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# MCQ in Engineering Mathematics Part 8 | ECE Board Exam

This is the Multiples Choice Questions in Engineering Mathematics Part 8 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 8 of the Series

Choose the letter of the best answer in each questions.

351. Locate the centroid of the area bounded by the parabola x2 = 8y and x2 = 16(y โ 2) in the first quadrant.

a. x = 2.12; y = 1.6

b. x = 3.25; y = 1.2

c. x = 2.67; y = 2.0

d. x = 2; y = 2.8

Solution:

352. Given the area in the first quadrant bounded by x2 = 8y, the line y โ 2 and the y-axis. What is the volume generated this area is revolved about the line y โ 2 = 0?

a. 53.31 cu units

b. 45.87 cu units

c. 28.81 cu units

d. 33.98 cu units

Solution:

353. Given the area in the first quadrant bounded by x2 = 8y, the line x = 4 and the x-axis. What is the volume generated by revolving this area about y-axis?

a. 78.987 cu units

b. 50.265 cu units

c. 61.523 cu units

d. 82.285 cu units

Solution:

354. Given the area in the first quadrant bounded by x2 = 8y, the line y โ 2 = 0 and the y-axis. What is the volume generated when this area is revolved about the x-axis?

a. 20.32 cu units

b. 34.45 cu units

c. 40.21 cu units

d. 45.56 cu units

Solution:

355. Find the volume formed by revolving the hyperbola xy = 6 from x = 2 to x = 4 about the x-axis.

a. 23.23 cu units

b. 25.53 cu units

c. 28.27 cu units

d. 30.43 cu units

Solution:

356. The region in the first quadrant under the curve y = sin h x from x = 0 to x = 1 is revolved about the x-axis. Compute the volume of solid generated.

a. 1.278 cu units

b. 2.123 cu units

c. 3.156 cu units

d. 1.849 cu units

Solution:

357. A square hole of side 2 cm is chiseled perpendicular to the side of a cylindrical post of radius 2 cm. If the axis of the hole is going to be along the diameter of the circular section of the post, find the volume cut off.

a. 15.3 cu cm

b. 23.8 cu cm

c. 43.7 cu cm

d. 16.4 cu cm

Solution:

358. A hole radius 1 cm is bored through a sphere of radius 3 cm, the axis of the hole being a diameter of a sphere. Find the volume of the sphere which remains.

a. (60ฯโ2)/3 cu cm

b. (64ฯโ2)/3 cu cm

c. (66ฯโ3)/3 cu cm

d. (70ฯโ2)/3 cu cm

Solution:

359. Find the volume of common to the cylinders x2 + y2 = 9 and y2 + z2 = 9.

a. 241 cu m

b. 533 cu m

c. 424 cu m

d. 144 cu m

Solution:

360. Given is the area in the first quadrant bounded by x2 = 8y, the line y โ 2 = 0 and the y-axis. What is the volume generated when this area is revolved about the line y โ 2 = 0.

a. 28.41

b. 26.81

c. 27.32

d. 25.83

Solution:

361. Given is the area in the first quadrant bounded by x2 = 8y, the line x = 4 and the x-axis. What is the volume generated when this area is revolved about the y-axis?

a. 50.26

b. 52.26

c. 53.26

d. 51.26

Solution:

362. The area bounded by the curve y2 = 12 and the line x = 3 is revolved about the line x = 3. What is the volume generated?

a. 185

b. 187

c. 181

d. 183

Solution:

363. The area in the second quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?

a. 2218.63

b. 2228.83

c. 2233.43

d. 2208.53

Solution:

364. The area enclosed by the ellipse (x2)/9 + (y2)/4 = 1 is revolved about the line x = 3, what is the volume generated?

a. 370.3

b. 360.1

c. 355.3

d. 365.10

Solution:

365. Find the volume of the solid formed if we rotate the ellipse (x2)/9 + (y2)/4 = 1 about the line 4x + 3y = 20.

a. 40 ฯ2 cu units

b. 45 ฯ2 cu units

c. 48 ฯ2 cu units

d. 53 ฯ2 cu units

Solution:

