This is the Multiple Choice Questions Part 10 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**

**MCQs from Number 451 – 500**Answer key:

**PART X**

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

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

451. Determine x so that 2x + 1, x^{2} + x + 1, 3x^{2} – 3x + 3 are consecutive terms of an arithmetic progression.

- a. 3
- b. 2
- c. 5
- d. 4

452. An equipment costs P50,000.00 and depreciates 20% of the original costs during the first year, 16% during the second year, 12% during the third year, and so on, for 5 years. What is the value at the end of 5 years?

- a. 15,000
- b. 25,000
- c. 30,000
- d. 20,000

453. Find the sum of the first 100 positive integers that is exactly divisible by 7.

- a. 35,350
- b. 25,053
- c. 53,350
- d. 25,536

454. Find the 50^{th} term of a geometric progression if the 20^{th} term is 1200 and the 30^{th} term is also 1200.

- a. 1200
- b. 2400
- c. 1400
- d. 4100

455. A woman started a chain letter by writing to four friends and requesting each to copy the letter and send it to four other friends. If the chain was unbroken until the 5^{th} set of letters was mailed, how much was spent for postage at P8.00 per letter?

- a. 16,219
- b. 10,912
- c. 21,835
- d. 13,291

456. A soccer ball is dropped from height of 6 meters. On each rebound it rises 2/3^{ }of the height from which it last fell. What distance has it traveled at the instant it strikes the ground for the 7^{th} time?

- a. 27.89 m
- b. 19.86 m
- c. 20.87 m
- d. 24.27 m

457. The arithmetic mean of two numbers is 4, and their harmonic mean is 15/4. Find the numbers.

- a. 3 & 5
- b. 1 & 7
- c. 2 & 6
- d. 0 & 8

458. Find the real values of x and y satisfying the given equation: (2x + 3y) + i(3x – 5y) = 8 – i7.

- a. x = 1, y = -2
- b. x = -2, y = -1
- c. x = 2, y = 1
- d. x = 1, y = 2

459. From the equation 12x^{3} – 8x^{2} + kx + 18 = 0, find the value of k if one root is the negative of the other.

- a. -17
- b. -12
- c. -27
- d. -36

460. In how many ways can a group of 6 people be seated on a row of 6 seats if a certain 2 refuse to sit next to each other?

- a. 240 ways
- b. 480 ways
- c. 180 ways
- d. 320 ways

461. How many different 8-digit numbers can be formed from the digits 2, 2, 2, 5, 5, 7, 7, 7?

- a. 320
- b. 560
- c. 520
- d. 480

462. In how many ways can 10 different magazines be divide among A, B, and C so that A gets 5 magazines, B 3 magazines and C 2 magazines?

- a. 2,520
- b. 2,250
- c. 2,050
- d. 2,052

463. What is the probability of drawing 6 white balls from a jar containing 9 white, 4 red, and 3 blue balls?

- a. 0.01
- b. 0.02
- c. 0.10
- d. 0.03

464. Ten books consisting of 5 mathematics books, 3 physics books, and 2 chemistry books are placed in a bookcase at random. What is the probability that the same books are all together?

- a. 1/420
- b. 3/520
- c. 2/241
- d. 5/2463

465. In a racing contest, there are 240 vehicles which will have provisions that will last for 15 hours. Assuming constant hourly consumption for each vehicle, how long will the fuels provisions last if 8 vehicles withdraw from the race every hour after the first?

- a. 63
- b. 18
- c. 20
- d. 25

466. A clerk submitted the following reports. The average rate of production of radios is 1.5 units for every 1.5 hrs. work by 1.5 workers. How many radios were produce in one month by 30 men working 200 hrs during the month?

- a. 4000
- b. 3800
- c. 5000
- d. 4200

467. A piece of rod of length 52 cm. is cut into two unequal parts. Each part is then bent to form a square. It is found that the total area of the two squares is 97cm^{2}. Find the difference between the sides of each square.

