# MCQ in Engineering Mathematics Part 7 | ECE Board Exam

(Last Updated On: January 11, 2021) 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

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

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

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

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

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)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solution:

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

a. 4

b. 8

c. 16

d. 2

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

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

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

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

Solution:

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

a. a2

b. a

c. 2a

d. a3

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

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

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

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

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

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

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

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

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

Solution:

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

a. πa

b. 2πa

c. 3πa/2

d. 2πa/3

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

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

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

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

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)

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

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)

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

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

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

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

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

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