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MCQ in Algebra and General Mathematics Part 8 | ECE Board Exam

(Last Updated On: January 2, 2021)

MCQs in Algebra and General Mathematics Part 8

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

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 √(x – 2) / √x = 1

a. -1, -4

b. 1, 4

c. 4

d. 0

View Answer:

Answer: Option C

Solution:

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

a. 6

b. 7

c. -6

d. 36

View Answer:

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

View Answer:

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

View Answer:

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. 6√2

b. 72

c. 24√2

d. 48

View Answer:

Answer: Option C

Solution:

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

View Answer:

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

View Answer:

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

View Answer:

Answer: Option C

Solution:

359. What is the product of the two real solutions of the equation: 2x = 3 – x2

a. 2

b. -2

c. 6

d. -3

View Answer:

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

View Answer:

Answer: Option B

Solution:

361. Find the sum and product of roots of the equation x3 + 2x2 – 23x – 60 = 0.

a. -2, 60

b. 2, 17

c. 17, -60

d. 2, -60

View Answer:

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

View Answer:

Answer: Option A

Solution:

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

a. 121

b. 89

c. 98

d. 112

View Answer:

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

View Answer:

Answer: Option C

Solution:

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

a. y = x3

b. y = x2

c. y = x

d. y = 3x

View Answer:

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

View Answer:

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.

View Answer:

Answer: Option C

Solution:

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

a. – 40,000

b. – 200

c. 0.0004

d. 0.00004

View Answer:

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

View Answer:

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

View Answer:

Answer: Option A

Solution:

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

a. 6x

b. x6

c. 4x6

d. 4x4

View Answer:

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

View Answer:

Answer: Option C

Solution:

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

View Answer:

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

View Answer:

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.

View Answer:

Answer: Option D

Solution:

376. Find the equation whose roots are two times the roots of the equation x3 – 6x2 + 11x – 6 = 0.

a. x3 – 12x2 + 44x – 48 = 0

b. x3 – 12x2 – 44x – 48 = 0

c. x3 + 12x2 + 44x – 48 = 0

d. x3 – 12x2 + 44x + 48 = 0.

View Answer:

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

View Answer:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

Answer: Option C

Solution:

380. If (x -3) is a factor of the polynomial x4 – 4x3 – 7x2 + kx + 24, what is the value of k?

a. 11

b. 17

c. 22

d. 34

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

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

View Answer:

Answer: Option A

Solution:

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

View Answer:

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

View Answer:

Answer: Option C

Solution:

387. Find the mean proportional between

a. 3

b. √2

c. 6

d. 2√2

View Answer:

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

View Answer:

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

View Answer:

Answer: Option A

Solution:

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

a. 258

b. 218

c. 128

d. 15

View Answer:

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

View Answer:

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

View Answer:

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%

View Answer:

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%

View Answer:

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

View Answer:

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

View Answer:

Answer: Option B

Solution:

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

a. 2

b. 1

c. 1/2

d. 1/3

View Answer:

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

View Answer:

Answer: Option D

Solution:

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

View Answer:

Answer: Option A

Solution:

400. z varies directly as x and inversely as y2. 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

View Answer:

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
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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