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# MCQ in Fundamentals in Algebra Part 2 | Math Board Exam

This is the Multiples Choice Questions Part 2 of the Series in Fundamentals in Algebra as one of the Engineering Mathematics topic. 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 Basic Rules in Algebra | MCQ in Properties of Equality | MCQ in Properties of Zero | MCQ in Properties of Exponent | MCQ in Properties of Radicals | MCQ in Surds | MCQ in Special Products | MCQ in Properties of Proportion | MCQ in Remainder Theorem | MCQ in Factor Theorem

#### Continue Practice Exam Test Questions Part 2 of the Series

Choose the letter of the best answer in each questions.

Problem 51 (ME Board)

Change 0.222โฆ common fraction.

A. 2/10

B. 2/9

C. 2/13

D. 2/7

Solution:

Problem 52 (ME Board)

Change 0.2272722โฆ to a common fraction.

A. 7/44

B. 5/48

C. 5/22

D. 9/34

Solution:

Problem 53 (ME Board)

What is the value of 7! or 7 factorial?

A. 5040

B. 2540

C. 5020

D. 2520

Solution:

Problem 54 (ME October 1994)

The reciprocal of 20 is:

A. 0.50

B. 20

C. 0.20

D. 0.05

Solution:

Problem 55

If p is an odd number and q is an even number, which of the following expressions must be even?

A. p + q

B. p – q

C. pq

D. p/q

Solution:

Problem 56 (ECE March 1996)

MCMXCIV is a Roman Numeral equivalent to:

A. 2974

B. 3974

C. 2174

D. 1994

Solution:

Problem 57 (ECE April 1998)

What is the lowest common factor of 10 and 32?

A. 320

B. 2

C. 180

D. 90

Solution:

Problem 58

4xy โ 4x2 โy2 is equal to:

A. (2x – y)2

B. (-2x – y)2

C. (-2x + y)2

D. โ(2x – y)2

Solution:

Problem 59

Factor x4 โ y2 + y โ x2 as completely as possible.

A. (x2 + y)(x2 + y -1)

B. (x2 + y)(x2 – y -1)

C. (x2 – y)(x2 – y -1)

D. (x2 – y)(x2 + y -1)

Solution:

Problem 60 (ME April 1996)

Factor the expression x2 + 6x + 8 as completely as possible.

A. (x + 8)(x – 2)

B. (x + 4)(x + 2)

C. (x + 4)(x – 2)

D. (x – 8)(x – 2)

Solution:

Problem 61 (ME October 1997)

Factor the expression x3 + 8.

A. (x – 2)(x2 + 2x + 4)

B. (x + 4)(x2 + 2x + 2)

C. (-x + 2)(-x2 + 2x + 2)

D. (x + 2)(x2 – 2x + 4)

Solution:

Problem 62 (ME October 1997)

Factor the expression (x4 โ y4) as completely as possible.

A. (x + y)(x2 + 2xy + y)

B. (x2 + y2)(x2 – y2)

C. (x2 + y2)(x + y)(x – y)

D. (1 + x2)(1 + y)(1 – y2)

Solution:

Problem 63 (ME October 1997)

Factor the expression 3x3 + 3x2 – 18x as completely as possible.

A. 3x(x + 2)(x – 3)

B. 3x(x – 2)(x + 3)

C. 3x(x – 3)(x + 6)

D. (3x2 – 6x)(x – 1)

Solution:

Problem 64 (ME April 1998)

Factor the expression 16 โ 10x + x2.

A. (x + 8)(x – 2)

B. (x – 8)(x – 2)

C. (x – 8)(x + 2)

D. (x + 8)(x + 2)

Solution:

Problem 65

Factor the expression x6 โ 1 as completely as possible.

A. (x + 1)(x – 1)(x4 + x2 – 1)

B. (x + 1)(x – 1)(x4 + 2x2 + 1)

C. (x + 1)(x – 1)(x4 – x2 + 1)

D. (x + 1)(x – 1)(x4 + x2 + 1)

Solution:

Problem 66

What are the roots of the equation (x – 4)2(x + 2) = (x + 2)2(x – 4)?

A. 4 and -2 only

B. 1 only

C. -2 and 4 only

D. 1, -2, and 4 only

Solution:

Problem 67

If f(x) = x2 + x + 1, then f(x) โ f(x-1) =

A. 0

B. x

C. 2x

D. 3

Solution:

Problem 68

Which of the following is not an identity?

