This is the Uncategorized Multiples Choice Questions Part 13 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**

**MCQs from Number 601 – 650**Answer key:

**PART 13**

### Continue Part XIII of the Series

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

601. A train weighing 12 000 kN is accelerate up a 2% grade with velocity increasing from 30 kph to 50 kph in a distance of 500 m. Determine the horse power developed by the train.

- a. 5.394 kW
- b. 5.120 kW
- c. 4.468 kW
- d. 4.591 kW

602. An elevator has an empty weight of 5160 N. It is designed to carry a maximum load of 20 passengers from the ground floor to the 25^{th} floor of the building in a time of 18 seconds. Assuming the average weight of the passenger to be 710 N. and the distance between floors is 3.5 m, what is the minimum constant power needed for the elevator motor?

- a. 85.5 kW
- b. 97.4 kW
- c. 94.3 kW
- d. 77.6 kW

603. An engine hoist 1.50 m^3 of a concrete in a 2200 N bucket moves a distance of 12 m in 20 seconds. If concrete weighs 23.5 kN/m^3, determine the engine horsepower assuming 80 efficiency.

- a. 32.12 hp
- b. 42.23 hp
- c. 37.74 hp
- d. 28.87 hp

604. A train weighs 15 000 kN. The train’s resistance is 9 n per kilo-Newton. If 5000 is available to pull this train up to 2% grade, what will be its maximum speed in kph?

- a. 46.2 kph
- b. 50 kph
- c. 40 kph
- d. 35 kph

605. An engine having a 40 hp rating is used as an engine hoist to lift a certain weight of height 8 m. Determine the maximum weight it could lift in a period of 20 sec.

- a. 85.5 kW
- b. 97.4 kW
- c. 74.6 kW
- d. 77.6 kW

606. A 100 kg body moves to the right 5 m/s and another 140 kg body moves to the left at 3 m/s. They collided and after impact the 100 kg body rebounds to the left at 2 m/s. Compute the coefficient of restitution.

- a. 0.40
- b. 0.50
- c. 0.30
- d. 0.60

607. A ball is dropped from an initial height of 6m above a solid floor, how high will the ball rebound if the coefficient of restitution is e = 0.92?

- a. 5.08
- b. 5.52
- c. 5.41
- d. 5.12

608. A ball strikes the ground at an angle of 30° with the ground surface; the ball then rebounds at a certain angle Î¸ with the ground surface. If the coefficient of restitution is 0.80, find the value of Î¸.

- a. 18.48°
- b. 24.79°
- c. 32.2°
- d. 26.7°

609. A ball is thrown with an initial horizontal velocity of 30 m/s from a height of 3 m above the ground and 40 m from a vertical wall. How high above the ground will the ball strike if the coefficient of restitution is 0.70?

- a. 1.11 m
- b. 2.52 m
- c. 1.46 m
- d. 0.89 m

610. Two cars having equal weights of 135 kN are traveling on a straight horizontal track with velocities of 3 m/s to the right and 1.5 m/s to the left respectively. They collide and are coupled during impact. Neglecting friction due to skidding, determine their final common velocity and the gain or loss in kinetic energy after impact.

- a. 1.25 m/s; 66.35 kN-m
- b. 2.06 m/s; 57.25 kN-m
- c. 3.12 m/s; 77.36 kN-m
- d. 7.74 m/s; 69.67 kN-m

611. A man weighing 68 kg jumps from a pier with horizontal velocity of 6 m/s onto a boat that is rest on the water. If the boat weighs 100 kg, what is the velocity of the boat when the man comes to rest relative to the boat?

- a. 2.43 m/s
- b. 3.53 m/s
- c. 2.88 m/s
- d. 1.42 m/s

612. A man weighing 68 kg jumps from a pier with horizontal velocity of 5 m/s onto a 100 kg boat moving towards the dock at 4 m/s What would be the velocity of the boat after the man lands on it?

- a. -0.56 m/s
- b. -0.36 m/s
- c. -0.78 m/s
- d. -1.33 m/s

613. A ball is thrown at an angle of 40° from the horizontal toward a smooth floor and it rebounds at an angle of 25° with the horizontal floor. Compute the value of coefficient of restitution.

