MCQ in Engineering Mathematics Part 7 | ECE Board Exam

(Last Updated On: January 11, 2021)

MCQs in Engineering Mathematics

This is the Multiples Choice Questions in Engineering Mathematics Part 7 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 7 of the Series

MCQ in Engineering Mathematics Part 6 | Math Board Exam

Choose the letter of the best answer in each questions.

301. Find the area bounded by the curve y = cos hx, x = 0, x = 1 and y = 0.

a. 1.073

b. 1.175

c. 1.234

d. 1.354

View Answer:

Answer: Option B

Solution:

302. Find the area in the first quadrant under the curve y – sin hx from x = 0 to x = 1.

a. 0.345

b. 0.453

c. 0.543

d. 0.623

View Answer:

Answer: Option C

Solution:

303. Find the area of the region in the first quadrant bounded by the curves y = sin x, y = cos x and the y-axis.

a. 0.356

b. 0.414

c. 0.486

d. 0.534

View Answer:

Answer: Option B

Solution:

304. Find the area of the region bounded by the x-axis, the curve y = 6x – x2 and the vertical lines x = 1 and x = 4.

a. 22

b. 23

c. 24

d. 25

View Answer:

Answer: Option C

Solution:

305. Find the area bounded by the curve y = ex, y = e-x and x = 1, by integration.

a. [(e – 1)2]/e

b. (e2 – 1)/e

c. (e – 1)/e

d. [(e – 1)2]/(e2)

View Answer:

Answer: Option A

Solution:

306. Suppose a company wants to introduce a new machine that will produce a rate of annual savings S(x) = 150 – x2 where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x2) + (11x/4). For how many years will it be profitable to use this new machine?

a. 7 yrs

b. 6 yrs

c. 8 yrs

d. 10 yrs

View Answer:

Answer: Option C

Solution:

307. Suppose a company wants to introduce a new machine that will produce a rate of annual savings S(x) = 150 – x2 where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x2) + (11x/4). What are the net total savings during the first year of use of the machine?

a. 122

b. 148

c. 257

d. 183

View Answer:

Answer: Option B

Solution:

308. Suppose a company wants to introduce a new machine that will produce a rate of annual savings S(x) = 150 – x2 where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x2) + (11x/4). What are the net total savings over the entire period of use of the machine?

a. 653

b. 711

c. 771

d. 826

View Answer:

Answer: Option C

Solution:

309. The price in pesos for a certain product is expressed as p(x) = 900 – 80x – x2 when the demand for the product is x units. Also the function p(x) = x2 + 10x gives the price in pesos when the supply is x units. Find the consumer and producers surplus.

a. P3400; P4422

b. P4000; P3585

c. P4500; P3375

d. P5420; P3200

View Answer:

Answer: Option C

Solution:

310. A horse is tied outside of a circular fence of radius 4 m by a rope having a length of 4π m. Determine the area on which the horse can graze.

a. 398.29 sq m

b. 413.42 sq m

c. 484.37 sq m

d. 531.36 sq m

View Answer:

Answer: Option B

Solution:

311. A dog is tied to an 8m circular tank by a 3 m length of cord. The cord remains horizontal. Find the area over which the dog can move.

a. 10.286 sq m

b. 13.164 sq m

c. 15.298 sq m

d. 16.387 sq m

View Answer:

Answer: Option D

Solution:

312. Find the area bounded by the curve y2 = 8(x – 4), the line y = 4, y-axis and x-axis.

a. 18.67

b. 14.67

c. 15.67

d. 17.67

View Answer:

Answer: Option A

Solution:

313. Find the area enclosed by the parabola y2 = 8x and the latus rectum.

a. 32/3 sq units

b. 29/4 sq units

c. 41/2 sq units

d. 33/2 sq units

View Answer:

Answer: Option A

Solution:

314. What is the area bounded y the curve x2 = -9y and the line y + 1 = 0

a. 6 sq units

b. 5 sq units

c. 2 sq units

d. 4 sq units

View Answer:

Answer: Option D

Solution:

315. What is the area bounded by the curve y2 = x and the line x – 4 = 0.

a. 23/4 sq units

b. 32/3 sq units

c. 54/4 sq units

d. 13/5 sq units

View Answer:

Answer: Option B

Solution:

