This is the Multiples Choice Questions in Engineering Mathematics Part 10 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 X of the Series

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

451. A simple beam having a span of 6m has a weight of 20 kN/m. It carries a concentrated load of 20 kN at the left end and 40 kN at 2m from the right end of the beam. If it is supported at 2 m from the left end and the right end, compute the reaction at the right end of the beam.

- a. 20 kN
- b. 30 kN
- c. 40 kN
- d. 50 kN

452. When one boy is sitting 1.20 m from the center of a seesaw another boy must sit on the other side 1.50 m from the center to maintain an even balance. However, when the first boy carries an additional weight of 14 kg and sit 1.80 m from the center, the second boy must move 3m from the center to balance, Neglecting the weight of the see weight of the heaviest boy.

- a. 42 kg
- b. 35 kg
- c. 58 kg
- d. 29 kg

453. A wire connects a middle of links AC and AB compute the tension in the wire if AC carries a uniform load of 600 N/m. AC is 4.5 m long and BC is 7.5 m. point A is hinged on the wall and joint C is also hinged connecting the links AC and CB. AC is horizontal while B is supported by roller acting on the wall AB.

- a. 2200 N
- b. 2700 N
- c. 300 N
- d. 3600 N

454. An airtight closed box of weight P is suspended from a spring balance. A bird of weight W is place on the floor of the bow, and the balance reads W + P. If the bird flies without accelerating. What is the balance reading?

- a. P – W
- b. P
- c. P + W
- d. P + 2W

455. A tripod whose legs are each 4 meters long supports a load of 1000 kg. the feet of the tripod are at the vertices of a horizontal equilateral triangle whose side are 3.5 meters. Determine the load of each leg.

- a. 214.69 kg
- b. 347.29 kg
- c. 386.19 kg
- d. 446.27 kg

456. A uniform square table top ABCD having sides 4m long is supported by three vertical supports at A, E and F, E is midway n the side BC and F is 1m from D along the side DC. Determine the share of load in percent carried by supports at A, E and F.

- a. A = 29%, E = 42%, F = 29%
- b. A = 32%, E = 46%, F = 20%
- c. A = 28%, E = 40%, F = 32%
- d. A = 36%, E = 32%, F = 32%

457. The square steel plate has a mass of 1800 kg with mass at its center G. Calculate the tension at each of the three cables with which the plate is lifted while remaining horizontal.

- a. Ta = Tb = 6.23 kN, Tc = 10.47 kN
- b. Ta = Tb = 7.47 kN, Tc = 7.84 kN
- c. Ta = Tb = 5.41 kN, Tc = 9.87 kN
- d. Ta = Tb = 4.42 kN, Tc = 6.27 kN

458. A horizontal Circular platform of radius R is supported at three points A, B and C on its circumference. A and B are 90 degrees apart and C is 120 degrees from A. The platform carries a vertical load of 400 kN at its center and 100 kN at a point d on the circumference diametrically opposite A. Compute the reaction at C.

- a. 253.45 kN
- b. 321.23 kN
- c. 310.10 kN
- d. 287.67 kN

459. A ladder 4m long having a mass of 15 kg is resting against a floor and an wall for which the coefficients of static friction are 0.30 for the floor to which a man having a mass of 70 kg can climb without causing the plank to slip if the plank makes an angle of 40 degrees with the horizontal.

- a. 2
- b. 1
- c. 2.5
- d. 3

460. A homogenous block having dimension of 4 cm by 8 cm is resting on an inclined plane making an angle of θ with the horizontal. The block has a weight of 20 kN. If the coefficient of friction between the block and the inclined plane is 0.55, find the value of θ before the block starts to move. The 8cm side is perpendicular to the inclined plane.

- a. 23.4°
- b. 26.57°
- c. 27.7°
- d. 28.81°

461. A uniform ladder on a wall at A and at the floor at B. Point A is 3.6 m above the floor and point B is 1.5 m away from the wall. Determine the minimum coefficient of friction at B required for a mass weighing 65 kg to use the ladder assuming that there is no friction at A.

