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

โ 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

Answer: **Option B
**

Solution:

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

a. 0.345

b. 0.453

c. 0.543

d. 0.623

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

Answer: **Option B**

Solution:

304. Find the area of the region bounded by the x-axis, the curve y = 6x โ x^{2} and the vertical lines x = 1 and x = 4.

a. 22

b. 23

c. 24

d. 25

Answer: **Option C**

Solution:

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

a. [(e โ 1)^{2}]/e

b. (e^{2} โ 1)/e

c. (e โ 1)/e

d. [(e โ 1)^{2}]/(e^{2})

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 โ x^{2} where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x^{2}) + (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

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 โ x^{2} where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x^{2}) + (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

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 โ x^{2} where x is the number of yrs of operation of the machine, while producing a rate of annual costs of C(x) = (x^{2}) + (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

Answer: **Option C**

Solution:

309. The price in pesos for a certain product is expressed as p(x) = 900 โ 80x โ x^{2} when the demand for the product is x units. Also the function p(x) = x^{2} + 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

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 4ฯ 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

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

Answer: **Option D**

Solution:

312. Find the area bounded by the curve y^{2} = 8(x โ 4), the line y = 4, y-axis and x-axis.

a. 18.67

b. 14.67

c. 15.67

d. 17.67

Answer: **Option A**

Solution:

313. Find the area enclosed by the parabola y^{2} = 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

Answer: **Option A**

Solution:

314. What is the area bounded y the curve x^{2} = -9y and the line y + 1 = 0

a. 6 sq units

b. 5 sq units

c. 2 sq units

d. 4 sq units

Answer: **Option D**

Solution:

315. What is the area bounded by the curve y^{2} = x and the line x โ 4 = 0.

a. 23/4 sq units

b. 32/3 sq units

c. 54/4 sq units

d. 13/5 sq units

Answer: **Option B**

Solution:

316. Find the area bounded by the parabola x^{2} = 4y and y = 4.

a. 13.23 sq units

b. 21.33 sq units

c. 31.32 sq units

d. 33.21 sq units

Answer: **Option B**

Solution:

317. What is the area bounded by the curve y^{2} = -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

Answer: **Option C**

Solution:

318. Find the area enclosed by the curve x^{2} + 8y + 16 = 0 the x-axis, y-axis and the line x โ 4 = 0.

a. 10.67

b. 9.67

c. 8.67

d. 7.67

Answer: **Option A**

Solution:

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

a. 44/3

b. 64/3

c. 74/3

d. 54/3

Answer: **Option B**

Solution:

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

a. 1 sq unit

b. 2 sq units

c. 3 sq units

d. 4 sq units

Answer: **Option A**

Solution:

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

a. 1 sq units

b. 2 sq units

c. 3 sq unit

d. 4 sq units

Answer: **Option B**

Solution:

322. Find the area bounded by the curve r^{2} = 4cos2ฯ.

a. 8 sq units

b. 2 sq units

c. 4 sq units

d. 6 sq units

Answer: **Option C**

Solution:

323. Find the area enclosed by the curve r^{2} = 4cosฯ.

a. 4

b. 8

c. 16

d. 2

Answer: **Option B**

Solution:

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

a. 2ฯ/5, 2

b. 3ฯ/2, 2

c. ฯ/5, 2

d. 3ฯ/10, 2

Answer: **Option A**

Solution:

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

a. ฯ/5, 2

b. 3ฯ/2, 2

c. ฯ, 5

d. 3ฯ/10, 2

Answer: **Option C**

Solution:

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

a. 2ฯ, 5

b. 3ฯ/2, 5

c. ฯ/2, 5

d. ฯ, 5

Answer: **Option A**

Solution:

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

a. ฯ, 3

b. ฯ/2, 3

c. 3/2, 3

d. 2ฯ, 3

Answer: **Option D**

Solution:

328. Find the area of the curve r^{2} = a^{2}cosฯ.

a. a^{2}

b. a

c. 2a

d. a^{3}

Answer: **Option A**

Solution:

329. Find the area of the region bounded by the curve r^{2} = 16cosฮธ.

a. 27 sq units

b. 30 sq units

c. 32 sq units

d. 35 sq units

Answer: **Option C**

Solution:

330. Find the area enclosed by the curve r = a (1 โ sinฮธ).

a. (3a^{2})ฯ/2

b. (2a^{2})ฯ

c. (3a^{2})ฯ

d. (3a^{2})ฯ/5

Answer: **Option A**

Solution:

331. Find the surface area of the portion of the curve x^{2} = 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

Answer: **Option D**

Solution:

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

a. 0.486

b. 0.542

c. 0.638

d. 0.782

Answer: **Option C**

Solution:

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

a. 4ฯ

b. 8ฯ

c. 12ฯ

d. 16ฯ

Answer: **Option B**

Solution:

334. Compute the surface area generated when the first quadrant portion if the curve x^{2} โ 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

Answer: **Option C**

Solution:

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

a. 16, 32

b. 18, 36

c. 12, 24

d. 15, 30

Answer: **Option A**

Solution:

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

a. ฯ; 2ฯ

b. 2ฯ; 4ฯ

c. 3ฯ; 6ฯ

d. 4ฯ; 8ฯ

Answer: **Option B**

Solution:

337. Find the length of the curve r = a (1 โ cos ฮธ) from ฮธ = 0 to ฮธ = ฯ and also the total length of curve.

a. 2a; 4a

b. 3a; 6a

c. 4a; 8a

d. 5a; 10a

Answer: **Option C**

Solution:

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

a. ฯa

b. 2ฯa

c. 3ฯa/2

d. 2ฯa/3

Answer: **Option A**

Solution:

339. Find the length of the curve having a parametric equations of x = a cos^{3} ฮธ y = a sin^{2} ฮธ from ฮธ = 0 to ฮธ = 2ฯ.

a. 5a

b. 6a

c. 7a

d. 8a

Answer: **Option B**

Solution:

340. Find the centroid of the area bounded by the curve y = 4 โ x^{2} the line x = 1 and the coordinate axes.

a. 0.46

b. 1.57

c. 1.85

d. 2.16

Answer: **Option C**

Solution:

341. Find the centroid of the area under y = 4 โ x^{2} in the first quadrant.

a. 0.75

b. 0.25

c. 0.50

d. 1.15

Answer: **Option A**

Solution:

342. Find the centroid of the area in first quadrant bounded by the curve y^{2} = 4ax and latus rectum.

a. 1a

b. 2a/5

c. 3a/5

d. 4a/5

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)

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

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)

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

Answer: **Option A**

Solution:

347. Locate the centroid of the area bounded by the parabola y^{2} = 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

Answer: **Option D**

Solution:

348. Find the centroid of the area bounded by the curve x^{2} = โ(y โ 4), the x-axis and the y-axis on the first quadrant.

a. 7/4, 6/5

b. 5/4, 7/5

c. ยพ, 8/5

d. ยผ, 9/5

Answer: **Option C**

Solution:

349. Locate the centroid of the area bounded by the curve y^{2} = -3(x โ 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

Answer: **Option B**

Solution:

350. Locate the centroid of the area bounded by the curve 5y^{2} = 16x and y^{2} = 8x โ 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

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**

**MCQ from Number 1 โ 50**Answer key:

**PART 1**

**MCQ from Number 51 โ 100**Answer key:

**PART 2**

**MCQ from Number 101 โ 150**Answer key:

**PART 3**

**MCQ from Number 151 โ 200**Answer key:

**PART 4**

**MCQ from Number 201 โ 250**Answer key:

**PART 5**

**MCQ from Number 251 โ 300**Answer key:

**PART 6**

**MCQ from Number 301 โ 350**Answer key:

**PART 7**

**MCQ from Number 351 โ 400**Answer key:

**PART 8**

**MCQ from Number 401 โ 450**Answer key:

**PART 9**

**MCQ from Number 451 โ 500**Answer key:

**PART 10**

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