This is the Multiple Choice Questions Part 11 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 11 of the Series

โ MCQ in Algebra and General Mathematics Part 10 | Math Board Exam

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

501. The y coordinates of all the points of intersection of the parabola y^{2} = x + 2 and the circle x^{2} + y^{2} = 4 are given by

a. 2 , -2

b. 0 , โ3 , – โ3

c. 1 , 2 , -1

d. 1 , -2 , 1

Answer: **Option B**

Solution:

502. What is the smallest positive zero of function f(x) = 1/2 – sin(3x + Pi/3)?

a. Pi/3

b. Pi/6

c. Pi/18

d. Pi/36

Answer: **Option B**

Solution:

503. A cylinder of radius 5 cm is inserted within a cylinder of radius 10 cm. The two cylinders have the same height of 20 cm. What is the volume of the region between the two cylinders?

a. 500Pi

b. 1000Pi

c. 1500Pi

d. 2000Pi

Answer: **Option C**

Solution:

504. A data set has a standard deviation equal to 1. If each data value in the data set is multiplied by 4, then the value of the standard deviation of the new data set is equal to

a. 3

b. 1

c. 2

d. 4

Answer: **Option C**

Solution:

505. A cone made of cardboard has a vertical height of 8 cm and a radius of 6 cm. If this cone is cut along the slanted height to make a sector, what is the central angle, in degrees, of the sector?

a. 216

b. 180

c. 90

d. 36

Answer: **Option A**

Solution:

506. If sin(x) = -1/3 and Pi โค x โค 3Pi/2, then cot(2x) = ?

a. 4โ2

b. 2โ2

c. โ2

d. 7/(4โ2)

Answer: **Option D**

Solution:

507. If in a triangle ABC, sin(A) = 1/5, cos(B) = 2/7, then cos(C) = ?

a. (โ45 – 2โ24)/35

b. (โ45 + 2โ24)/35

c. (7โ24 + 10)/35

d. 0.85

Answer: **Option A**

Solution:

508. What value of x makes the three terms x, x/(x + 1) and 3x/[(x + 1)(x + 2)] those of a geometric sequence?

a. 1

b. 1/2

c. 1/4

d. -1/2

Answer: **Option D**

Solution:

509. The sum of the sides of a triangle is equal to 100 cm. If the angles of the triangle are in the continued proportions of 1:2:4. Compute the shortest side of the triangle.

a. 17.545

b. 19.806

c. 18.525

d. 14.507

Answer: **Option B**

Solution:

510. The sides of the triangular field which contains an area of 2400 sq. cm. are in continued proportion of 3:5:7. Find the smallest side of the triangle.

a. 45.74

b. 63.62

c. 95.43

d. 57.67

Answer: **Option D**

Solution:

511. In triangle ABC, angle A=80 deg. And point D is inside the triangle. If BD and CD are bisectors of angle B and C, solve for the angle BDC.

a. 100 deg.

b. 130 deg.

c. 120 deg.

d. 140 deg.

Answer: **Option B**

Solution:

512. Simplify the equation Sin2x (1 + cot2x).

a. 0

b. cos2x

c. 1

d. sec2xsin2x

Answer: **Option C**

Solution:

513. Assuming the earth to be a sphere of radius 3960 mi, find the distance of point 36ยฐ N latitude from the equator.

a. 2844 mi

b. 2488 mi.

c. 2484 mi.

d. 4288 mi.

Answer: **Option B**

Solution:

514. If sinx cosx + sin2x = 1, what are the values of x in degrees?

a. 32.2, 69.3

b. -32.2, 69.3

c. 20.9, 69.1

d. 20.9, -69.1

Answer: **Option C**

Solution:

515. If sin3x = cos6y then:

a. x โ 2y = 30

b. x + y = 180

c. x + 2y = 30

d. x + y = 90

Answer: **Option C**

Solution:

516. Evaluate cot^{-1} [2cos (sin^{-1}0.5)].

a. 20ยฐ

b. 45ยฐ

c. 30ยฐ

d. 60ยฐ

Answer: **Option C**

Solution:

517. An airplane can fly at airspeed of 300 mph. if there is a wind blowing towards the east at 50 mph, what should be the planes compass heading in order for its course to be 30 degrees. What will be the planes groundspeed if it flies at this course?

