# MCQ in Engineering Mathematics Part 8 | ECE Board Exam

(Last Updated On: February 1, 2020) 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%).

### The Series

Following is the list of multiple choice questions in this brand new series:

Engineering Mathematics MCQs
PART 1: MCQs from Number 1 – 50                                 Answer key: PART I
PART 2: MCQs from Number 51 – 100                             Answer key: PART 2
PART 3: MCQs from Number 101 – 150                          Answer key: PART 3
PART 4: MCQs from Number 151 – 200                          Answer key: PART 4
PART 5: MCQs from Number 201 – 250                          Answer key: PART 5
PART 6: MCQs from Number 251 – 300                          Answer key: PART 6
PART 7: MCQs from Number 301 – 350                          Answer key: PART 7
PART 8: MCQs from Number 351 – 400                          Answer key: PART 8
PART 9: MCQs from Number 401 – 450                          Answer key: PART 9
PART 10: MCQs from Number 451 – 500                        Answer key: PART 10

### Continue Pratice Exam Test Questions Part VIII of the Series

Choose the letter of the best answer in each questions.

351. Locate the centroid of the area bounded by the parabola x^2 = 8y and x^2 = 16(y – 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

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

• a. 53.31 cu units
• b. 45.87 cu units
• c. 28.81 cu units
• d. 33.98 cu units

353. Given the area in the first quadrant bounded by x^2 = 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

354. Given the area in the first quadrant bounded by x^2 = 8y, the line y – 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

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

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

357. A square hole of side 2 cm is chiseled perpendicular to the side of a cylindrical post of radius 2cm. 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

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. (60π√2)/3 cu cm
• b. (64π√2)/3 cu cm
• c. (66π√3)/3 cu cm
• d. (70π√2)/3 cu cm

359. Find the volume of common to the cylinders x^2 + y^2 = 9 and y^2 + z^2 = 9.

• a. 241 cu m
• b. 533 cu m
• c. 424 cu m
• d. 144 cu m

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

• a. 28.41
• b. 26.81
• c. 27.32
• d. 25.83

361. Given is the area in the first quadrant bounded by x^2 = 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

362. The area bounded by the curve y^2 = 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

363. The area in the second quadrant of the circle x^2 + y^2 = 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

364. The area enclosed by the ellipse (x^2)/9 + (y^2)/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

365. Find the volume of the solid formed if we rotate the ellipse (x^2)/9 + (y^2)/4 = 1 about the line 4x + 3y = 20.

• a. 40 π^2 cu units
• b. 45 π^2 cu units
• c. 48 π^2 cu units
• d. 53 π^2 cu units

366. The area on the first and second quadrant of the circle x^2 + y^2 = 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

367. The area on the first quadrant of the circle x^2 + y^2 = 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

368. The area on the second and third quadrant of the circle x^2 + y^2 =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

369. The area on the first quadrant of the circle x^2 + y^2 = 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

370. The area enclosed by the ellipse (x^2)/16 + (y^2)/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

371. The area enclosed by the ellipse 9x^2 + 16y^2 =  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

372. Find the volume of an ellipsoid having the equation (x^2)/25 + (y^2)/16 + (z^2)/4 = 1.

• a. 167.55
• b. 178.40
• c. 171.30
• d. 210.20

373. Find the volume of a prolate spheroid having the equation (x^2)/25 + (y^2)/9 + (z^2)/9 = 1.

• a. 178.90 cu units
• b. 184.45 cu units
• c. 188.50 cu units
• d. 213.45 cu units

374. The region in the first quadrant which is bounded by the curve y^2 = 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

375. The region in the first quadrant which is bounded by the curve x^2 = 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

376. The area bounded by the curve x^3 = 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

377. The area bounded by the curve x^3 = y, and the x-axis is to be revolved about the x-axis. Determine the centroid of the volume generated.

• a. ¾
• b. 5/4
• c. 7/4
• d. 9/4

378. The region in the 2nd quadrant, which is bounded by the curve x^2 = 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

379. The region in the 1st quadrant, which is bounded by the curve y^2 = 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

380. Find the moment of inertia of the area bounded by the curve x^2 = 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

381. Find the moment of inertia of the area bounded by the curve x^2 = 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

382. Find the moment of inertia of the area bounded by the curve x^2 = 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

383. Find the moment of inertia of the area bounded by the curve x^2 = 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

384. Find the moment of inertia of the area bounded by the curve y^2 = 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

385. Find the moment of inertia of the area bounded by the curve y^2 = 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

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

• a. 1.3
• b. 2.3
• c. 1.6
• d. 1.9

387. Find the moment of inertia of the area bounded by the curve y^2 = 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

388. Find the moment of inertia with respect to x-axis of the area bounded by the parabola y^2 = 4x and the line x = 1.

• a. 2.35
• b. 2.68
• c. 2.13
• d. 2.56

389. What is the integral of sin^6(φ)cos^4 (φ) dφ if the upper limit is π/2 and lower limit is 0?

• a. 0.1398
• b. 1.0483
• c. 0.0184
• d. 0.9237

390. Evaluate the integral of cos^7 φ sin^5 φ dφ if the upper limit is 0.

• a. 0.1047
• b. 0.0083
• c. 1.0387
• d. 1.3852

391. What is the integral of sin^4 x dx if the lower limit is 0 and the upper limit is π/2?

• a. 1.082
• b. 0.927
• c. 2.133
• d. 0.589

392. Evaluate the integral of cos^5 φ dφ if the lower limit is 0 and the upper limit is π/2.

• a. 0.084
• b. 0.533
• c. 1.203
• d. 1.027

393. Evaluate the integral (cos3A)^8 dA from 0 to π/6.

• a. 27π/363
• b. 35π/768
• c. 23π/765
• d. 12π/81

394. What is the integral of sin^5 x cos^3 x dx if the lower limit is 0 and the upper limit is π/2?

• a. 0.0208
• b. 0.0833
• c. 0.0278
• d. 0.0417

395. Evaluate the integral of 15sin^7 (x) dx from 0 to π/2.

• a. 6.857
• b. 4.382
• c. 5.394
• d. 6.139

396. Evaluate the integral of 5 cos^6 x sin^2 x dx if the upper limit is π/2 and the lower limit is 0.

• a. 0.186
• b. 0.294
• c. 0.307
• d. 0.415

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

• a. 2
• b. π
• c. 6
• d. π/2

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

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

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

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