316. Find the area bounded by the parabola x2 = 4y and y = 4.

a. 13.23 sq units

b. 21.33 sq units

c. 31.32 sq units

d. 33.21 sq units

View Answer:

Answer: Option B

Solution:

317. What is the area bounded by the curve y2 = -2x and the line x = -2.

a. 18/3 sq units

b. 19/5 sq units

c. 16/3 sq units

d. 17/7 sq units

View Answer:

Answer: Option C

Solution:

318. Find the area enclosed by the curve x2 + 8y + 16 = 0 the x-axis, y-axis and the line x – 4 = 0.

a. 10.67

b. 9.67

c. 8.67

d. 7.67

View Answer:

Answer: Option A

Solution:

319. Find the area bounded by the parabola y = 6x – x2 and y = x2 – 2x. Note, the parabola intersects at point (0,0) and (4,8).

a. 44/3

b. 64/3

c. 74/3

d. 54/3

View Answer:

Answer: Option B

Solution:

320. Find the area of the portion of the curve y = cos x from x = 0 to x = π/2.

a. 1 sq unit

b. 2 sq units

c. 3 sq units

d. 4 sq units

View Answer:

Answer: Option A

Solution:

321. Find the area of the portion of the curve y = sin x from x = 0 to x = π.

a. 1 sq units

b. 2 sq units

c. 3 sq unit

d. 4 sq units

View Answer:

Answer: Option B

Solution:

322. Find the area bounded by the curve r2 = 4cos2φ.

a. 8 sq units

b. 2 sq units

c. 4 sq units

d. 6 sq units

View Answer:

Answer: Option C

Solution:

323. Find the area enclosed by the curve r2 = 4cosφ.

a. 4

b. 8

c. 16

d. 2

View Answer:

Answer: Option B

Solution:

324. Determine the period and amplitude of the function y = 2sin5x.

a. 2π/5, 2

b. 3π/2, 2

c. π/5, 2

d. 3π/10, 2

View Answer:

Answer: Option A

Solution:

325. Determine the period and amplitude of the function y = 5cos2x.

a. π/5, 2

b. 3π/2, 2

c. π, 5

d. 3π/10, 2

View Answer:

Answer: Option C

Solution:

326. Determine the period and amplitude of the function y = 5sinx.

a. 2π, 5

b. 3π/2, 5

c. π/2, 5

d. π, 5

View Answer:

Answer: Option A

Solution:

327. Determine the period and amplitude of the function y = 3 cos x.

a. π, 3

b. π/2, 3

c. 3/2, 3

d. 2π, 3

View Answer:

Answer: Option D

Solution:

328. Find the area of the curve r2 = a2cosφ.

a. a2

b. a

c. 2a

d. a3

View Answer:

Answer: Option A

Solution:

329. Find the area of the region bounded by the curve r2 = 16cosθ.

a. 27 sq units

b. 30 sq units

c. 32 sq units

d. 35 sq units

View Answer:

Answer: Option C

Solution:

330. Find the area enclosed by the curve r = a (1 – sinθ).

a. (3a2)π/2

b. (2a2

c. (3a2

d. (3a2)π/5

View Answer:

Answer: Option A

Solution:

331. Find the surface area of the portion of the curve x2 = y from y = 1 to y = 2 when it is revolved about the y-axis.

a. 16.75

b. 17.86

c. 18.94

d. 19.84

View Answer:

Answer: Option D

Solution:

332. Find the area of the surface generated by rotating the portion of the curve y = (x3)/3 from x = 0 to x = 1 about the x-axis.

a. 0.486

b. 0.542

c. 0.638

d. 0.782

View Answer:

Answer: Option C

Solution:

333. Find the surface area of the portion of the curve x2 + y2 = 4 from x = 0 to x = 2 when it is revolved about the y-axis.

a. 4π

b. 8π

c. 12π

d. 16π

View Answer:

Answer: Option B

Solution:

334. Compute the surface area generated when the first quadrant portion if the curve x2 – 4y + 8 = 0 from x = 0 to x = 2 is revolved about the y-axis.

a. 26.42

b. 28.32

c. 30.64

d. 31.64

View Answer:

Answer: Option C

Solution:

335. Find the total length of the curve r = 4 (1 – sin θ) from θ = 90 deg to θ = 270 deg and also the total perimeter of the curve.