- a. 0.42
- b. 0.50
- c. 0.48
- d. 0.54

462. A block having a mass of 250 kg is placed on top of an inclined plane having a slope of 3 vertical to 4 horizontal. If the coefficient of friction between the block and the inclined plane is 0.15, determine the force P that may be applied parallel to the inclined plane to keep block from sliding down the plane.

- a. 980.86 N
- b. 1088.2 N
- c. 1177.2 N
- d. 1205.30 N

463. A 3.6 m ladder weighing 180 N is resting on a horizontal floor at A and on the wall at B making an angle of 30 degrees from the vertical wall. When a man weighing 800 N reaches a point 2.4 m from the lower end (point A), the ladder is just about to slip. Determine the coefficient of friction between the ladder and the floor if the coefficient of friction between the ladder and the wall is 0.20.

- a. 0.28
- b. 0.35
- c. 0.42
- d. 0.56

464. A dockworker adjusts a spring line (rope) which keeps the ship from drifting along side a wharf. If he exerts a pull of 200 N on the rope, which ahs 1 ¼ turns around the mooring bit, what force T can he support? The coefficient of friction between the rope and the cast-steel mooring bit is 0.30.

- a. 2110 N
- b. 1860 N
- c. 155 N
- d. 142 N

465. Determine the distance “x” to which the 90 kg painter can climb without causing the 4m ladder to slip at its lower end A. The top of the 15 kg ladder has a small roller, and the ground coefficient of static friction is 0.25. the lower end of the ladder is 1.5 m away from the wall.

- a. 0.1 m
- b. 3.17 m
- c. 2.55 m
- d. 1.58 m

466. The uniform pole of length 4 m and mass 100 kg is leaned against a vertical wall. If the coefficient of static friction between the supporting surfaces and the ends of the poles is 0.25, calculate the maximum angle θ at which the pole may be placed with the vertical wall before it starts to slip.

- a. 28.07°
- b. 26.57°
- c. 31.6°
- d. 33.5°

467. A horizontal force P acts on the top of a 30 kg block having a width of 25 cm, and a height of 50 cm. if the coefficient of friction between the block and the plane is 0.33, what is the value of P for motion to impend?

- a. 5.3 kg
- b. 6.6 kg
- c. 7.5 kg
- d. 8.2 kg

468. A 600 N block rests on a 30° plane. If the coefficient of static friction is 0.30 and the coefficient of kinetic friction is 0.20, what is the value of P applied horizontally to prevent the block from sliding down the plane?

- a. 141.85 N
- b. 183.29 N
- c. 119.27 N
- d. 126.59 N

469. A 600 N block rests on a 30° plane. If the coefficient of static friction is 0.30 and the coefficient of kinetic friction is 0.20, what is the value of P applied horizontally to keep the block moving up the plane?

- a. 427.46 N
- b. 527.31 N
- c. 569.29 N
- d. 624.17 N

470. Solve for the force P to obtain equilibrium. Angle of friction is 25° between block and the inclined plane.

- a. 69.38 kg
- b. 77.65 kg
- c. 84.22 kg
- d. 96.46 kg

471. A 200 kg crate impends to slide down a ramp inclined at an angle of 19.29° with the horizontal. What is the frictional resistance? Use g = 9.81 m/s^2.

- a. 648.16 N
- b. 638.15 N
- c. 618.15 N
- d. 628.15 N

472. A 40 kg block is resting on an inclined plane making an angle of 20° from the horizontal. If the coefficient of friction is 0.60, determine the force parallel to the incline that must be applied to cause impending motion down the plane. Use g = 9.81

- a. 77 N
- b. 82 N
- c. 72 N
- d. 87 N

473. A 40 kg block is resting on an inclined plane making an angle of θ from the horizontal. Coefficient of friction is 0.60, find the value of θ when force P = 36.23 is applied to cause the motion upward along the plane.

- a. 20°
- b. 30°
- c. 28°
- d. 23°

474. A 40 kg block is resting on an inclined plane making an angle θ from the horizontal. The block is subjected to a force 87 N parallel to the inclined plane which causes an impending motion down the plane. If the coefficient of motion is 0.60, compute the value of θ.