- a. 0.46
- b. 0.66
- c. 0.56
- d. 0.76

614. Car B is moving at a speed of 12 m/s and is struck by car A which is moving at a speed of 20 m/s. The weight of car A is 14 tons and of car B is 10 tons. Determine the velocities of the car after impact assuming that the bumpers got locked after impact. Both cars are moving in the same direction to the right.

- a. 16.67 m/s
- b. 14.25 m/s
- c. 15.42 m/s
- d. 13.62 m/s

615. Two cars A and B have weights equal to 12 tons and 8 tons respectively are moving in opposite directions. The speed of car A is 22 m/s to the right and that of car B is 18 m/s to the left. Two cars bumped each other. Determine the velocity of the cars after impact assuming the bumpers get locked.

- a. 8 m/s
- b. 6 m/s
- c. 4 m/s
- d. 3 m/s

616. A 6000 N drop hammer falling freely trough a height of 0.9 m drives a 3000 N pile 150mm vertically to the ground. Assuming the hammer and the pile to cling together after the impact, determine the average resistance to penetration of the pile.

- a. 42 364 N
- b. 32 976 N
- c. 30 636 N
- d. 28 476 N

617. Two identical balls collide as shown. What is V2’ if the coefficient of restitution is 0.8?

- a. 2.4 m/s
- b. 3.6 m/s
- c. 4.8 m/s
- d. 5.6 m/s

618. A 16 gm mass is moving at 30 cm/s while a 4 gm mass is moving opposite direction at 50 cm/sec. They collide head on and stick together. Their velocity after collision is:

- a. 0.07 m/s
- b. 0.14 m/s
- c. 0.21 m/s
- d. 0.28 m/s

619. A bullet weighing 0.014 kg and moving horizontally with a velocity of 610 m/s strikes centrally a block of wood having a mass of 4.45 kg which is suspended by a cord from a point 1.2 m above the center of the block. To what angle from the vertical will the block and embedded bullet swing?

- a. 28.64°
- b. 29.32°
- c. 30.12°
- d. 31.79°

620. A body having a mass of 100 kg and having velocity of 10 m/s to the right collides with an 80 kg mass having a velocity of 5 m/s to the left. If the coefficient of restitution is 0.5, determine the loss of kinetic energy after impact.

- a. 3750 N-m
- b. 4260 N-m
- c. 3640 N-m
- d. 4450 N-m

621. A 0.44 N bullet is fired horizontally to an 89.18 N block of wood resting on a horizontal surface which the coefficient of friction is 0.30. If the block is moved a distance 375 mm along the surface, what was the velocity of the bullet before striking?

- a. 142.52 m/s
- b. 204.61 m/s
- c. 303.49 m/s
- d. 414.25 m/s

622. A 60 ton rail car moving at 1 mile per hour is instantaneously coupled to a stationary 40 to rail car. What is the speed of the coupled cars?

- a. 0.88 mi/hr
- b. 1.0 mi/hr
- c. 0.60 mi/hr
- d. 0.40 mi/hr

623. What momentum does a 40 lbm projectile posses if the projectile is moving 420 mph?

- a. 24 640 lbf-sec
- b. 16 860 lbf-sec
- c. 765 lbf-sec
- d. 523.6 lbf-sec

624. A 300 kg block is in contact with a level of coefficient of kinetic friction is 0.10. if the block is acted upon by a horizontal force of 50 kg what time will elapse before the block reaches a velocity of 48.3 m/min from rest? If the 50 kg is then removed, hos much longer will the block continue to move?

- a. 12.08 sec; 8.05 sec
- b. 15.28 sec; 9.27 sec
- c. 10.42 sec; 7.64 sec
- d. 13.52 sec; 10.53 sec

625. A 100 kg body moves to the right at 5 m/s and another body of mass W is moves to the left 3 m/s. they meet each other and after impact the 100 kg body rebounds to the left at 2 m/s. Determine the mass of the body if coefficient of restitution is 0.5.

