This is the Multiple Choice Questions Part 8 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 8 of the Series

โ MCQ in Algebra and General Mathematics Part 7 | Math Board Exam

**Choose the letter of the best answer in each questions.**

351. Find the value of x which will satisfy the equation โ(x โ 2) / โx = 1

a. -1, -4

b. 1, 4

c. 4

d. 0

Answer: **Option C**

Solution:

352. Find the geometric mean between the terms -4 and -9

a. 6

b. 7

c. -6

d. 36

Answer: **Option C**

Solution:

353. What is the average value of 7/8 and 3/4?

a. 5/4

b. 5/8

c. 5/16

d. 13/16

Answer: **Option D**

Solution:

354. A solution is made of water and pure acid. If 75% of the solution is water, how many litters of pure acid are in 20 liters of this solution?

a. 10

b. 5

c. 25

d. 15

Answer: **Option B**

Solution:

355. The diagonal of a square has a measure of 12 inches. What is the perimeter, in inches, of this square.

a. 6โ2

b. 72

c. 24โ2

d. 48

Answer: **Option C**

Solution:

356. In the right triangle ABC, C is a right angle and the measure of angle B is 60ยฐ. If BC is 20 inches long, then how long is AC?

a. 20โ3

b. 20

c. โ3

d. 20/โ3

Answer: **Option A**

Solution:

357. If x = 2.0001, which of the following expressions has the largest value?

a. 2 / (x + 2)

b. 2 / (x – 2)

c. (x + 2) / 2

d. 2 / x

Answer: **Option B**

Solution:

358. In the rectangle ABCD, the measure of the length AD is 3 times the measure of the width AB. What is the slope of the line segment BD?

a. 3

b. 1/3

c. -1/3

d. -3

Answer: **Option C**

Solution:

359. What is the product of the two real solutions of the equation: 2x = 3 – x^{2}

a. 2

b. -2

c. 6

d. -3

Answer: **Option D**

Solution:

360. The ratio of the circumference of any circle to the diameter of the circle is:

a. An integer

b. An irrational number

c. A rational number

d. A whole number

Answer: **Option B**

Solution:

361. Find the sum and product of roots of the equation x^{3} + 2x^{2} โ 23x โ 60 = 0.

a. -2, 60

b. 2, 17

c. 17, -60

d. 2, -60

Answer: **Option A**

Solution:

362. The ratio of three numbers is 2:5:7. If 7 is subtracted from the second number, the resulting numbers form an arithmetic progression. Determine the smallest of the three numbers.

a. 28

b. 15

c. 21

d. 70

Answer: **Option A**

Solution:

363. Determine the sum of the first 4 terms of the sequence whose general term is given by 3n โ 2.

a. 121

b. 89

c. 98

d. 112

Answer: **Option D**

Solution:

364. Find the sum of all positive integers between 84 and 719 which are exactly divisible by 5.

a. 23,750

b. 45,680

c. 50,800

d. 38,460

Answer: **Option C**

Solution:

365. If 3log x โ log y = 0, express y in terms of x.

a. y = x^{3}

b. y = x^{2}

c. y = x

d. y = 3x

Answer: **Option A**

Solution:

366. In a certain A.P. the first, fourth and eight terms are themselves form a geometric progression. What is the common ratio of the G.P.?

a. 4/3

b. 5/4

c. 4/5

d. 3/4

Answer: **Option A**

Solution:

367. Three men A, B, and C can do a piece of work in t hours working together. Working alone, A can do the work in 6 hours more, B in 1 hour more, and C in twice the time if all working together. How long would it take to finish the work if all working together?

a. 20 mins.

b. 30 mins.

c. 40 mins.

d. 50 mins.