A. (x – 1)2 = x2 – 2x + 1

B. (x + 3)(2x – 2) = 2(x2 + 2x – 3)

C. x2 – (x – 1)2 = 2x – 1

D. 2(x – 1) + 3(x + 1) = 5x + 4

Solution:

Problem 69 (ME October 1997)

Solve for x: 4 + ((x + 3)/(x โ 3)) โ ((4x2)/(x2 โ 9)) = ((x + 9)/(x + 3)) .

A. -18 = -18

B. 12 = 12 or -3 = -3

C. Any value

D. -27 = -27 or 0 = 0

Solution:

Problem 70 (ME October 1997)

Solve the simultaneous equations: 3x โ y = 6; 9x โ y = 12.

A. x = 3; y = 1

B. x = 1; y = -3

C. x = 2; y = 2

D. x = 4; y = 2

Solution:

Problem 71 (ME April 1998)

Solve algebraically:

4x2 + 7y2 = 32

11y2 โ 3x2 = 41

A. y = 4, x = ยฑ1ย  and y = -4, x = ยฑ1

B. y = +2, x = ยฑ1ย  and y = -2, x = ยฑ1

C. x = 2, y = 3ย  and x = -2, y = -3

D. x = 2, y = -2ย  and x = 2, y = -2

Solution:

Problem 72 (CE May 1997)

Solve for w from the following equations:

3x โ 2y + w = 11

x + 5y โ 2w = -9

2x + y โ 3w = -6

A. 1

B. 2

C. 3

D. 4

Solution:

Problem 73

When (x + 3)(x – 4) + 4 is divided by x โ k, the remainder is k. Find the value of k.

A. 4 or 2

B. 2 or -4

C. 4 or -2

D. -4 or -2

Solution:

Problem 74

Find k in the equation 4x2 + kx + 1 = 0 so that it will only have one real root.

A. 1

B. 2

C. 3

D. 4

Solution:

Problem 75

Find the remainder when (x12 + 2) is divided by (x โ โ3)

A. 652

B. 731

C. 231

D. 851

Solution:

Problem 76 (CE November 1997)

If 3x3 โ 4x2y + 5xy2 + 6y3 is divided by (x2 โ 2xy + 3y2), the remainder is

A. 0

B. 1

C. 2

D. 3

Solution:

Problem 77 (CE November 1007 & May 1999)

If (4y3 + 8y + 18y2 โ 4) is divided by (2y + 3), the remainder is:

A. 10

B. 11

C. 12

D. 13

Solution:

Problem 78 (ECE April 1999)

Given f(x) = (x + 3)(x – 4) + 4 when divided by (x – k), the remainder is k. Find k.

A. 2

B. 3

C. 4

D. -3

Solution:

Problem 79 (EE March 1998)

The polynomial x3 + 4x2 – 3x + 8 is divided by x – 5. What is the remainder?

A. 281

B. 812

C. 218

D. 182

Solution:

Problem 80

Find the quotient of 3x5 โ 4x3 + 2x2 + 36x + 48 divided by x3 โ 2x2 + 6.

A. -3x2 โ 4x + 8

B. 3x2 + 4x + 8

C. 3x2 โ 4x โ 8

D. 3x2 + 6x + 8

Solution:

Problem 81

If 1/x = a + b and 1/y = a โ b, then x โ y is equal to:

A. 1/2a

B. 1/2b

C. 2a/(a2 โ b2)

D. 2b/(a2 โ b2)

Solution:

Problem 82

If x-1/x = 1, find the value of x3 โ 1/x3.

A. 1

B. 2

C. 3

D. 4

Solution:

Problem 83

If 1/x + 1/y = 3 and 2/x โ 1/y = 1. Then x is equal to:

A. ยฝ

B. 2/3

C. ยพ

D. 4/3

Solution:

Problem 84

Simplify the following expression: ((5x)/(2x2 + 7x + 3)) โ ((x + 3)/(2x2 โ 3x โ 2)) + ((2x + 1)/(x2 + 6 โ 6)).

A. 2/(x – 3)

B. (x – 3)/5

C. (x + 3)/(x – 1)

D. 4/(x + 3)

Solution:

Problem 85

If 3x = 4y then ((3x2)/(4y2)) is equal to:

A. ยพ

B. 4/3

C. 2/3

D. 3/2

Solution:

Problem 86

Simplify: (a + 1/a)2 โ (a โ 1/a)2.

