This is the Multiples Choice Questions in Engineering Mathematics Part 11 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**

**MCQs from Number 501 – 550**Answer key:

**PART 11**

### Continue Practice Exam Test Questions Part XI of the Series

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

501. A train passing at point A at a speed of 72 kph accelerates at 0.75 m/s^2 from one minute along a straight path then decelerates at 1.0 m/s^2. How far from point a will be 2 min after passing point A.

- a. 6.49 km
- b. 7.30 km
- c. 4.65 km
- d. 3.60 km

502. A car accelerate 8 seconds from rest, the acceleration increasing uniformly from zero to 12 m/s^2. During the next 4 sec, the car decelerates at a constant rate of -11 m/s^2. Compute the distance the car has traveled after 12 sec from the start.

- a. 232 m
- b. 240 m
- c. 302 m
- d. 321 m

503. A car moving at 6 m/s accelerates at 1.5 m/s^2 for 15 sec, then decelerates at a rate of 1.2 m/s^2 for 12 sec. Determine the total distance traveled.

- a. 433.75 m
- b. 543.80 m
- c. 384.90 m
- d. 558.75 m

504. A train starting at initial velocity of 30 kph travels a distance 21 km in 8 min. determine the acceleration of the train at this instant.

- a. 0.0865 m/s^2
- b. 0.0206 m/s^2
- c. 0.3820 m/s^2
- d. 0.0043 m/s^2

505. From a speed of 75 kph, a car decelerates at the rate of 500 m/min^2 along a straight path. How far in meters will it travel in 45 sec?

- a. 790.293 m
- b. 791.357 m
- c. 796.875 m
- d. 793.328 m

506. An object experiences rectilinear acceleration a(t) = 10 – 2t. How far does it travel in 6 sec if its initial velocity is 10 m/s?

- a. 182
- b. 168
- c. 174
- d. 154

507. An object experiences the velocity as shown in the diagram. How far will it move in 6 seconds?

- a. 40 m
- b. 60 m
- c. 80 m
- d. 100 m

508. An object is accelerating to the right along a straight path at 2 m/s. the object begins with a velocity 10 m/s to the left. How far does it travel in 15 seconds?

- a. 125 m
- b. 130 m
- c. 140 m
- d. 100 m

509. What is the acceleration of a body that increases in velocity from 20 m/s to 40 m/s in 3 sec? Answer in SI.

- a. 8.00 m/s^2
- b. 6.67 m/s^2
- c. 50. m/s^2
- d. 7.0 m/s^2

510. A shell is fired vertically upward with an initial velocity of 2000 fps. It is timed to burst in 7 sec. Four seconds after firing the first shell, a second shell is fired with the same velocity. This shell is time to burst in 5 sec. An observer stationed in a captive balloon near the line of fire hears both burst. At the same instance what is the elevation or height of the balloon. Assume velocity of sound to be 1100 fps.

- a. 10 304 ft
- b. 18 930 ft
- c. 13 400 ft
- d. 14 030 ft

511. An object from a height of 92 m and strikes the ground with a speed of 19 m/s. Determine the height that the object must fall in order to strike with a speed of 24 m/s.

- a. 110.12 m
- b. 184.29 m
- c. 146.94 m
- d. 205.32 m

512. A ball is dropped from a balloon at a height of 195 m. if the balloon is rising 29.3 m/s. Find the highest point reached by the ball and the time of flight.

- a. 238.8 m
- b. 487.3 m
- c. 328.4 m
- d. 297.3 m

513. 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 and the height of the window above the ground level.

- a. 24.4 m/s; 81.3 m
- b. 36.2 m/s; 66.79 m
- c. 42.3 m/s; 48.2 m
- d. 53.2 m/s; 36.8 m

514. A ball is dropped freely from a balloon at a height 195 m. If the balloon is rising 29.3 m/s. Find the highest point reached by the ball and the velocity of the ball as it strikes the ground.

- a. 43.76 m; 68.44 m/s
- b. 22.46 m; 71.66 m/s
- c. 36.24 m; 69.24m/s
- d. 12.8 m; 31.2 m/s

515. How far does the automobile move while its speed increases uniformly from 15 kph to 45 kph in 20 sec?

- a. 185 m
- b. 167 m
- c. 200 m
- d. 172 m

516. An automobile is moving at 20 kph and accelerates at 0.5 m/s^2 for a period of 45 sec. Compute the distance traveled by the car at the end of 45 sec.

- a. 842.62 m
- b. 765.45 m
- c. 672.48 m
- d. 585.82 m

517. A ball is thrown vertically upward with an initial velocity of 3m/sec from a window of a tall building, which is 70 m above the ground level. How long will it take for the ball to hit the ground?

- a. 3.8 sec
- b. 4.1 sec
- c. 5.2 sec
- d. 6.1 sec

518. A ball is thrown vertically upward with an initial velocity of 3 m/sec from a window of a tall building. The ball strikes the ground 4 sec later. Determine the height of the window above the ground.

