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.

### Multiple Choice Questions Topic Outline

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

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

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

**Algebra and General Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

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

**PART II**

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

**PART III**

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

**PART IV**

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

**PART V**

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

**PART VI**

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

**PART VII**

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

**PART VIII**

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

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

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

- a. -1, -4
- b. 1, 4
- c. 4
- d. 0

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

- a. 6
- b. 7
- c. -6
- d. 36

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

- a. 5/4
- b. 5/8
- c. 5/16
- d. 13/16

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

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

- a. 6√2
- b. 72
- c. 24√2
- d. 48

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

- a. 20√3
- b. 20
- c. √3
- d. 20/√3

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

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

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

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

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

- a. -2, 60
- b. 2, 17
- c. 17, -60
- d. 2, -60

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

363. Determine the sum of the first 4 terms of the sequence whose general term is given by 3^{n} – 2.

- a. 121
- b. 89
- c. 98
- d. 112

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

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

- a. y = x
^{3} - b. y = x
^{2} - c. y = x
- d. y = 3x

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

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.

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

- a. – 40,000
- b. – 200
- c. 0.0004
- d. 0.00004

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

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

371. Which of the following is equivalent to (x)(x)(x)(x^{3}), for all x?

- a. 6x
- b. x
^{6} - c. 4x
^{6} - d. 4x
^{4}

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

373. What time after 2 o’clock 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

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

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

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

- a. x
^{3}– 12x^{2}+ 44x – 48 = 0 - b. x
^{3}– 12x^{2}– 44x – 48 = 0 - c. x
^{3}+ 12x^{2}+ 44x – 48 = 0 - d. x
^{3}– 12x^{2}+ 44x + 48 = 0.

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

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

379. A club has 25 members, 4 of whom are ECE’s. 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

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

- a. 11
- b. 17
- c. 22
- d. 34

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

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

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

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

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

- a. 4, -5, 2
- b. -8, 6, -4
- c. 5, -6, 8
- d. 2, -7, 4

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

387. Find the mean proportional between

- a. 3
- b. √2
- c. 6
- d. 2√2

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. 160L
- b. 190L
- c. 150L
- d. 120L

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 3MPH, find the speed of the yacht in still water.

- a. 12 MPH
- b. 16MPH
- c. 15MPH
- d. 18MPH

390. Determine the 5^{th} term of the sequence whose sum of n terms is given by 2^{n+3 }– 5.

- a. 258
- b. 218
- c. 128
- d. 15

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

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

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%

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%

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

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

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

- a. 2
- b. 1
- c. 1/2
- d. 1/3

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

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

- a. 5
- b. 7
- c. 6
- d. 8

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

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