# MCQ in Algebra and General Mathematics Part 7 | ECE Board Exam

(Last Updated On: January 2, 2021) This is the Multiple Choice Questions Part 7 of the Series in Algebra and General Mathematics topics in Engineering Mathematics. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

• MCQ in Algebraic functions | MCQ in theory of Equations | MCQ in Factorization and Algebraic functions | MCQ in Ratio, Proportion and Variation | MCQ in Matrix theory | MCQ in Arithmetic and Geometric Progression | MCQ in Equations and Inequalities | MCQ in Linear and Quadratic Equations | MCQ in Complex Number System | MCQ in Polynomials | MCQ in Mathematical Induction | MCQ in Logic and Probability | MCQ in Statistics| MCQ in System of Numbers and Conversion | MCQ in Fundamentals in Algebra | MCQ in Binomial Theorems and Logarithms | MCQ in Age Problems | MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Motion Problems | MCQ in Clock Problems | MCQ in Variation | MCQ in Progression | MCQ in Miscellaneous Problems

#### Continue Practice Exam Test Questions Part 7 of the Series

Choose the letter of the best answer in each questions.

301. Find the harmonic mean between the numbers 3/8 and 4.

a. 35/34

b. 24/35

c. 42/35

d. 35/24

View Answer:

Answer: Option B

Solution:

302. The terms of a sum may be grouped in any manner without affecting the result. this is law known as:

a. Commutative Law

b. Distributive Law

c. Associative Law

d. Reflexive Law

View Answer:

Answer: Option C

Solution:

303. A number is divided into two parts such that when the greater part is divided by the smaller part, the quotient is 3, and the remainder is 5. Find the smaller number if the sum of the two numbers is 37.

a. 8

b. 29

c. 22

d. 16

View Answer:

Answer: Option A

Solution:

304. Mary was four times as old as Lea ten years ago. If she is now twice as old as Lea, how old is Mary.

a. 25

b. 40

c. 30

d. 15

View Answer:

Answer: Option C

Solution:

305. The sum of three succeeding odd integers is 75. The largest integer is

a. 25

b. 29

c. 27

d. 31

View Answer:

Answer: Option C

Solution:

306. A ship propelled to move at 25 mi/ hr in still water, travels 4.2 miles upstream in the same time that it can travel 5.8 miles downstream. Find the speed of the stream.

a. 4

b. 6

c. 8

d. 10

View Answer:

Answer: Option A

Solution:

307. Jose’s rate of doing work three times as fast as Bong. On given day Jose and Bong work together for 4 hours then Bong was called away and Jose finishes the rest of the job in 2 hours. How long would it take Bong to do the complete job alone?

a. 18 hrs.

b. 22 hrs.

c. 16 hrs.

d. 31 hrs.

View Answer:

Answer: Option B

Solution:

308. The length of a rectangle is 3 times its width. If the width of the rectangle is 5 inches, what is the rectangle’s area, in square inches?

a. 15

b. 20

c. 30

d. 75

View Answer:

Answer: Option D

Solution:

309. For all x >2, (2x2 + 2x – 12) / (x – 2) simplifies to

a. 2(x + 3)

b. 2(x – 2)

c. x + 3

d. 2(x + 3)(x – 2)

View Answer:

Answer: Option A

Solution:

310. If the hypotenuse of a right triangle is 10 inches long and one of its legs is 5 inches long, how long is the other leg?

a. 5

b. 5 √3

c. 5√5

d. 7.5

View Answer:

Answer: Option B

Solution:

311. In the standard (x,y) coordinate plane, the graph of (x + 3)2 + (y + 5)2 = 16 is a circle. What is the circumference of the circle, expressed in coordinate units?

a. 4π

b. 5π

c. 3π

d. 8π

View Answer:

Answer: Option D

Solution:

312. How many solutions are there to the equation x2 – 7 = 0?

a. 1

b. 2

c. 4

d. 7

View Answer:

Answer: Option B

Solution:

313. A circle with center (4,-5) is tangent to the y-axis in the standard (x,y) coordinate plane. What is the radius of this circle?

a. 4

b. 5

c. 16

d. 25

View Answer:

Answer: Option A

Solution:

314. Angle A is an acute angle and sin(A) = 11/14. What is the value of cos(A)?

a. √3 / 14

b. 5√3 / 14

c. √(3/14)

d. 5/14

View Answer:

Answer: Option B

Solution:

315. What are the values of a and b, if any, where – a|b + 4| > 0?

a. a > 0 and b ≠ 4

b. a < 0 and b ≥ -4

c. a < 0 and b ≠ -4

d. a < 0 and b ≤ -4

View Answer:

Answer: Option C

Solution:

316. In a shipment of televisions, 1/50 of the televisions are defective. What is the ratio of defective to non defective televisions?

a. 1/50

b. 1/49

c. 49/1

d. 50/1

View Answer:

Answer: Option B

Solution:

317. Which of the following is divisible (with no remainder) by 4?

a. 214133

b. 510056

c. 322569

d. 952217

View Answer:

Answer: Option B

Solution:

318. A particle travels 1 x 106 meters per second in a straight line for 5 x 10-6 seconds. How many meters has it traveled?

a. 4

b. 5

c. 6

d. 7

View Answer:

Answer: Option B

Solution:

319. The length of sides AB and AC in the triangle below are equal. What is the measure of angle ∠ A if angle ∠ C is 70°?

a. 70°

b. 55°

c. 40°

d. 110°

View Answer:

Answer: Option C

Solution:

320. ABC is an equilateral triangle. AH is perpendicular to BC and has a length of 2√3 inches. What is the area, in square inches, of triangle Δ ABC.

a. 3√3

b. 2√3

c. 4√3

d. 8√3

View Answer:

Answer: Option C

Solution:

321. Find the value of k in the quadratic equation (2k + 2) x2 + (4 – 4k) x + k – 2 = 0 so that the roots are reciprocal of each other.

a. 4

b. 2

c. -4

d. -2

View Answer:

Answer: Option C

Solution:

322. Solve for x if 8y = 3x – 11

a. 8/3) y + 11

b. (8/3) y – 11

c. (8y – 11)/3

d. (8y + 11)/3

View Answer:

Answer: Option D

Solution:

323. When graphed in the (x, y) coordinate plane, at what point do the lines 2x + 3y = 5 and x = -2 intersect?

a. (-2, 0)

b. (-2, 5)

c. (0, 5)

d. (-2, 3)

View Answer:

Answer: Option D

Solution:

324. The area of a trapezoid is 0.5h(b1 + b2), where h is the altitude, and b1 and b2 are the lengths of the parallel bases. If a trapezoid has an altitude of 15 inches, an area of 105 square inches, and one of the bases 22 inches, what is the perimeter, in inches, of the trapezoid?

a. 8

b. 45

c. 60

d. 30

View Answer:

Answer: Option A

Solution:

325. If you drove at average speed of 66 miles per hour, what distance, in miles, did you drive in 99 minutes?

a. 65.34

b. 108.9

c. 150

d. 90.45

View Answer:

Answer: Option B

Solution:

326. If x and y are any real numbers such that 0 < x < 2 < y , which of these must be true?

a. x < (xy)/2 < y

b. 0 < xy < 2x

c. x < xy < 2

d. 0 < xy < 2

View Answer:

Answer: Option A

Solution:

327. In the right triangle ABC below, what is the cosine of angle A if the opposite side is 3 and the adjacent side is 4.

a. 5/3

b. 5/4

c. 3/5

d. 4/5

View Answer:

Answer: Option C

Solution:

328. In a triangle ABC with segment BD, B is on AD, ∠ BAC and ∠ ACB measure 26° and 131° respectively. What is the measure of ∠CBD?

a. 26°

b. 157°

c. 23°

d. 154°

View Answer:

Answer: Option B

Solution:

329. The total surface area of all six sides of the rectangular box below is equal to 128 square inches. What is x in inches?

a. 6

b. 4

c. 2

d. 8

View Answer:

Answer: Option A

Solution:

330. ABC is a right triangle. ABDE is a square of area 200 square inches and BCGF is a square of 100 square inches. What is the length, in inches, of AC?

a. 10√3

b. 10√2

c. 10√1

d. 10

View Answer:

Answer: Option A

Solution:

331. What is the slope of the line: 4x = -3y + 8

a. 4

b. -3/4

c. -4/3

d. 3

View Answer:

Answer: Option C

Solution:

332. Which of the following is equal to √45

a. 5√3

b. 9√5

c. 3√5

d. 3

View Answer:

Answer: Option C

Solution:

333. What is the smallest value of x that satisfies the equation: x(x + 4) = -3

a. 1

b. -1

c. 3

d. -3

View Answer:

Answer: Option D

Solution:

334. A group of 7 friends are having lunch together. Each person eats at least 3/4 of a pizza. What is the smallest number of whole pizzas needed for lunch?

a. 7

b. 5

c. 6

d. 8

View Answer:

Answer: Option C

Solution:

335. There are n students in a school. If r% among the students are 12 years or younger, which of the following expressions represents the number of students who are older than 12?

a. n(1 – r)

b. 100(1 – r)n

c. n(1 – r) / 100

d. n(100 – r) / 100

View Answer:

Answer: Option D

Solution:

336. The measures of angles A, B and C of a triangle are in the ratio 3:4:5. What is the measure, in degrees, of the largest angle?

a. 75°

b. 15°

c. 12°

d. 90°

View Answer:

Answer: Option A

Solution:

337. If x + 4y = 5 and 5x + 6y = 7, then 3x + 5y = ?

a. 12

b. 6

c. 4

d. 2

View Answer:

Answer: Option B

Solution:

338. For all real numbers x, the minimum value of 1 + 2cos(4x) is

a. 0

b. -1

c. -2

d. -4

View Answer:

Answer: Option B

Solution:

339. What is the largest possible product for 2 odd integers whose sum is equal to 32?

a. 64

b. 255

c. 256

d. 1024

View Answer:

Answer: Option B

Solution:

340. If (a + b)2 = 25 and (a – b) 2 = 45, then a2 + b2 = ?

a. 35

b. 70

c. 140

d. 280

View Answer:

Answer: Option A

Solution:

341. If a = 3, then 2 / (1/7 + 1/a) = ?

a. 21 / 10

b. 21 / 5

c. 21 / 15

d. 21 / 3

View Answer:

Answer: Option B

Solution:

342. A company makes a profit equal to 25% of its sales. The profit is shared equally among the 4 owners of the company. If the company generates sales of \$5,000,000, how much money does each one of the owners get?

a. 312,500

b. 500,000

c. 1,250,000

d. 12,500,000

View Answer:

Answer: Option A

Solution:

343. If the expression x3 + 2hx – 2 is equal to 6 when x = -2, what is the value of h?

a. -2

b. -4

c. 4

d. 6

View Answer:

Answer: Option B

Solution:

344. If -3/(a – 3) = 3/(a + 2), then a = ?

a. 1/2

b. 1/4

c. 1

d. 2

View Answer:

Answer: Option A

Solution:

345. Which integer is nearest to √2100 / √7

a. 17

b. 18

c. 19

d. 16

View Answer:

Answer: Option A

Solution:

346. The two legs of a right triangle measure 6 and 8 inches respectively. What is the area of the circle that contains all 3 vertices of the triangle?

a. 24Pi

b. 25Pi

c. 35Pi

d. 34Pi

View Answer:

Answer: Option B

Solution:

347. X and Y are acute angles such that tan y = cot x. What is the sum, in degrees, of the measures of the angles X and Y?

a. 90°

b. 45°

c. 60°

d. 30°

View Answer:

Answer: Option A

Solution:

348. What is the value of the adjacent side if the opposite side is 1 inch and the 2 other angles of the right triangle is 30° and 60°

a. 1/√3

b. √2

c. √3

d. 6/√3

View Answer:

Answer: Option A

Solution:

349. Which of the lines below is not parallel to the line 6x – 2y = 10?

a. 3x – y = 7

b. -6x + 2y = 20

c. 3x + y = 7

d. 6x – 2y = 5

View Answer:

Answer: Option C

Solution:

350. For what value of k the equation below has no value of x: 2x + 3 = x – 2kx – 5

a. 1

b. -1

c. 0.5

d. -0.5

View Answer:

Answer: Option D

Solution:

### Online Questions and Answers in Algebra and General Mathematics Series

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

MCQ in Algebra and General 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

### Online Questions and Answers in Fundamentals in Algebra Series

Following is the list of practice exam test questions in this brand new series:

MCQ in Fundamentals in Algebra
PART 1: MCQ from Number 1 – 50                           Answer key: PART 1
PART 2: MCQ from Number 51 – 100                      Answer key: PART 2

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