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

468. Solve the trigonometric equation: 3sec^{2}x – 4 = 0

- a. Pi / 3 + 2n*Pi , 5Pi / 3 + 2n*Pi
- b. Pi / 6 + 2n*Pi , 11 Pi / 6 + 2n*Pi
- c. Pi / 3 + n*Pi , 5Pi / 3 + n*Pi
- d. Pi / 6 + n*Pi , 11 Pi / 6 + n*Pi

469. In what quadrant will the angle Ó¨ terminate, if sin Ó¨ is positive and sec Ó¨ is negative?

- a. I
- b. III
- c. II
- d. IV

470. If sec (2x – 3) = 1 / [sin(5x – 9)], determine the value x in degrees.

- a. 14.57°
- b. 16.36°
- c. 18.65°
- d. 14.61°

471. What is the maximum value of 3 – 2 cos Ó¨?

- a. 2
- b. 3
- c. 4
- d. 5

472. Solve the trigonometric equation: 2cosx + 1 = 0

- a. Pi / 3 + 2n*Pi , 5Pi / 3 + 2n*Pi
- b. -1/2
- c. 2Pi / 3 + 2n*Pi , 4Pi / 3 + 2n*Pi
- d. Pi / 2 + n*Pi

473. If log x + log5 = log (x + 5), what is the value of x?

- a. 0
- b. 1.25
- c. 1.5
- d. 2

474. If the angles of the triangle are 2x, x + 15, and 2x + 15, find the smallest of the angle in mills.

- a. 500 mils
- b. 600 mils
- c. 800 mils
- d. 900 mils

475. If (log_{10}x)^{2} = 3 – log_{10}x^{2}. Which of the following choices can be a value of x?

- a. 10
^{-3} - b. 10
^{2} - c. x
^{10} - d. 10
^{x}

476. Find the value of x in the equation (√5)^{2cosx} = 5.

- a. 0°
- b. 45°
- c. 30°
- d. 60°

477. If a^{x} = b^{y} and b^{p} = a^{q} , then

- a. px = qy
- b. xy = pq
- c. x
^{p}= y^{q} - d. qx = py

478. Solve the trigonometric equation: (3cosx + 7) (-2sinx – 1) = 0

- a. 7Pi / 6 + 2n*Pi , 11Pi / 6 + 2n*Pi
- b. Pi / 3 + 2n*Pi , 2Pi / 3 + 2n*Pi
- c. 7Pi / 6 + n*Pi , 11Pi / 6 + n*Pi
- d. -7 / 3 , -1 / 2

479. If the bearing of point A from B is S 40° W, then the bearing of B from A is:

- a. N40° E
- b. S40° W
- c. N50° W
- d. N50° E

480. A clock has a dial face of 12 in. radius. The minute hand is 9 inches while the hour hand is 6 inches. The plane of rotation of the hour hand is 2 inches above the plane of rotation of the minute hand. Find the distance between the tips of the minute and hour hand at 5:40 a.m.

- a. 7.48 in
- b. 6.48 in
- c. 9.17 in
- d. 10.16 in

481. Two towers are 60 m apart from each other. From the top of the shorter tower, the angle of elevation of the top of the taller tower is 40°. How high is the taller tower if the height of the smaller tower is 40m?

- a. 90 m
- b. 100 m
- c. 80 m
- d. 70 m

482. Considering the earth to be a sphere of radius 6400 km, find the radius of the 6^{0th }parallel of latitude.

- a. 3,200 km
- b. 1,300 km
- c. 2,300 km
- d. 3,100 km

483. Solve the trigonometric equation: (6tan^{2}x – 2) (2tan^{2}x – 6) = 0

- a. Pi / 6 + n*Pi , 5Pi / 6 + 2n*Pi , Pi / 3 + n*Pi , 2Pi / 3 + n*Pi
- b. Pi / 6 , 5Pi / 6
- c. sqrt(3) , sqrt(3)
- d. Pi / 3 + n*Pi , 2Pi / 3 + n*Pi

484. From a point on a level ground, the angles of elevation of the top and bottom of the ABS-CBN tower situated on the top of the hill are measured as 48° and 40°, respectively. Find the height of the hill if the height of the tower is 116 feet.