- a. 100 kg
- b. 140 kg
- c. 150 kg
- d. 200 kg

626. A wood block weighing 44.75 N rests on a rough horizontal plane, the coefficient of friction being 0.40. if a bullet weighing 0.25 N is fired horizontally into the block with the velocity of 600m/s, how far will the block be displaced from its initial position? Assume that the bullet remains inside the block.

- a. 1.41 m
- b. 2.42 m
- c. 1.89 m
- d. 0.98 m

627. The system is used to determine experimentally the coefficient of restitution. If ball A is released from rest an ball B swings through Î¸ = 53.1°, after being struck, determine the coefficient of restitution. Weight of A is 150 N while that of b is 100 N.

- a. 0.537
- b. 0.291
- c. 1.083
- d. 0.926

628. The ball A and B are attached to stiff rods of negligible weight. Ball A is released from rest and allowed to strike B. If the coefficient of restitution is 0.60, determine the angle Î¸ through which ball B will swing. If the impact lasts for 0.01 sec, also find the average impact force. Mass of A is 15 kg and that of B is 10 kg.

- a. 57.63° ; 7660 N
- b. 60.58° ; 6270 N
- c. 64.85° ; 6720 N
- d. 73.32° ; 7670 N

629. A 1500 N block is in contact with a level plane whose coefficient of kinetic friction is 0.10. If the block is acted upon a horizontal force of 250 N, at what time will elapse before the block reaches a velocity of 14.5 m/s starting from rest?

- a. 16.93 sec
- b. 18.36 sec
- c. 21.12 sec
- d. 22.17 sec

630. A 1600 N block is in contact with a level plane whose coefficient of kinetic friction is 0.20. If the block is acted upon a horizontal force of 300 N initially when the block is at rest and the force is removed when the velocity of the block reaches 16m/s. How much longer will the block continue to move?

- a. 8.15 sec
- b. 6.25 sec
- c. 4.36 sec
- d. 5.75 sec

631. A bullet weighing 0.30 N is moving 660 m/s penetrates an 50 N body and emerged with a velocity of 180 m/s. For how long will the body moves before it stops? Coefficient of friction is 0.40.

- a. 5.24 sec
- b. 6.84 sec
- c. 7.34 sec
- d. 8.36 sec

632. A 1000 N block is resting on an incline plane whose slope is 3 vertical to 4 horizontal. If a force of 1500 N acting parallel to the inclined plane pushes the block up the inclined plane, determine the time required to increase the velocity of the block from 3m/s to 15m/s. Coefficient of friction between the block and the plane is 0.20.

- a. 1.65 sec
- b. 1.86 sec
- c. 2.17 sec
- d. 3.64 sec

633. The 9 kg block is moving to the right with a velocity of 0.6 m/s on the horizontal surface when a force P is applied to it at t = 0. Calculate the velocity V2 of the block when the t = 0.4 sec. the kinetic coefficient of friction is Mk = 0.30.

- a. 1.23 m/s
- b. 1.82 m/s
- c. 2.64 m/s
- d. 2.11 m/s

634. A 50 kg block initially at rest is acted upon by a force P which varies as shown. Knowing the coefficient of kinetic friction between the block and the horizontal surface is 0.20, compute the velocity of the block after 5 s, and after 8s.

- a. 10.65 m/s; 17.705 m/s
- b. 13.23 m/s; 15.534 m/s
- c. 15.19 m/s; 16.804 m/s
- d. 17.46 m/s; 14.312 m/s

635. The motion of the block starting from rest is governed by the a-t curve shown. Determine the velocity and distance traveled after 9 sec. Neglecting friction.

- a. 66 m/s; 228 m
- b. 45 m/s; 233 m
- c. 57 m/s, 423 m
- d. 72 m/s; 326 m

636. From the V-t curve shown compute the distance traveled by a car starting form rest after 6 sec.

- a. 50m
- b. 60 m
- c. 70 m
- d. 80 m

637. A bullet weighing 50 g is fired into a block of wood weighing 20 lbs on a top of a horizontal table. The block moves 45 cm. the coefficient of friction between the block and table is 0.30. What is the speed of the bullet in kph before hitting the block? Assume that the bullet is embedded of the block.