A. -4

B. 0

C. 4

D. -2/a2

Solution:

Problem 87 (ECE November 1996)

The quotient of (x5 + 32) by (x + 2) is:

A. x4 โ x3 + 8

B. x3 +2x2 โ 8x + 4

C. x4 โ 2x3 + 4x2 โ 8x + 16

D. x4 + 2x3 + x2 + 16x + 8

Solution:

Problem 88 (ME April 1996)

Solve the simultaneous equations:

y – 3x + 4 = 0

y + x2/y = 24/y

A. x = (-6 + 2โ14)/5 or (-6 โ 2โ14)/5

y = (2 + 6โ14)/5 or (-2 + 6โ14)/5

B. x = (6 + 2โ15)/5 or (6 โ 2โ15)/5

y = (-2 + 6โ14)/5 or (-2 โ 6โ15)/5

C. x = (6 + 2โ14)/5 or (6 โ 2โ14)/5

y = (-2 + 6โ14)/5 or (-2 โ 6โ14)/5

D. x = (6 + 2โ14)/5 or (6 โ 2โ14)/5

y = (-6+ 2โ14)/5 or (-6 + 2โ14)/5

Solution:

Problem 89 (CE May 1996)

Find the value of A in the equation. ((x2 = 4x + 10)/(x3 + 2x2 + 5x)) = A/x + ((B(2x + 2))/(x2 + 2x + 5)) + (C/(x2 + 2x + 5))

A. 2

B. -2

C. -1/2

D. ยฝ

Solution:

Problem 90

Find A and B such that ((x + 10)/(x2 โ 4)) = (A/(x โ 2)) + (B/(x + 2))

A. A = -3; B = 2

B. A = -3; B = -2

C. A = 3; B = 2

D. A = 3; B = 2

Solution:

Problem 91 (ME October 1996)

Resolve ((x + 2)/(x2 โ 7x + 12)ย  into partial fraction.

A. (6/(x โ 4)) โ (2/(x โ 3))

B. (6/(x โ 4)) + (7/(x โ 3))

C. (6/(x โ 4)) โ (5/(x โ 3))

D. (6/(x โ 4)) + (5/(x โ 3))

Solution:

Problem 92 (ECE April 1998)

The arithmetic mean of 80 numbers is 55. If two numbers namely 250 and 850 are removed what is the arithmetic mean of the remaining numbers?

A. 42.31

B. 57.12

C. 50

D. 38.62

Solution:

Problem 93 (ECE April 1998)

The arithmetic mean of 6 numbers is 17. If two numbers are added to the progression, the new set of number will have an arithmetic mean of 19. What are the two numbers if their difference is 4?

A. 21, 29

B. 23, 27

C. 24, 26

D. 22, 28

Solution:

Problem 94

If 2x โ 3y = x + y, then x2 : y2 =

A. 1:4

B. 4:1

C. 1:16

D. 16:1

Solution:

Problem 95

If 1/a :1/b : 1/c = 2 : 3 : 4, then (a + b + c) : (b + c) is equal to:

A. 13:7

B. 15:6

C. 10:3

D. 7:9

Solution:

Problem 96

Find the mean proportional to 5 and 20.

A. 8

B. 10

C. 12

D. 14

Solution:

Problem 97

Find the fourth proportional of 7, 12, and 21.

A. 36

B. 34

C. 32

D. 40

Solution:

Problem 98 (ECE November 1997)

If (x + 3):10 = (3x โ 2) : 8, find (2x โ1)

A. 1

B. 2

C. 3

D. 4

Solution:

Problem 99

Solve for x: -4 < 3x – 1 < 11.

A. 1 < x < -4

B. -1< x < 4

C. 1 < x < 4

D. -1 < x < -4

Solution:

Problem 100

Solve for x: x2 + 4x > 12.

A. -6 > x > 2

B. 6 > x > -2

C. -6 > x > -2

D. 6 > x > 2

Solution:

### 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 โ 50                           Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                      Answer key: PART 2

### 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 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                          Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                        Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                         Answer key: PART 5
PART 6: MCQ from Number 251 โ 300                         Answer key: PART 6
PART 7: MCQ from Number 301 โ 350                         Answer key: PART 7
PART 8: MCQ from Number 351 โ 400                         Answer key: PART 8
PART 9: MCQ from Number 401 โ 450                         Answer key: PART 9
PART 10: MCQ from Number 451 โ 500                        Answer key: PART 10

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