MCQs in Fundamentals in Algebra Part II

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.

Multiple Choice Questions Topic Outline

• MCQs in Basic Rules in Algebra | MCQs in Properties of Equality | MCQs in Properties of Zero | MCQs in Properties of Exponent | MCQs in Properties of Radicals | MCQs in Surds | MCQs in Special Products | MCQs in Properties of Proportion | MCQs in Remainder Theorem | MCQs in Factor Theorem

Online Questions and Answers in Fundamentals in Algebra Series

Following is the list of multiple choice questions in this brand new series:

Fundamentals in Algebra MCQs

PART 1: MCQs from Number 1 – 50                        Answer key: PART I

PART 2: MCQs from Number 51 – 100                   Answer key: PART II

Continue Practice Exam Test Questions Part II of the Series

Choose the letter of the best answer in each questions.

Problem 51 (ME Board)

Change 0.222… common fraction.

• A. 2/10
• B. 2/9
• C. 2/13
• D. 2/7

Problem 52 (ME Board)

Change 0.2272722… to a common fraction.

• A. 7/44
• B. 5/48
• C. 5/22
• D. 9/34

Problem 53 (ME Board)

What is the value of 7! or 7 factorial?

• A. 5040
• B. 2540
• C. 5020
• D. 2520

Problem 54 (ME October 1994)

The reciprocal of 20 is:

• A. 0.50
• B. 20
• C. 0.20
• D. 0.05

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

Problem 56 (ECE March 1996)

MCMXCIV is a Roman Numeral equivalent to:

• A. 2974
• B. 3974
• C. 2174
• D. 1994

Problem 57 (ECE April 1998)

What is the lowest common factor of 10 and 32?

• A. 320
• B. 2
• C. 180
• D. 90

Problem 58

4xy – 4x² –y² is equal to:

• A. (2x-y)²
• B. (-2x-y)²
• C. (-2x+y)²
• D. –(2x-y)²

Problem 59

Factor x⁴ – y² + y – 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)

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)

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)

Problem 62 (ME October 1997)

Factor the expression (x⁴ – 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)

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)

Problem 64 (ME April 1998)

Factor the expression 16 – 10x + x².

• A. (x+8)(x-2)
• B. (x-8)(x-2)
• C. (x-8)(x+2)
• D. (x+8)(x+2)

Problem 65

Factor the expression x⁶ – 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)

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

Problem 67

If f(x) = x² + x + 1, then f(x) – f(x-1) =

• A. 0
• B. x
• C. 2x
• D. 3

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

Problem 69 (ME October 1997)

Solve for x: 4 + ((x + 3)/(x – 3)) – ((4x²)/(x² – 9)) = ((x + 9)/(x + 3)) .

• A. -18 = -18
• B. 12 = 12 or -3 = -3
• C. Any value
• D. -27 = -27 or 0 = 0

Problem 70 (ME October 1997)

Solve the simultaneous equations: 3x – y = 6; 9x – y = 12.

• A. x = 3; y = 1
• B. x = 1; y = -3
• C. x = 2; y = 2
• D. x = 4; y = 2

Problem 71 (ME April 1998)

Solve algebraically:

4x² + 7y² = 32

11y² – 3x² = 41

• A. y = 4, x = ±1  and y = -4, x = ±1
• B. y = +2, x = ±1  and y = -2, x = ±1
• C. x = 2, y = 3  and x = -2, y = -3
• D. x = 2, y = -2  and x = 2, y = -2

Problem 72 (CE May 1997)

Solve for w from the following equations:

3x – 2y + w = 11

x + 5y – 2w = -9

2x + y – 3w = -6

• A. 1
• B. 2
• C. 3
• D. 4

Problem 73

When (x+3)(x-4) + 4 is divided by x – 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

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

Problem 75

Find the remainder when (x¹² + 2) is divided by (x – √3)

• A. 652
• B. 731
• C. 231
• D. 851

Problem 76 (CE November 1997)

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

• A. 0
• B. 1
• C. 2
• D. 3

Problem 77 (CE November 1007 & May 1999)

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

• A. 10
• B. 11
• C. 12
• D. 13

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

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

Problem 80

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

• A. -3x² – 4x + 8
• B. 3x² + 4x + 8
• C. 3x² – 4x – 8
• D. 3x² + 6x + 8

Problem 81

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

• A. 1/2a
• B. 1/2b
• C. 2a/(a² – b²)
• D. 2b/(a² – b²)

Problem 82

If x-1/x = 1, find the value of x³ – 1/x³.

• A. 1
• B. 2
• C. 3
• D. 4

Problem 83

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

• A. ½
• B. 2/3
• C. ¾
• D. 4/3

Problem 84

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

• A. 2/(x-3)
• B. (x-3)/5
• C. (x+3)/(x-1)
• D. 4/(x+3)

Problem 85

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

• A. ¾
• B. 4/3
• C. 2/3
• D. 3/2

Problem 86

Simplify: (a+1/a)² – (a – 1/a)².

• A. -4
• B. 0
• C. 4
• D. -2/a²

Problem 87 (ECE November 1996)

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

• A. x⁴ – x³ + 8
• B. x³ +2x² – 8x + 4
• C. x⁴ – 2x³ + 4x² – 8x + 16
• D. x⁴ + 2x³ + x² + 16x + 8

Problem 88 (ME April 1996)

Solve the simultaneous equations:

y - 3x + 4 = 0

y + x²/y = 24/y

• A. x = (-6 + 2√14)/5 or (-6 – 2√14)/5

                    y = (2 + 6√14)/5 or (-2 + 6√14)/5

• B. x = (6 + 2√15)/5 or (6 – 2√15)/5

                   y = (-2 + 6√14)/5 or (-2 – 6√15)/5

• C. x = (6 + 2√14)/5 or (6 – 2√14)/5

                   y = (-2 + 6√14)/5 or (-2 – 6√14)/5

• D. x = (6 + 2√14)/5 or (6 – 2√14)/5

                    y = (-6+ 2√14)/5 or (-6 + 2√14)/5

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. ½

Problem 90

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

• A. A = -3; B = 2
• B. A = -3; B = -2
• C. A = 3; B = 2
• D. A = 3; B = 2

Problem 91 (ME October 1996)

Resolve ((x + 2)/(x2 – 7x + 12)  into partial fraction.

• A. (6/(x – 4)) – (2/(x – 3))
• B. (6/(x – 4)) + (7/(x – 3)) 
• C. (6/(x – 4)) – (5/(x – 3))
• D. (6/(x – 4)) + (5/(x – 3)) 

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

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

Problem 94

If 2x – 3y = x + y, then x² : y² =

• A. 1:4
• B. 4:1
• C. 1:16
• D. 16:1

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

Problem 96

Find the mean proportional to 5 and 20.

• A. 8
• B. 10
• C. 12
• D. 14

Problem 97

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

• A. 36
• B. 34
• C. 32
• D. 40

Problem 98 (ECE November 1997)

If (x + 3):10 = (3x – 2) : 8, find (2x –1)

• A. 1
• B. 2
• C. 3
• D. 4

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

Problem 100

Solve for x: x² + 4x > 12.

• A. -6 > x > 2
• B. 6 > x > -2
• C. -6 > x > -2
• D. 6 > x > 2

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