- a. 1068.77 kph
- b. 1843.53 kph
- c. 1144.38 kph
- d. 1683.78 kph

638. A block weighing 60 N is subjected to a horizontal force P = (10 + t^3) and a friction resisting equal to (6 + t^2). Compute the velocity of the block 2 s after it has started from rest.

- a. 1.4 m/s
- b. 1.8 m/s
- c. 2.4 m/s
- d. 2.8 m/s

639. A price tag of P1200 is specified if paid within 60 days but offers 3% discount for cash in 30 days. Find the rate of interest.

- a. 37.11%
- b. 38.51 %
- c. 40.21 %
- d. 39.31 %

640. It is the practice of almost all banks in the Philippines that when they grant a loan, the interest the interest for one year is automatically deducted from the principal amount upon release of money to a borrower. Let us that you applied for a loan with a bank and the P80 000 was approved with interest rate of 14% which P11 200was deducted and you were given a check of P68 800. Since you have to pay the amount of P80 000 in one year after, what then will be the effective interest rate?

- a. 16.20%
- b 16.18%
- c. 16.30%
- d. 16.28%

641. Mr. J. dela Cruz borrowed money from a bank. He received from the bank P1 340 and promised to pay P1 500 at the end of 9 months. Determine the simple interest rate and the corresponding discount rate or often referred to as “Banker’s Discount”.

- a. 12.95%; 17.33 %
- b. 15.92%; 13.73 %
- c. 18.28%; 13.12 %
- d. 19.25%; 13.33%

642. A man borrowed from a bank with a promissory note that he signed in the amount of P25000 for a period of one year. He received only the amount of P21, 915 after the bank collected the interest and additional amount of P85 00 for notarial and inspection fees. What was the rate of interest that the bank collected in advance?

- a. 10.32%
- b. 18.37%
- c. 16.43%
- d. 13.64%

643. Agnes Abadilla was granted a loan of P20 000 by her employer CPM Industrial Fabricator and Construction Corporation with an interest rate of 6% for 180 days on the principal collected in advance. The corporation will accept a promissory note for P20 000 non-interest for 180 days. If discounted at once, find the proceeds on the note.

- a. P18 000
- b. P18 400
- c. P18 800
- d. P19 000

644. P400 is borrowed for 75 days at 16% per annum simple interest. How much will be due at the end of 75 days?

- a. P4168.43
- b. P5124.54
- c. P4133.33
- d. P5625.43

645. Mr. Almagro made a money market of P1 000 000 for 30 days at 7.5% per year. If the withholding tax is 20%, what is the net interest that he will receive at the end of the month?

- a. P3 000
- b. P4 000
- c. P6 000
- d. P5 000

646. L for a motorboat specifies a cost of P1200 due at the end of 100 days but offers 4% discount for cash in 30 days. What is the highest rate, simple interest at which the buyer can afford to borrow money in order to take advantage of the discount?

- a. 18.4%
- b. 19.6%
- c. 20.9%
- d. 21.4%

647. In buying a computer disk, the buyer was offered the options of paying P250 cash at the end of 30 days or P270 at the end of 120 days. At what rate is the buyer paying simple interest if he agree to pay at the end of 120 days.

- a. 40%
- b. 32%
- c. 28%
- d. 25%

648. On March 1, 1996 Mr. Almagro obtains a loan of P1500 from Mr. Abella and signs a note promising to pay the principal and accumulated simple interest at rate of 5% at the end of 120 day. On March 15, 1996, Mr. Abella discounts the note at the bank whose discount rate is 6%. What does he receive?

- a. P 2 201.48
- b. P1 123.29
- c. P1 513.56
- d. P938.20

649. A deposit of P110 000 was made for 31 days. The net interest after deducting 20% withholding tax is P890.36. Find the rate of return annually.

- a. 12.25
- b. 11.75
- c. 12.75
- d. 11.95

650. If you borrowed money from your friend with simple interest of 12%, find the present worth of P50 000, which is due at the end of 7 months.

- a. P46 200
- b. P44 893
- c. P46 729
- d. P45 789

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