366. The area on the first and second quadrant of the circle x2 + y2 = 36 is revolved about the line x = 6. What is the volume generated?

a. 2131.83

b. 2242.46

c. 2421.36

d. 2342.38

Solution:

367. The area on the first quadrant of the circle x2 + y2 = 25 is revolved about the line x = 5. What is the volume generated?

a. 355.31

b. 365.44

c. 368.33

d. 370.32

Solution:

368. The area on the second and third quadrant of the circle x2 + y2 =3 6 is revolved about the line x = 4. What is the volume generated?

a. 2320.30

b. 2545.34

c. 2327.25

d. 2520.40

Solution:

369. The area on the first quadrant of the circle x2 + y2 = 36 is revolved about the line y + 10 = 0. What is the volume generated?

a. 3924.60

b. 2229.54

c. 2593.45

d. 2696.50

Solution:

370. The area enclosed by the ellipse (x2)/16 + (y2)/9 = 1 on the first and 2nd quadrant is revolved about the x-axis. What is the volume generated?

a. 151.40

b. 155.39

c. 156.30

d. 150.41

Solution:

371. The area enclosed by the ellipse 9x2 + 16y2 =ย  144 on the first quadrant is revolved about the y-axis. What is the volume generated?

a. 54.80

b. 98.60

c. 100.67

d. 200.98

Solution:

372. Find the volume of an ellipsoid having the equation (x2)/25 + (y2)/16 + (z2)/4 = 1.

a. 167.55

b. 178.40

c. 171.30

d. 210.20

Solution:

373. Find the volume of a prolate spheroid having the equation (x2)/25 + (y2)/9 + (z2)/9 = 1.

a. 178.90 cu units

b. 184.45 cu units

c. 188.50 cu units

d. 213.45 cu units

Solution:

374. The region in the first quadrant which is bounded by the curve y2 = 4x, and the lines x = 4 and y = 0, is revolved about the x-axis. Locate the centroid of the resulting solid of revolution.

a. 8/3

b. 7/3

c. 10/3

d. 5/3

Solution:

375. The region in the first quadrant which is bounded by the curve x2 = 4y, and the line x = 4, is revolved about the line x = 4. Locate the centroid of the resulting solid of revolution.

a. 0.8

b. 0.5

c. 1

d. 0.6

Solution:

376. The area bounded by the curve x3 = y, the line y = 8 and the y-axis is to be revolved about the y-axis. Determine the centroid of the volume generated.

a. 4

b. 5

c. 6

d. 7

Solution:

377. The area bounded by the curve x3 = y, and the x-axis is to be revolved about the x-axis. Determine the centroid of the volume generated.

a. ยพ

b. 5/4

c. 7/4

d. 9/4

Solution:

378. The region in the 2nd quadrant, which is bounded by the curve x2 = 4y, and the line x = -4, is revolved about the x-axis. Locate the cenroid of the resulting solid of revolution.

a. -4.28

b. -3.33

c. -5.35

d. -2.77

Solution:

379. The region in the 1st quadrant, which is bounded by the curve y2 = 4x, and the line x = -4, is revolved about the line x = 4. Locate the cenroid of the resulting solid of revolution.

a. 1.25 units

b. 2 units

c. 1.50 units

d. 1 unit

Solution:

380. Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y = 1 and the y-axis on the first quadrant with respect to x-axis.

a. 6/5

b. 7/2

c. 4/7

d. 8/7

Solution:

381. Find the moment of inertia of the area bounded by the curve x2 = 4y, the line y=1 and the y-axis on the first quadrant with respect to y-axis.

a. 19/3

b. 16/15

c. 13/15

d. 15/16

Solution:

382. Find the moment of inertia of the area bounded by the curve x2 = 8y, the line x = 4 and the x-axis on the first quadrant with respect to x-axis.

a. 1.52

b. 2.61

c. 1.98

d. 2.36

Solution:

383. Find the moment of inertia of the area bounded by the curve x2 = 8y, the line x = 4 and the x-axis on the first quadrant with respect to y-axis.

a. 21.8

b. 25.6

c. 31.6

d. 36.4

Solution:

384. Find the moment of inertia of the area bounded by the curve y2 = 4x, the line x = 1 and the x-axis on the first quadrant with respect to x-axis.

a. 1.067

b. 1.142

c. 1.861

d. 1.232

Solution:

385. Find the moment of inertia of the area bounded by the curve y2 = 4x, the line x = 1 and the x-axis on the first quadrant with respect to y-axis.

a. 0.436

b. 0.571

c. 0.682

d. 0.716

Solution:

386. Determine the moment of inertia with respect to x-axis of the region in the first quadrant which is bounded by the curve y2 = 4x, the line y = 2 and y-axis.

a. 1.3

b. 2.3

c. 1.6

d. 1.9

Solution:

387. Find the moment of inertia of the area bounded by the curve y2 = 4x, the line y = 2 and the y-axis on the first quadrant with respect to y-axis.

a. 0.095

b. 0.064

c. 0.088

d. 0.076

Solution:

388. Find the moment of inertia with respect to x-axis of the area bounded by the parabola y2 = 4x and the line x = 1.

a. 2.35

b. 2.68

c. 2.13

d. 2.56

Solution:

389. What is the integral of sin6 (ฯ)cos4 (ฯ) dฯ if the upper limit is ฯ/2 and lower limit is 0?

a. 0.1398

b. 1.0483

c. 0.0184

d. 0.9237

Solution:

390. Evaluate the integral of cos7 ฯ sin5 ฯ dฯ if the upper limit is 0.

a. 0.1047

b. 0.0083

c. 1.0387

d. 1.3852

Solution:

391. What is the integral of sin4 x dx if the lower limit is 0 and the upper limit is ฯ/2?

a. 1.082

b. 0.927

c. 2.133

d. 0.589

Solution:

392. Evaluate the integral of cos5 ฯ dฯ if the lower limit is 0 and the upper limit is ฯ/2.

a. 0.084

b. 0.533

c. 1.203

d. 1.027

Solution:

393. Evaluate the integral (cos3A)8 dA from 0 to ฯ/6.

a. 27ฯ/363

b. 35ฯ/768

c. 23ฯ/765

d. 12ฯ/81

Solution:

394. What is the integral of sin5 x cos3 x dx if the lower limit is 0 and the upper limit is ฯ/2?

a. 0.0208

b. 0.0833

c. 0.0278

d. 0.0417

Solution:

395. Evaluate the integral of 15sin7 (x) dx from 0 to ฯ/2.

a. 6.857

b. 4.382

c. 5.394

d. 6.139

Solution:

396. Evaluate the integral of 5 cos6 x sin2 x dx if the upper limit is ฯ/2 and the lower limit is 0.

a. 0.186

b. 0.294

c. 0.307

d. 0.415

Solution:

397. Evaluate the integral of 3(sin x)3 dx from 0 to ฯ/2.

a. 2

b. ฯ

c. 6

d. ฯ/2

Solution:

398. A rectangular plate is 4 feet long and 2 feet wide. It is submerged vertically in water with the upper 4 feet parallel and to 3 feet below the surface. Find the magnitude of the resultant force against one side of the plate.

a. 38 w

b. 32 w

c. 27 w

d. 25 w

Solution:

399. Find the force on one face of a right triangle of sides 4 m, and altitude of 3 m. The altitude is submerged vertically with the 4 m side in the surface.

a. 53.22 kN

b. 58.86 kN

c. 62.64 kN

d. 66.27 kN

Solution:

400. A plate in the form of a parabolic segment of base 12 m and height of 4 m is submerged in water so that the base is in the surface of the liquid. Find the force on the face of the plate.

a. 489.1 kN

b. 510.5 kN

c. 520.6 kN

d. 502.2 kN

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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