/s

d. 3.60 cm/s

Solution:

239. Two sides of a triangle are 30 cm and 40 cm respectively. How fast is the area of the triangle increasing if the angle between the sides is 60 degrees and is increasing at the rate of 4 deg/sec?

a. 14.68

b. 20.94

c. 24.58

d. 29.34

Solution:

240. A man 6 ft tall is walking toward a building at the rate of 5 ft/sec. If there is a light on the ground 50 ft from a bldg, how fast is the manโs shadow on the bldg growing shorter when he is 30 ft from the bldg?

a. -7.35 fps

b. -5.37 fps

c. -4.86 fps

d. -3.75 fps

Solution:

241. The volume of the sphere is increasing at the rate of 6 cu cm/hr. At what rate is its surface area increasing when the radius is 50 cm (in cu cm/hr)?

a. 0.24

b. 0.36

c. 0.40

d. 0.50

Solution:

242. A particle moves in a plane according to the parametric equations of motions: x = t2, y = t3. Find the magnitude of the acceleration when t = 2/3.

a. 4.47

b. 5.10

c. 4.90

d. 6.12

Solution:

243. A particle moves along the right-hand part of the curve 4y3 = x2 with a speed Vy = dy/dx = constant at 2. Find the speed of motion when y = 4.

a. 12.17

b. 14.10

c. 15.31

d. 16.40

Solution:

244. The equations of motion of a particle moving in a plane are x = t2, y = 3t โ 1 when t is the time and x and y are rectangular coordinates. Find the speed of motion at the instant when t = 2.

a. 5

b. 7

c. 9

d. 10

Solution:

245. A particle moves along the parabola y2 = 4x with a constant horizontal component velocity of 2 m/s. Find the vertical component of the velocity at the point (1, 2).

a. 2 m/s

b. 4 m/s

c. 5 m/s

d. 7 m/s

Solution:

246. The acceleration of the particle is given by a = 2 + 12t in m/s2 where t is the time in minutes. If the velocity of this particle is 11 m/s after 1 min, find the velocity after 2 minutes.

a. 26 m/s

b. 31 m/s

c. 37 m/s

d. 45 m/s

Solution:

247. A particle moves along a path whose parametric equations are x = t3 and y = 2t2. What is the acceleration when t = 3 sec.

a. 10.59 m/sec2

b. 15.93 m/sec2

c. 18.44 m/sec2

d. 23.36 m/sec2

Solution:

248. A vehicle moves along a trajectory having coordinates given as x = t3 and y = 1 โ t2. The acceleration of the vehicle at any point of the trajectory is a vector having magnitude and direction. Find the acceleration when t = 2.

a. 12.17

b. 12.45

c. 13.20

d. 15.32

Solution:

249. The search light of a lighthouse which is positioned 2 km from the shoreline is tracking a car which is traveling at a constant speed along the shore. If the searchlight is rotating at the rate of 0.25 rev per hour, determine the speed of the car when it is 1 km away from the point on the shore nearest to the lighthouse.

a. 4.16 kph

b. 3.93 kph

c. 2.5 kph

d. 1.8 kph

Solution:

250. A light is at the top of a pole 80 ft high. A ball is dropped at the same height from a point 20 ft from the light. Assuming that the ball falls according to S = 16t2, how fast is the shadow of the ball moving along the ground 1 second later?

a. -140 ft/sec

b. -180 ft/sec

c. -200 ft/sec

d. -240 ft/sec

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

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