- a. 28°
- b. 30°
- c. 20°
- d. 23°

475. A rectangular block having a width of 8cm and height of 20 cm, is reating on a horizontal plane. If the coefficient of friction between he horizontal plane and the block is 0.40, at what point above the horizontal plane should horizontal force P will be applied at which tipping will occur?

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

476. A ladder is resting on a horizontal plane and a vertical wall. If the coefficient of friction between the ladder, the horizontal plane and the vertical wall is 0.40, determine the angle that the ladder makes with the horizontal at which it is about to slip.

- a. 33.6°
- b. 46.4°
- c. 53.13°
- d. 64.13°

477. Three identical blocks A, B and C are placed on top of each other are place on a horizontal plane with block B on top of A and C on top of B. The coefficient of friction between all surfaces is 0.20. if block C is prevented from moving by a horizontal cable attached to a vertical wall, find the horizontal force in Newton that must be applied to B without causing motion to impend. Each block has a mass of 50 kg.

- a. 280.5 Newtons
- b. 274.7 Newtons
- c. 321.3 Newtons
- d. 294.3 Newtons

478. A car moving downward on an inclined plane which makes an angle of θ from the horizontal. The distance from the front wheel to the rear wheel is 400 cm and its centroid is located at 50 cm from the surface of the plane. If only rear wheels provide breaking, what is the value of θ so that the car will start to slide if the coefficient of friction is 0.6?

- a. 15.6°
- b. 18.4°
- c. 16.8°
- d. 17.4°

479. A 40kg block is resting on an inclined plane making an angle of 20° from the horizontal. If the coefficient of friction is 0.60, determine the force parallel to the inclined plane that must be applied to cause impending motion up the plane.

- a. 354.65 N
- b. 355.42 N
- c. 439.35 N
- d. 433.23 N

480. A block weighing 40 kg is placed on an inclined plane making an angle of θ from th horizontal. If the coefficient of friction between the block and the inclined plane is 0.30, find the value of θ, when the block impends to slide downward.

- a. 13.60°
- b. 14.50°
- c. 15.80°
- d. 16.70°

481. A block having a weight W is resting on an inclined plane making an angle of 30° from the horizontal. If the coefficient of friction between the block and the inclined plane is 0.50. Determine the value of W is a force 300 N applied parallel to the inclined plane to cause an impending motion upward.

- a. 321.54 N
- b. 493.53 N
- c. 450.32 N
- d. 354.53 N

482. 40 kg block is resting on an inclined plane making an angle of 20° from the horizontal. The block is subjected to a force 87 N parallel to the inclined plane which causes an impending motion down the plane. Compute the coefficient of friction between the block and the inclined plane.

- a. 0.50
- b. 0.60
- c. 0.70
- d. 0.80

483. A 20 kg cubical block is resting on an inclined plane making an angle of 30° with the horizontal. If the coefficient of friction between the block and the inclined plane is 0.30, what force applied at the uppermost section which is parallel to the inclined plane will cause the 20 kg block to move up?

- a. 130 N
- b. 134 N
- c. 146 N
- d. 154 N

484. The coefficient of friction between the 60 kN block is to remain in equilibrium, what is the maximum allowable magnitude for the force P?

- a. 18 kN
- b. 12 kN
- c. 15 kN
- d. 24 kN

485. Find the value of P acting to the left that is required to pull the wedge out under the 500kg block. Angle of friction is 20° for all contact surfaces.

- a. 253.80 kg
- b. 242.49 kg
- c. 432.20 kg
- d. 120.50 kg

486. The accurate alignment of a heavy duty engine on its bed is accomplished by a screw adjusted wedge with a 20° taper as shown in the figure. Determine the horizontal thrust P in adjusting screw necessary to raise the mounting if the wedge supports one fourth of the total engine weight of 20 000 N. The total coefficient of friction for all surfaces is 0.25.

- a. 4550 N
- b. 4640 N
- c. 5460 N
- d. 6540 N

487. Two blocks connected by a horizontal link AB are supported on two rough planes as shown. The coefficient of friction for block A on the horizontal plane is 0.40. the angle of friction for block B on the inclined plane is 15°. What is the smallest weight of block A for which equilibrium of the system can exists?

