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

⇐ MCQ in Algebra and General Mathematics Part 6 | Math Board Exam

**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

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

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

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

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

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

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.

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

Answer: **Option D**

Solution:

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

a. 2(x + 3)

b. 2(x – 2)

c. x + 3

d. 2(x + 3)(x – 2)

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

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

Answer: **Option D**

Solution:

312. How many solutions are there to the equation x^{2} – 7 = 0?

a. 1

b. 2

c. 4

d. 7

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

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

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

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

Answer: **Option B**

Solution:

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

a. 214133

b. 510056

c. 322569

d. 952217

Answer: **Option B**

Solution:

318. A particle travels 1 x 10^{6} 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

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°

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

Answer: **Option C**

Solution:

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

a. 4

b. 2

c. -4

d. -2

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

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)

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

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

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

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

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°

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

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

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

Answer: **Option C**

Solution:

332. Which of the following is equal to √45

a. 5√3

b. 9√5

c. 3√5

d. 3

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

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

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

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°

Answer: **Option A**

Solution:

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

a. 12

b. 6

c. 4

d. 2

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

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

Answer: **Option B**

Solution:

340. If (a + b)^{2} = 25 and (a – b) ^{2} = 45, then a^{2} + b^{2} = ?

a. 35

b. 70

c. 140

d. 280

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

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

Answer: **Option A**

Solution:

343. If the expression x^{3} + 2hx – 2 is equal to 6 when x = -2, what is the value of h?

a. -2

b. -4

c. 4

d. 6

Answer: **Option B**

Solution:

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

a. 1/2

b. 1/4

c. 1

d. 2

Answer: **Option A**

Solution:

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

a. 17

b. 18

c. 19

d. 16

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

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°

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

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

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

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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

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

**PART 2**

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

**PART 3**

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

**PART 4**

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

**PART 5**

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

**PART 6**

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

**PART 7**

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

**PART 8**

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

**PART 9**

**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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

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

**PART 2**

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