- a. 66.331 m
- b. 67.239 m
- c. 54.346 m
- d. 72.354 m

519. A stone was dropped freely from a balloon at a height of 190 m above the ground. The balloon is moving upward at a speed of 30 m/s. Determine the velocity of the stone at it hits the ground.

- a. 56.43 m/s
- b. 62.45 m/s
- c. 68.03 m/s
- d. 76.76 m/s

520. A ball is thrown vertically at a speed of 20 m/s from a building 100 m above the ground. Find the velocity and the position of the ball above the ground after 5 seconds.

- a. 3.34 m, 45.23 m/s
- b. 4.54 m, 47.68 m/s
- c. 5.67 m, 56.42 m/s
- d. 6.23 m, 34.76 m/s

521. A ball is thrown vertically at a speed of 30 m/s from a building 200 m above the ground. Determine the velocity and the time that it strikes the ground.

- a. 11.50 sec, 65.80 m/s
- b. 11.45 sec, 66.59 m/s
- c. 10.30 sec, 67.21 m/s
- d. 10.14 sec, 69.45 m/s

522. A ball is thrown vertically with a velocity of 20 m/s from the top of a building 100 m high. Find the velocity of the ball at a height of 40 m above the ground.

- a. 39.71 m/s
- b. 40.23 m/s
- c. 39.88 m/s
- d. 39.68 m/s

523. A ball is shot at a ground level at an angle of 60 degrees with the horizontal with an initial velocity of 100 m/s. Determine the height of the ball after 2 seconds.

- a. 162.46 m
- b. 153.59 m
- c. 175.48 m
- d. 186.42 m

524. A ball is shot at an average speed of 200 m/s at an angle of 20° with the horizontal. What would be the velocity of the ball after 8 seconds?

- a. 215.53 m/s
- b. 154.34 m/s
- c. 188.21 m/s
- d. 198.37 m/s

525. A projectile has a velocity of 200 m/s acting at an angle 20 degrees with the horizontal. How long will it take for the projectile to hit the ground surface?

- a. 13.95 sec
- b. 15.75 sec
- c. 10.11 sec
- d. 24.23 sec

526. A solid homogenous circular cylinder and a solid homogenous sphere are placed at equal distances from the end of an inclined plane. Assuming that no slipping occurs as the two bodies roll down the plane, which of them will reach the end of the plane first? Assume that they have the same weight and radius.

- a. sphere
- b. cylinder
- c. both cylinder and sphere
- d. none of these

527. A homogenous sphere rolls down as inclined plane making an angle of 30° with the horizontal. Determine the minimum value of the coefficient of friction which will prevent slipping.

- a. 0.625
- b. 0.362
- c. 1.028
- d.0.165

528. At what weight “h” above the billiard table surface should a billiard ball of radius 3 cm be struck by a horizontal impact in order that the ball will start moving with no friction between the ball and the table?

- a. 4.9 cm
- b. 3.4 cm
- c. 4.2 cm
- d. 5.5 cm

529. A common swing 7.5 m high is designed for a static load of 1500 N (tension in the rope is equal to 1500 N). Two boys each weighing 500 N are swinging on it. How much many degrees on each side of the vertical can they swing without exceeding the designed load?

- a. 30.35°
- b. 41.41°
- c. 45.45°
- d. 54.26°

530. A wooden block weighing 20 N rests on a turn table having a radius of 2 m at a distance on 1 m from the center. The coefficient of friction between the block and the turn table is 0.30. The rotation of the table is governed by the equation Ø = 4t^2 where Ø is in radians and t in seconds. If the table starts rotating from rest at t = 0, determine the time elapsed before the block will begin to slip.

- a. 0.21 sec
- b. 0.55 sec
- c. 1.05 sec
- d. 0.10 sec

531. A ball at the end of a cord 121 cm long is swinging with a complete vertical circle just enough velocity to keep it in the top. If the ball is released from the cord where it is at the top point of its path, where will it strike the ground 245 cm below the center of the circle.

- a. 263.63 cm
- b. 332.64 cm
- c. 258.37 cm
- d. 297.61 cm

532. At what RPM is the Ferris wheel turning when the riders feel “weightless” or zero gravity every time the each rider is at the topmost part of the wheel 9m in radius?

- a. 8.58 rpm
- b. 9.97 rpm
- c. 10.73 rpm
- d. 9.15 rpm

533. A wooden block having a weight of 50 N is placed at a distance 1.5 m from the center of a circular platform rotating at a speed of 2 radians per second. Determine the minimum coefficient of friction of the blocks so that it will not slide. Radius of circular platform is 3 m.

- a. 0.21
- b. 0.84
- c. 0.61
- d. 1.03

534. A 2 N weight is swing in a vertical circle of 1m radius and the end of the cable will break if the tension exceeds 500 N. Which of the following most nearly gives the angular velocity of the weight when the cable breaks?