- a. 500 kN
- b. 1500 kN
- c. 2000 kN
- d. 1000 kN

488. Is the system in equilibrium? If not, find the force P so that the system will be in equilibrium.

- a. 80 kg
- b. 90 kg
- c. 100 kg
- d. 70 kg

489. A 12 kg block of steel is at rest on a horizontal cable. The coefficient of static friction between the block a table is 0.52. What is the magnitude of the force acting upward 62° from the horizontal that will just start the block moving?

- a. 65.9 N
- b. 78.1 N
- c. 70.2 N
- d. 72.4 N

490. The pull required to overcome the rolling resistance of a wheel is 90 N acting at the c enter of the wheels. If the weight of the wheel is 18 000 N and the diameter of the wheel is 300mm, determine the coefficient of rolling resistance.

- a. 0.60 mm
- b. 0.75 mm
- c. 0.50 mm
- d. 0.45 mm

491. A 1000 kN weight is to be moved by using 50 mm diameter rollers. If the coefficient of the rolling resistance for the rollers and floor is 0.08 mm and that for rollers and weight is 0.02 mm. determine the pull required.

- a. 1000 N
- b. 1500 N
- c. 2000 N
- d. 2500 N

492. A ball is thrown vertically upward with an initial velocity of 3 m/sec from a window of a tall building. The ball strikes at the sidewalk at ground level 4 sec later. Determine the velocity with which the ball hits the ground.

- a. 30.86 m/sec
- b. 36.24 m/sec
- c. 42.68 m/sec
- d. 25.27 m/sec

493. A train starts from rest at station P and stops from station Q which is 10 km from station P. the maximum possible acceleration of the train is 15 km/hour/min. if the maximum allowable speed is 60 kph, what is the least time the train go from P to Q?

- a. 10 min
- b. 12 min
- c. 15 min
- d. 20 min

494. A car starting from rest picks up at a uniform rate and passes three electric post in succession. The posts are spaced 360 m apart along a straight road. The car takes 10 sec to travel from first post to sec post and takes 6 sec to go from the second to the third post. Determine the distance from the starting point to the first post.

- a. 73.5 m
- b. 80.3 m
- c. 77.5 m
- d. 70.9 m

495. A stone is dropped from the deck of Mactan Bridge. The sound of the splash reaches the deck 3 seconds later. If sound travels 342 m/s in still air, how high is the deck of Mactan Bridge above the water?

- a. 45.2 m
- b. 40.6 m
- c. 57.3 m
- d. 33.1 m

496. At a uniform rate of 4 drops per second, water is dripping from a faucet. Assuming the acceleration of each drop to be 9.81 m/sec^2 and no air resistance, find the distance between two successive drops in mm if the upper drop has been in motion for 3/8 seconds.

- a. 1340 mm
- b. 2340 mm
- c. 2231 mm
- d. 1230 mm

497. A racing car during the Marlboro Championship starts from rest and has a constant acceleration of 4 m/sec^2. What is its average velocity during the first 5 seconds of motion?

- a. 4 m/s
- b. 6 m/s
- c. 10 m/s
- d. 12 m/s

498. A train is to commute between Tutuban station and San Andres station with a top speed of 250 kph but can not accelerate nor decelerate faster than 4 m/s. What is its min. distance between the two stations in order for the train to be able to reach its top speed?

- a. 1106.24
- b. 1205.48
- c. 1309.26
- d. 1026.42

499. A block having a weight of 400 N rests on an inclined plane making an angle of 30° with the horizontal is initially at rest after it was released for 3 sec, find the distance the block has traveled assuming there is no friction between the block and plane. Determine the velocity after 3 seconds.

- a. 14.71 m/sec
- b. 15.39 m/sec
- c. 14.60 m/sec
- d. 13.68 m/sec

500. A car accelerates for 6 sec from an initial velocity of 10 m/s. the acceleration is increasing uniformly from zero to 8 m/s^2 in 6 sec. during the next 2 seconds, the car decelerates at a constant rate of m/s^2. Compute the total distance the car has traveled from the start after 8 sec.

- a. 169 m
- b. 172 m
- c. 180 m
- d. 200 m