- a. 348.56 m
- b. 368.36 m
- c. 258.96 m
- d. 358.49 m

485. A ladder, with its foot in the street, makes an angle of 30° with the street when its top rests on a building on one side of the street and makes an angle of 40° with the street when its top rests on a building on the other side of the street. If the ladder is 50 ft. long, how wide is the street?

- a. 96.2 ft.
- b. 81.6 ft.
- c. 78.5 ft.
- d. 64.3 ft.

486. A wall is 15 ft high and 10 ft from a building. Find the length of the shortest ladder which will just touch the top of the wall and reach a window 20.5 ft above.

- a. 42.54 m
- b. 35.54 m
- c. 54.45 m
- d. 47.45 m

487. A poll tilts toward the sun at an angle 10° from the vertical casts a shadow 9 meters long. If the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole?

- a. 10.2
- b. 7.54
- c. 10.45
- d. 8.25

488. If cos Ï´ =√3 / 2, find 1 – tan^{2}Ó¨..

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

489. Solve the trigonometric equation “-2sec^{2}x + 4 = -2secx” in the interval [0, 2Pi].

- a. Pi / 3 , 5Pi / 3 , Pi
- b. Pi
- c. -1 , 2
- d. Pi / 6 , 5Pi / 6 , Pi

490. Solve the trigonometric equation 2sinx cos(-x) = 2sin(-x)sin(x)” in the interval [0, 2Pi].

- a. 0 , Pi , 3Pi / 4 , 7Pi / 4
- b. 3Pi / 4 , 7Pi / 4
- c. 0 , Pi / 2
- d. Pi / 6 , 4Pi / 3

491. From a helicopter flying at 30,000 feet, the angles of depression of two cities are 28° and 55°. How far apart are the two cities?

- a. 35,415.56 ft
- b. 23,587.67 ft
- c. 53,452.67 ft
- d. 43,254.76 ft

492. Two angles are adjacent and form an angle of 120°. If the larger angle is 20° less than three times the smaller angle, find the larger angle.

- a. 75°
- b. 30°
- c. 85°
- d. 65°

493. A pine tree broken over by the wind forms a right triangle with the ground. If the broken part makes an angle of 50° with the ground and the top of the tree is now 20 ft from its base, how tall was the pine tree?

- a. 55 ft
- b. 65 ft
- c. 45 ft
- d. 35 ft

494. A ball, 5 ft in diameter, rolls up an incline of 18°20’. What is the height of the center of the ball above the base of the incline when the ball has rolled up 5 ft up the incline?

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

495. If coversed Sin Ó¨ = 0.134, find the value of versed Sin Ó¨.

- a. 0.8
- b. 0.3
- c. 0.5
- d. 0.2

496. A vertical pole consists of two parts, each one half of the whole pole. At a point in the horizontal plane which passes through the foot of the pole and 36 m from it, the upper half of the pole subtend an angle whose tangent is 1/3. How high is the pole?

- a. 72
- b. 25
- c. 46
- d. 66

497. Solve the trigonometric equation “sin2x = -sin(-x)” in the interval [0, 2Pi].

- a. 0 , 2Pi
- b. 0 , Pi / 3 , Pi , 5Pi / 3
- c. 0 , Pi
- d. Pi / 3 , Pi

498. If the sides of the triangle are 2x+3, x^{2}+3x+3, and x^{2}+2x, find the greatest angle.

- a. 100 deg.
- b. 130 deg.
- c. 120 deg.
- d. 110 deg.

499. ABDE is a square section and BDC is an equilateral triangle with C outside the square. Compute the value of angle ACE.

- a. 30 deg.
- b. 60 deg.
- c. 50 deg.
- d. 20 deg.

500. The angle of elevation of the top of a tower from a point A is 23°30’. From another point B, the angle of elevation of the top of the tower is 55°30’. The point A and B are 217.45 m apart and on the same horizontal plane as the foot of the tower. The horizontal angle subtended by A and B at the foot of the tower is 90 degrees. Find the height of the tower.

- a. 90.6 m
- b. 86.7 m
- c. 89.5 m
- d. 55.9 m

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