This is the Multiple Choice Questions Part 9 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**

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

**PART IX**

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

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

401. When two dice are thrown, what is the probability that the sum of the two faces shown is 6?

- a. 1/36
- b. 1/6
- c. 1/9
- d. 5/36

402. An ECE class of 40 students took examinations in Electronics and Communications. If 30 passed in Electronics, 36 passed in Communication and 2 failed in both subjects, how many students passed in both subjects?

- a. 28
- b. 30
- c. 26
- d. 32

403. The excess of the sum of the fourth and fifth parts over the difference of the half and third parts of a number is 119. Find the number.

- a. 240
- b. 320
- c. 420
- d. 230

404. What is the area, in square feet, of the triangle whose sides have lengths equal to 10, 6 and 8 feet?

- a. 24
- b. 48
- c. 30
- d. 40

405. Solve for x if the equation is 3^{102} + 9*3^{100} + 3^{103}/3 = x

- a. 3
^{101} - b. 3
^{102} - c. 3
^{103} - d. 3
^{104}

406. Of the 80 students in class, 25 are studying German, 15 French and 13 Spanish. 3 are studying German and French; 4 are studying French and Spanish; 2 are studying German and Spanish; and none is studying all 3 languages at the same time. How many students are not studying any of the three languages?

- a. 18
- b. 53
- c. 62
- d. 36

407. There were 2 small circles C1 and C2 inside a large circle AB. AB is a diameter of the large circle. The centers C1 and C2 of the smaller circles are on AB. The two small circles are congruent and tangent to each other and to the larger circle. The circumference of circle C1 is 8Pi. What is the area of the large circle?

- a. 64Pi
- b. 32Pi
- c. 156Pi
- d. 128Pi

408. DE is parallel to CB and (length of AE / length of EB) is 4. If the area of triangle AED is 20 square inches, what is the area, in square inches, of triangle ABC?

- a. 31.25
- b. 80
- c. 320
- d. 1,600

409. Round (202)^{2} to the nearest hundred.

- a. 48,000
- b. 40,800
- c. 42,000
- d. 44,000

410. If w workers, working at equal rates, can produce x toys in n days, how many days it takes c workers, working at same equal rates, to produce y toys?

- a. y*w*c/(w*n)
- b. y*w/(w*n*c)
- c. y*w*n / x
- d. y*w*n / (x*c)

411. A number of the form 213ab, where a and b are digits, has a reminder less than 10 when divided by 100. The sum of all the digits in the above number is equal to 13. Find the digit b.

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

412. Find a negative value of x that satisfies the equation: [(x+1)^{2} - (2x + 1)]^{1/2} + 2|x| - 6 = 0

- a. -4
- b. -3
- c. -2
- d. -1

413. If thrice the smaller number exceeds the larger by 12. Find the larger number if the two numbers are consecutive odd integers.

- a. 7
- b. 9
- c. 10
- d. 8

414. Determine how much water should be evaporated from 50kg of 30% salt solution to produce a 60% salt solution. All percentages are by weight.

- a. 25 kg
- b. 35 kg
- c. 15 kg
- d. 20 kg

415. A runs around a circular track in 60 seconds, and in 50 seconds. Five seconds after A starts, B starts from the same point in the same direction. When will they be together for the first time, assuming they run around the track continuously?

- a. 3.5 mins
- b. 6.5 mins
- c. 5.5 mins
- d. 7.5 mins

416. An antelope is now 50 of her leaps ahead of a cheetah which is pursuing her. How many more leaps will the antelope take before it is overtaken if she takes 5 leaps while the cheetah takes 4 leaps, but 2 of the cheetah’s leaps are equivalent to 3 of the antelope’s leaps?

- a. 350
- b. 325
- c. 420
- d. 250

417. Line L passes through the points (-2, 0) and (0, a). Line LL passes through the points (4, 0) and (6, 2). What value of a makes the two lines parallel?

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

418. Solve for x if the equation is 10^{4}(5^{4} - 2^{4}) / 21 = x

- a. 209,000
- b. 289,000
- c. 290,000
- d. 208,000

419. Two dice are tossed. What is the probability that the sum of the two dice is greater than 3?

- a. 3/4
- b. 5/6
- c. 11/12
- d. 1/4

420. If L is a line through the points (2,5) and (4,6), what is the value of k so that the point of coordinates (7,k) is on the line L?

- a. 5
- b. 6
- c. 15/2
- d. 11/2

421. Find a negative value of k so that the graph of y = x^{2} – 2x + 7 and the graph of y = kx + 5 are tangent?

- a. - 4√2
- b. - 2 - 2√2
- c. - 2
- d. - √2

422. The circle of equation (x - 3)^{2 }+ (y - 2)^{2} = 1 has center O. Point M(4,2) is on the circle. N is another point on the circle so that angle MON has a size of 30°. Find the coordinates of point N.

- a. (3 + √3/2 , 5/2)
- b. (5/2 , 3 + √3/2)
- c. (3 - √3/2 , 3/2)
- d. (3/2 , 3 - √3/2)

423. Vectors u and v are given by u = (2 , 0) and v = (-3 , 1). What is the length of vector w given by w = -u – 2v?

- a. 6
- b. √26
- c. 2√5
- d. 2

424. What is the smallest distance between the point(-2,-2) and a point on the circumference of the circle given by (x - 1)^{2} + (y - 2)^{ 2} = 4?