Answer: **Option C**

Solution:

368. Solve the z if the equation is 4 x 10^{-5} = z

a. โ 40,000

b. โ 200

c. 0.0004

d. 0.00004

Answer: **Option D**

Solution:

369. Two balls are drawn one at a time from a basket containing 4 black balls and 5 white balls. If the first ball is returned before the second ball is drawn, find the probability that both balls are black.

a. 0.198

b. 0.898

c. 0.167

d. 0.264

Answer: **Option A**

Solution:

370. There are 15 balls in a box: 8 balls are green, 4 are blue and 3 are white. Then 1 green and 1 blue balls are taken from the box and put away. What is the probability that a blue ball is selected at random from the box?

a. 3/13

b. 4/15

c. 3/15

d. 4/13

Answer: **Option A**

Solution:

371. Which of the following is equivalent to (x)(x)(x)(x3), for all x?

a. 6x

b. x^{6}

c. 4x^{6}

d. 4x^{4}

Answer: **Option B**

Solution:

372. A number between 1 and 10000 is randomly selected. What is the probability that it will be divisible by 4 and 5?

a. 0.03

b. 0.04

c. 0.05

d. 0.06

Answer: **Option C**

Solution:

373. What time after 2 oโclock will the hands of the clock extend in opposite directions for the first time?

a. 2:43.64

b. 2:43.46

c. 2:34.64

d. 2:34.46

Answer: **Option A**

Solution:

374. What is the sum of the geometric progression if there are 4 geometric means between 3 and 729?

a. 1212

b. 1092

c. 1908

d. 1209

Answer: **Option B**

Solution:

375. A boy on his bicycle to arrive at a certain time to a market that is 30 km from his school. After riding 10 km, he rested for half an hour, and as a result he was obliged to ride the rest of the trip 2 km/hr. faster. What was his original speed?

a. 7 km/hr.

b. 9 km/hr.

c. 10 km/hr.

d. 8 km/hr.

Answer: **Option D**

Solution:

376. Find the equation whose roots are two times the roots of the equation x^{3} โ 6x^{2} + 11x โ 6 = 0.

a. x^{3} โ 12x^{2} + 44x โ 48 = 0

b. x^{3} โ 12x^{2} โ 44x โ 48 = 0

c. x^{3} + 12x^{2} + 44x โ 48 = 0

d. x^{3} โ 12x^{2} + 44x + 48 = 0.

Answer: **Option A**

Solution:

377. How many 4-digits even numbers can be formed from the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 if each digit is to be used only once in each number?

a. 5,000

b. 3,256

c. 2,520

d. 5,986

Answer: **Option C**

Solution:

378. Rukia has nickels, dimes, and quarters amounting to $1.85. If he has twice as many dimes as quarters, and the number of nickels is two less than twice the number of dimes, how many quarters does he have?

a. 3

b. 8

c. 6

d. 10

Answer: **Option A**

Solution:

379. A club has 25 members, 4 of whom are ECEโs. In how many ways can a committee of 3 be formed so as to include at least one ECE?

a. 543

b. 126

c. 970

d. 314

Answer: **Option C**

Solution:

380. If (x -3) is a factor of the polynomial x^{4} โ 4x^{3} โ 7x^{2} + kx + 24, what is the value of k?

a. 11

b. 17

c. 22

d. 34

Answer: **Option C**

Solution:

381. A guy has 8 flowers of different variety. In how many ways can he select 2 or more flowers to form a bouquet?

a. 128

b. 247

c. 110

d. 540

Answer: **Option B**

Solution:

382. At a conference, after everyone had shaken hands with everyone else, it was found that 45 handshakes were exchanged. How many were at the conference?

a. 10

b. 30

c. 20

d. 40

Answer: **Option A**

Solution:

383. A bag contains 4 white balls and 3 black balls. Another bag contains 3 white balls and black balls. If one ball is drawn from each bag, determine the probability that the balls drawn will be 1 white and 1 black.

a. 27/58

b. 39/56

c. 29/56

d. 5/14

Answer: **Option C**

Solution:

384. If the sides of a right triangle are in A.P., then what is the ratio of its sides?

a. 3:4:5

b. 1:2:3

c. 4:5:6

d. 2:3:4

Answer: **Option A**

Solution:

385. If x: y: z = 4: -3: 2 and 2x + 4y โ 3z = 20, find x, y, z.

a. 4, -5, 2

b. -8, 6, -4

c. 5, -6, 8

d. 2, -7, 4

Answer: **Option B**

Solution:

386. How many numbers between 3000 and 5000 can be formed from the digits 0, 1, 2, 3, 4, 5, 6 if repetition is not allowed?

a. 96

b. 128

c. 240

d. 144

Answer: **Option C**

Solution:

387. Find the mean proportional between

a. 3

b. โ2

c. 6

d. 2โ2

Answer: **Option C**

Solution:

388. How many liters of a 25% acid solution must be added to 80 liters of a 40% acid solution to have a solution that is 30% acid?

a. 160 L

b. 190 L

c. 150 L

d. 120 L

Answer: **Option A**

Solution:

389. A yacht can travel 10 miles downstream in the same amount of time as it goes 6 miles upstream. If the velocity of the river current is 3 MPH, find the speed of the yacht in still water.

a. 12 MPH

b. 16 MPH

c. 15 MPH

d. 18 MPH

Answer: **Option A**

Solution:

390. Determine the 5th term of the sequence whose sum of n terms is given by 2n+3 โ 5.

a. 258

b. 218

c. 128

d. 15

Answer: **Option C**

Solution:

391. Find the sum of the first five terms of the geometric progression if the third term is 144 and the sixth term is 486.

a. 844

b. 972

c. 746

d. 548

Answer: **Option A**

Solution:

392. A and B working together can finish a job in 5 days, B and c together can finish the same job in 4 days, and A and C in 2.5 days. In how days can all of them do the job working together?

a. 1.06 days

b. 2.4 days

c. 3.2 days

d. 2.03 days

Answer: **Option D**

Solution:

393. If Chicago is 10% taller than Ishida and Ishida is 10% taller than Chad, then Ichigo is taller than Chad by how many percent?

a. 31%

b. 41%

c. 21%

d. 11%

Answer: **Option C**

Solution:

394. After the price of petroleum oil went up by 10%, a buyer reduced his oil consumption by the same percent. By what percent would his petroleum bill changed?

a. 1%

b. 11%

c. 10%

d. 0.1%

Answer: **Option A**

Solution:

395. Find the mean, median and mode respectively of the following numbers: 13, 13, 14, 12, 11, 10, 9, 11, 8, 11, 5, and 15.

a. 10, 10, 10

b. 10, 11, 10

c. 10, 11, 11

d. 11, 11, 11

Answer: **Option D**

Solution:

396. There are 4 white balls and 6 red balls in a sack. If the balls are taken out successively (the first ball is not replaced), what is the probability that the balls drawn are of different colors.

a. 23/90

b. 8/15

c. 24/103

d. 7/15

Answer: **Option B**

Solution:

397. Solve for x in the following equation: x + 3x + 5x + 7x + โฆ + 49x = 625

a. 2

b. 1

c. 1/2

d. 1/3

Answer: **Option B**

Solution:

398. An organization consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n

a. 70

b. 110

c. 50

d. 100

Answer: **Option D**

Solution:

399. In a certain family, the sum of the parentsโ ages is twice the sum of their childrenโs ages. Five years ago, the sum of the parentsโ ages was four times the sum of the childrenโs ages during that time. In fifteen years, the sum of the parentsโ ages will be equal to the sum of their childrenโs ages. How many children are there in the family?

a. 5

b. 7

c. 6

d. 8

Answer: **Option A**

Solution:

400. z varies directly as x and inversely as y^{2}. If x = 1 and y = 2, then z = 2. Find z when x = 3 and y = 4.

a. 1.5

b. 0.5

c. 2.5

d. 3.5

Answer: **Option A**

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 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**

### 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 โ 50**Answer key:

**PART 1**

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

**PART 2**

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