a. 16, 32

b. 18, 36

c. 12, 24

d. 15, 30

View Answer:

Answer: Option A

Solution:

336. Find the length of the curve r = 4sinθ from θ = 0 to θ = 90 deg and also the total length of the curve.

a. π; 2π

b. 2π; 4π

c. 3π; 6π

d. 4π; 8π

View Answer:

Answer: Option B

Solution:

337. Find the length of the curve r = a (1 – cos θ) from θ = 0 to θ = π and also the total length of curve.

a. 2a; 4a

b. 3a; 6a

c. 4a; 8a

d. 5a; 10a

View Answer:

Answer: Option C

Solution:

338. Find the total length of the curve r = a cos θ.

a. πa

b. 2πa

c. 3πa/2

d. 2πa/3

View Answer:

Answer: Option A

Solution:

339. Find the length of the curve having a parametric equations of x = a cos3 θ y = a sin2 θ from θ = 0 to θ = 2π.

a. 5a

b. 6a

c. 7a

d. 8a

View Answer:

Answer: Option B

Solution:

340. Find the centroid of the area bounded by the curve y = 4 – x2 the line x = 1 and the coordinate axes.

a. 0.46

b. 1.57

c. 1.85

d. 2.16

View Answer:

Answer: Option C

Solution:

341. Find the centroid of the area under y = 4 – x2 in the first quadrant.

a. 0.75

b. 0.25

c. 0.50

d. 1.15

View Answer:

Answer: Option A

Solution:

342. Find the centroid of the area in first quadrant bounded by the curve y2 = 4ax and latus rectum.

a. 1a

b. 2a/5

c. 3a/5

d. 4a/5

View Answer:

Answer: Option C

Solution:

343. A triangular section has coordinates of A(2, 2), B(11, 2) and C(5, 8). Find the coordinates of the centroid of the triangular section.

a. (7, 4)

b. (6, 4)

c. (8, 4)

d. (9, 4)

View Answer:

Answer: Option B

Solution:

344. The following cross section has the following given coordinates. Compute for the centroid of the given cross section A(2, 2); B(5, 8); C(7, 2); D(2, 0) and E(7, 0).

a. 4.6, 3.4

b. 4.8, 2.9

c. 5.2, 3.8

d. 5.3, 4.1

View Answer:

Answer: Option A

Solution:

345. Sections ABCD is a quadrilateral having the given coordinates A(2, 3); B(8, 9); C(11, 3); D(11, 0). Compute the coordinates of the centroid of the quadrilateral.

a. (6.22, 3.8)

b. (7, 4)

c. (7.33, 4)

d. (7.8, 4.2)

View Answer:

Answer: Option C

Solution:

346. A cross section consists of a triangle ABC and a semi circle with AC as its diameter. If the coordinates of A(2, 6); B(11, 9) and C(14, 6), compute the coordinates of the centroid of the cross section.

a. 4.6, 3.4

b. 4.8, 2.9

c. 5.2, 3.8

d. 5.3, 4.1

View Answer:

Answer: Option A

Solution:

347. Locate the centroid of the area bounded by the parabola y2 = 4x, the line y = 4 and the y-axis.

a. 2/5, 3

b. 3/5, 3

c. 4/5, 3

d. 6/5, 3

View Answer:

Answer: Option D

Solution:

348. Find the centroid of the area bounded by the curve x2 = –(y – 4), the x-axis and the y-axis on the first quadrant.

a. 7/4, 6/5

b. 5/4, 7/5

c. ¾, 8/5

d. ¼, 9/5

View Answer:

Answer: Option C

Solution:

349. Locate the centroid of the area bounded by the curve y2 = -3(x – 6)/2 the x-axis and the y-axis on the first quadrant.

a. 11/5, 11/8

b. 12/5, 9/8

c. 13/5, 7/8

d. 14/5, 5/8

View Answer:

Answer: Option B

Solution:

350. Locate the centroid of the area bounded by the curve 5y2 = 16x and y2 = 8x – 24 on the first quadrant.

a. x = 2.20; y = 1.51

b. x = 1.50; y = 0.25

c. x = 2.78; y = 1.39

d. x = 1.64; y = 0.26

View Answer:

Answer: Option A

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

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