a. 21.7ยฐ, 321.86 mph

b. 31.6ยฐ, 351.68 mph

c. 51.7ยฐ, 121.86 mph

d. 12.7ยฐ, 331.86 mph

Answer: **Option A**

Solution:

518. From the given parts of a spherical triangle ABC, compute for angle A. (a = 120ยฐ, b = 73ยฐ15โ, c = 62ยฐ45โ)

a. 127ยฐ45โ

b. 115ยฐ26โ

c. 185ยฐ15โ

d. 137ยฐ56โ

Answer: **Option D**

Solution:

519. The diagonals of a parallelogram are 18 cm and 30 cm respectively. One side of a parallelogram is 12 cm. Find the area of the parallelogram.

a. 214

b. 216

c. 361

d. 108

Answer: **Option B**

Solution:

520. A quadrilateral has sides equal to 12 cm, 20 cm, 8 cm, and 17 cm respectively. If the sum of the two opposite angles is 225ยฐ, find the area of the parallelogram.

a. 168.18

b. 78.31

c. 70.73

d. 186.71

Answer: **Option A**

Solution:

521. The sides of the cyclic quadrilateral are a = 3 cm, b = 3 cm, c = 4 cm and d = 4 cm. Find the radius of the circle that can be inscribed in it.

a. 2.71 cm

b. 3.1 cm

c. 1.51 cm

d. 1.71 cm

Answer: **Option D**

Solution:

522. How many diagonals can be drawn from a 12 sided polygon?

a. 66

b. 48

c. 54

d. 36

Answer: **Option C**

Solution:

523. Find the area of a regular polygon whose side is 25 m and apothem is 17.2 m.

a. 1075

b. 925

c. 1175

d. 1275

Answer: **Option A**

Solution:

524. Find the area of a pentagon which is circumscribing a circle having an area of 420.60 sq. cm.

a. 386.57

b. 450.54

c. 486.29

d. 260.24

Answer: **Option C**

Solution:

525. As x increases from Pi/4 to 3Pi/4, |sin(2x)|

a. always increases

b. always decreases

c. increases then decreases

d. decreases then increases

Answer: **Option D**

Solution:

526. If ax^{3} + bx^{2} + cx + d is divided by x – 2, then the reminder is equal to

a. a – b + c – d

b. 8a + 4b + 2c + d

c. -8a + 4b -2c + d

d. a + b + c + d

Answer: **Option B**

Solution:

527. A committee of 6 teachers is to be formed from 5 male teachers and 8 female teachers. If the committee is selected at random, what is the probability that it has an equal number of male and female teachers?

a. 140/429

b. 150/429

c. 160/429

d. 170/429

Answer: **Option A**

Solution:

528. The range of the function f(x) = -|x – 2| – 3 is

a. y โฅ 2

b. y โค -3

c. y โฅ -3

d. y โค -2

Answer: **Option B**

Solution:

529. What is the period of the function f(x) = 3sin^{2}(2x + Pi/4)?

a. 3Pi

b. 2Pi

c. Pi/2

d. Pi/3

Answer: **Option C**

Solution:

530. It is known that 3 out of 10 television sets are defective. If 2 television sets are selected at random from the 10, what is the probability that 1 of them is defective?

a. 1/15

b. 1/10

c. 1/2

d. 1/3

Answer: **Option A**

Solution:

531. In a triangle ABC, angle B has a size of 50ยฐ, angle A has a size of 32ยฐ and the length of side BC is 150 units. The length of side AB is

a. 232

b. 280

c. 260

d. 270

Answer: **Option B**

Solution:

532. For the remainder of the division of x^{3} – 2x^{2} + 3kx + 18 by x – 6 to be equal to zero, k must be equal to

a. 1

b. 5

c. -9

d. -10

Answer: **Option C**

Solution:

533. It takes pump (A) 4 hours to empty a swimming pool. It takes pump (B) 6 hours to empty the same swimming pool. If the two pumps are started together, at what time will the two pumps have emptied 50% of the water in the swimming pool?

a. 1 hour 12 minutes

b. 1 hour 20 minutes

c. 2 hours 30 minutes

d. 3 hours

Answer: **Option A**

Solution:

534. The graph of r = 10 cos(ฮ) , where r and ฮ are the polar coordinates, is

a. a circle

b. an ellipse

c. a horizontal line

d. a hyperbola

Answer: **Option A**

Solution:

535. If (2 – i)*(a – bi) = 2 + 9i, where *i* is the imaginary unit and a and b are real numbers, then a equals

a. 2

b. 1

c. 0

d. -1

Answer: **Option D**

Solution:

536. Lines L1 and L2 are perpendicular that intersect at the point (2, 3). If L1 passes through the point (0, 2), then line L2 must pass through the point

a. (0 , 3)

b. (1 , 1)

c. (3 , 1)

d. (5 , 0)

Answer: **Option C**

Solution:

537. In a plane there are 6 points such that no three points are collinear. How many triangles do these points determine?

a. 8

b. 10

c. 18

d. 12

Answer: **Option C**

Solution:

538. In a circle with a diameter of 10 meters, a regular five pointed star touching its circumference is inscribed. What is the area of the part not covered by the star?

a. 60.42

b. 40.58

c. 40.68

d. 50.47

Answer: **Option D**

Solution:

539. Find the area of a hexagon with a square having an area of 72 sq. cm. inscribed in a circle which is inscribed in a hexagon.

a. 124.71 sq. cm.

b. 150.26 sq. cm.

c. 150.35 sq. cm.

d. 130.77 sq. cm.

Answer: **Option A**

Solution:

540. The tangent and a secant are to a circle from the same external point. If the tangent is 6 inches and the external segment of the secant is 3 inches, compute the length of the secant.

a. 10

b. 13

c. 12

d. 14

Answer: **Option C**

Solution:

541. Two circles with radii 8 and 3 m are tangent to each other externally. What is the distance between the points of tangency of one of their common external tangencies?

a. 7.8 m

b. 9.8 m

c. 10.7 m

d. 6.7 m

Answer: **Option B**

Solution:

542. The diameters of the two circles that are tangent internally are 18 and 8, respectively. What is the length of the tangent segment from the center of the larger circle to the smaller circle?

a. 2

b. 4

c. 3

d. 5

Answer: **Option C**

Solution:

543. Three identical circles are tangent to each other externally. If the area of the curvilinear triangle enclosed between the points of tangency of the 3 circles is 16.13 cm^{2}, compute the radius of each circle.

a. 10 cm

b. 13 cm

c. 9 cm

d. 15 cm

Answer: **Option A**

Solution:

544. A semi โ circle of radius 14 cm is bent to form a rectangle whose length is 1 cm more than its width. Find the area of the rectangle.

a. 323.75 cm^{2}

b. 322.32 cm^{2}

c. 233.57 cm^{2}

d. 233.75 cm^{2}

Answer: **Option A**

Solution:

545. A swimming pool is constructed in the shape of two partially overlapping circles, each of radius 9 m. If the center each circle lies on the circumference of the other, find the perimeter of the swimming pool.

a. 85.7 m

b. 75.4 m

c. 56.5 m

d. 96.8 m

Answer: **Option B**

Solution:

546. The length of the side of a rhombus is 5 cm. If the shorter diagonal is of length 6 cm. What is the area of the rhombus?

a. 24 cm^{2}

b. 14 cm^{2}

c. 18 cm^{2}

d. 25 cm^{2}

Answer: **Option A**

Solution:

547. Two squares each of 12 cm sides overlap each other such that the overlapping region is a regular polygon. Determine the area of the overlapping region thus formed.

a. 110.9 cm^{2}

b. 119.3 cm^{2}

c. 121.5 cm^{2}

d. 117.4 cm^{2}

Answer: **Option B**

Solution:

548. The side of a regular pentagon is 25 cm. If the radius of its inscribed circle is 15 cm, find the area of the pentagon.

a. 937.5 cm^{2}

b. 784.6 cm^{2}

c. 825.75 cm^{2}

d. 857.65 cm^{2}

Answer: **Option A**

Solution:

549. The capacities of two hemispherical tanks are in the ratio 64:125. If 4.8 kg of paint is required to paint the outer surface of the smaller tank, then how many kilograms of paint would be needed to paint the outer surface of the larger tank?

a. 8.5 kg

b. 6.7 kg

c. 7.5 kg

d. 9.4 kg

Answer: **Option C**

Solution:

550. A wooden cone of altitude 10 cm is to be cut into two parts of equal weight. How far from the vertex should the cut parallel to the base be made?

a. 6.65 cm

b. 3.83 cm

c. 7.94 cm

d. 8.83 cm

Answer: **Option C**

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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