- a. 3
- b. 4
- c. 5
- d. 6

425. What is the equation of the horizontal asymptote of function: f(x) = 2/(x + 2) - (x + 3)/(x + 4)?

- a. - 4
- b. - 2
- c. - 1
- d. 1

426. The lines with equations x + 3y = 2 and -2x + ky = 5 are perpendicular for k = ?

- a. 1/3
- b. 2/3
- c. 2/4
- d. 1/4

427. If f(x) = (x - 1)^{2} and g(x) = √x, then (g _{o} f)(x) = ?

- a. |x - 1|
- b. x - 1
- c. 1 - x
- d. |1 - x|

428. The domain of f(x) = √(4 - x^{2}) / √(x^{2} - 1) is given by the interval

- a. (-2 , 2) U (-1 , 2)
- b. (-2 , -1) U (1 , 2)
- c. (-2 , 2) U (-1 , 1)
- d. (-2 , -1) U (1 , 2)

429. The area of the circle x^{2} + y^{2} - 8y - 48 = 0 is

- a. 96Pi
- b. 64Pi
- c. 48Pi
- d. 20Pi

430. An investor has P100,000, part of which he invested at 12% interest and the rest at 18%. He received a total annual interest of P15,300. How much did he invest at 18% interest rate?

- a. 65,000
- b. 60,000
- c. 55,000
- d. 75,000

431. For what value of k will the two equations 2x + 4 = 4(x - 2) and -x + k = 2x - 1 have the same solution?

- a. 6
- b. 2
- c. 17
- d. 20

432. An object travels at fifteen feet per minute. How many feet does it travel in 24 minutes and 40 seconds?

- a. 360
- b. 370
- c. 365
- d. 375

433. Solve for x if the equation is 4 / (√20 - √12) = x

- a. 1/2
- b. 4 / √8
- c. √5 - √3
- d. √5 + √3

434. DE is parallel to CB and (length of AE / length of EB) is 4. If the area of triangle AED is 20 square inches, what is the area, in square inches, of triangle ABC?

- a. 31.25
- b. 80
- c. 320
- d. 1,600

435. If a and b are both even numbers, which of the following could be and odd integer?

- a. a
^{2}+ b^{2} - b. (a + 1)
^{2}+ (b + 1)^{2} - c. (a + 1)*(b + 1) - 1
- d. (a + 1) / (b + 1)

436. If n is a positive integer such that n! / (n - 2)! = 342, find n.

- a. 19
- b. 17
- c. 18
- d. 16

437. What is the sum of the reciprocals of the solutions to the equation: x^{2} - (3/5)x = -11/3

- a. 5/3
- b. 9/55
- c. -11/3
- d. 94/65

438. A number is given as 987562153ab where a and b are digits. Which values of a and b, such that a + b = 11 and a < b, would result in 987562153ab being divisible by 4?

- a. a = 3 , b = 8
- b. a = 7 , b = 8
- c. a = 5 , b = 6
- d. a = 3 , b = 4

439. AC is parallel to DE. AE, FG and CD intersect at the point B. FG is perpendicular to AC and DE. The length of DE is 5 inches, the length of BG is 8 inches and the length of AC is 6 inches. What is the area, in square inches, of triangle ABC?

- a. 28.8
- b. 20
- c. 24
- d. 22

440. Points A, B and C are defined by their coordinates in a standard rectangular system of axes. What positive value of b makes triangle ABC a right triangle with AC its hypotenuse?

- a. 6
- b. √6
- c. 1 + √6
- d. 1 + 2√3

441. A vendor goes to market to buy fruits for resale at his store. He spends half his money for mangoes, and one-third of what remains for bananas. He spends 150 for other fruits and still has 200 left from the amount he originally had. How much money did he have at the start?

- a. 1050
- b. 5100
- c. 1500
- d. 1250

442. Seven carpenters and 5 masons earn a total of 2,300 per day. At the same rate of pay 3 carpenters and 8 masons earn 2,040. What are the wages per day of the carpenter and a mason?

- a. 200 & 180
- b. 300& 210
- c. 210& 170
- d. 270 &150

443. A man and a boy can do 15 days a piece of work which would be done by 7 men and 9 boys in 2 days. How long would it take one man do it alone?

- a. 20 days
- b. 30 days
- c. 15 days
- d. 40 days

444. A certain two-digit numbers is 1 less than five times the sum of its digits. If 9 were added to the number, its digits would be reversed. Find the number.

- a. 34
- b. 36
- c. 43
- d. 63

445. If one root of 9x^2 – 6x + k = 0 exceed the other by 2, find the value of k.

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

446. Solve: √(2x – 5) – √(x – 2) = 2.

- a. 3
- b. 18
- c. 9
- d. 27

447. A speed boat going across a lake 8 km wide proceeds 2 km at a certain speed and then completes the trip at a speed ½ km/hr faster. By doing this, the speed arrives 10 minutes earlier than if the original speed had been maintained. Find the original speed of the speed boat.

- a. 5 km/hr
- b. 4 km/hr
- c. 7 km/hr
- d. 6km/hr

448. An audience of 540 people is seated in rows having the same number of persons in each row. If 3 more persons seat in each row, it would require 2 rows less to seat the audience. How many persons were in each row originally?

- a. 17
- b. 30
- c. 27
- d. 31

449. Find the third proportional to 4 and 12.

- a. 48
- b. 20
- c. 36
- d. 16

450. How many terms of the progression 4, 7, 10, 13, … must be taken so that the sum will be 69.

- a. 6
- b. 9
- c. 8
- d. 12

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