- a. 24.9 rad/sec
- b. 37.2 rad/sec
- c. 49.4 rad/sec
- d. 58.3 rad/sec

535. A weight is attached to a chord and forms a conical pendulum when it is rotated about the vertical axis. If the period of rotation is 0.2 sec, determine the velocity of the weight if the chord makes an angle of 25° with the vertical.

- a. 0.146 m/s
- b. 0.823 m/s
- c. 1.028 m/s
- d. 0.427 m/s

536. A ball having a weight of 4N is attached to a cord 1.2 m long and is revolving around a vertical axis so that the cord makes an angle of 20° with the vertical axis. Determine the rpm.

- a. 22.12
- b. 24.16
- c. 25.18
- d. 28.17

537. A wheel is rotating at 4000 rpm. If it experience a deceleration of 20 rad/sec^2 through how many revolutions will it rotate before it stops?

- a. 400
- b. 698
- c. 520
- d. 720

538. Find the maximum acceleration of a mass at the end of a 2 m long string. It swing like a pendulum with a maximum angle of 30°.

- a. 3.61 m/s^2
- b. 4.91 m/s^2
- c. 6.21 m/s^2
- d. 7.21 m/s^2

539. A turbine started from rest to 180 rpm in 6 min at a constant acceleration. Find the number of revolution that it makes within the elapsed time.

- a. 550 revolutions
- b. 540 revolutions
- c. 630 revolutions
- d. 500 revolutions

540. Traffic travels at 65 mph around banked highway curved with a radius of 3000 feet. What banking angle is necessary such that friction will not be required to resist the centrifugal force?

- a. 3.2°
- b. 2.5°
- c. 5.4°
- d. 18°

541. The rated speed of a highway curve of 60m radius of 50 kph. If the coefficient of friction between the tires and the road is 0.60, what is the maximum speed at which a car can round a curve without skidding?

- a. 93.6 kph
- b. 84.2 kph
- c. 80.5 kph
- d. 105.2 kph

542. A solid disk flywheel (I = 200 kg.m) is rotating with a speed of 900 rpm. What is the rotational kinetic energy?

- a. 730 x 10^3 J
- b. 680 x 10^3 J
- c. 888 x 10^3 J
- d. 1100 x 10^3 J

543. A cyclist on a circular track of radius r = 800 ft. travelling at 27 ft/s. His speed at the tangential direction increases at the rate of 3 ft/s^2. What is the cyclist’s total acceleration?

- a. 2.8 ft/s^2
- b. -3.12 ft/s^2
- c. -5.1 ft/s^2
- d. 3.31 ft/s^2

544. An automobile travels on a perfectly horizontal, unbanked circular track of radius R. The coefficient of friction between the tires and the track is 0.3. If the car’s velocity is 15 m/s, what is the smallest radius it may travel without skidding?

- a. 68m
- b. 69.4 m
- c. 76.5 m
- d. 71.6 m

545. Determine the angle of super elevation for a highway curves of 183 m radius, so that there will be no “slide thrust” for a speed of 72 kilometer per hour. At what speed will skidding impend if the coefficient of friction is 0.3?

- a. 13.58°; 25.49 m/s
- b. 12.57°; 31.72 m/s
- c. 15.29°; 34.24 m/s
- d. 10.33°; 30.57 m/s

546. A child places a picnic basket on the outer rim of merry go round that has a radius of 4.6 m and revolves once every 24 sec. How large must the coefficient of static friction be for the basket to stay on the merry go round?

- a. 0.024
- b. 0.032
- c. 0.045
- d. 0.052

547. A driver’s manual that a driver traveling at 48 kph and desiring to stop as quickly as possible travels 4 m before the foot reaches the brake. The car travels and additional 21 m before coming to rest. What coefficient of friction is assumed in this calculation?

- a. 0.43
- b. 0.34
- c. 0.56
- d. 0.51

548. A point on the rim of a rotating flywheel changes its speed its speed from 1.5 m/s to 9 m/s while it moves 60 m. If the radius of the wheel is 1 m, compute the normal acceleration at the instant when its speed is 6 m/s.

- a. 18 m/s^2
- b. 20 m/s^2
- c. 24 m/s^2
- d. 36 m/s^2

549. The angular speed of a rotating flywheel a radius of 0.5 m, is 180/π rpm. Compute the value of its normal acceleration and the tangential speed.

- a. 16 m/s^2; 2 m/s
- b. 18 m/s^2; 3 m/s
- c. 14 m/s^2; 1.5 m/s
- d. 12 m/s^2; 1.0 m/s

550. A pulley has an angular velocity of 2 rad/sec, and a tangential speed of 4 m/s. Compute the normal acceleration.

- a. 8 m/sec^2
- b. 6 m/sec^2
- c. 4 m/sec^2
- d. 3 m/sec^2