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

⇐ MCQ in Fundamentals in Algebra Part 1 | Math Board Exam

**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

Answer: **Option B**

Solution:

**Problem 52 (ME Board)**

Change 0.2272722… to a common fraction.

A. 7/44

B. 5/48

C. 5/22

D. 9/34

Answer: **Option C**

Solution:

**Problem 53 (ME Board)**

What is the value of 7! or 7 factorial?

A. 5040

B. 2540

C. 5020

D. 2520

Answer: **Option A**

Solution:

**Problem 54 (ME October 1994)**

The reciprocal of 20 is:

A. 0.50

B. 20

C. 0.20

D. 0.05

Answer: **Option D**

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

Answer: **Option C**

Solution:

**Problem 56 (ECE March 1996)**

MCMXCIV is a Roman Numeral equivalent to:

A. 2974

B. 3974

C. 2174

D. 1994

Answer: **Option D**

Solution:

**Problem 57 (ECE April 1998)**

What is the lowest common factor of 10 and 32?

A. 320

B. 2

C. 180

D. 90

Answer: **Option B**

Solution:

**Problem 58**

4xy – 4x^{2} –y^{2} is equal to:

A. (2x – y)^{2}

B. (-2x – y)^{2}

C. (-2x + y)^{2}

D. –(2x – y)^{2}

Answer: **Option D**

Solution:

**Problem 59**

Factor x^{4} – y^{2} + y – x^{2} as completely as possible.

A. (x^{2} + y)(x^{2} + y -1)

B. (x^{2} + y)(x^{2} – y -1)

C. (x^{2} – y)(x^{2} – y -1)

D. (x^{2} – y)(x^{2} + y -1)

Answer: **Option D**

Solution:

**Problem 60 (ME April 1996)**

Factor the expression x^{2} + 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)

Answer: **Option B**

Solution:

**Problem 61 (ME October 1997)**

Factor the expression x^{3} + 8.

A. (x – 2)(x^{2} + 2x + 4)

B. (x + 4)(x^{2} + 2x + 2)

C. (-x + 2)(-x^{2} + 2x + 2)

D. (x + 2)(x^{2} – 2x + 4)

Answer: **Option D**

Solution:

**Problem 62 (ME October 1997)**

Factor the expression (x^{4} – y^{4}) as completely as possible.

A. (x + y)(x^{2} + 2xy + y)

B. (x^{2} + y^{2})(x^{2} – y^{2})

C. (x^{2} + y^{2})(x + y)(x – y)

D. (1 + x^{2})(1 + y)(1 – y^{2})

Answer: **Option C**

Solution:

**Problem 63 (ME October 1997)**

Factor the expression 3x^{3} + 3x^{2} – 18x as completely as possible.

A. 3x(x + 2)(x – 3)

B. 3x(x – 2)(x + 3)

C. 3x(x – 3)(x + 6)

D. (3x^{2} – 6x)(x – 1)

Answer: **Option A**

Solution:

**Problem 64 (ME April 1998)**

Factor the expression 16 – 10x + x^{2}.

A. (x + 8)(x – 2)

B. (x – 8)(x – 2)

C. (x – 8)(x + 2)

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

Answer: **Option B**

Solution:

**Problem 65**

Factor the expression x^{6} – 1 as completely as possible.

A. (x + 1)(x – 1)(x^{4} + x^{2} – 1)

B. (x + 1)(x – 1)(x^{4} + 2x^{2} + 1)

C. (x + 1)(x – 1)(x^{4} – x^{2} + 1)

D. (x + 1)(x – 1)(x^{4} + x^{2} + 1)

Answer: **Option D**

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

Answer: **Option A**

Solution:

**Problem 67**

If f(x) = x^{2} + x + 1, then f(x) – f(x-1) =

A. 0

B. x

C. 2x

D. 3

Answer: **Option C**

Solution:

**Problem 68**

Which of the following is not an identity?

A. (x – 1)^{2} = x^{2 }– 2x + 1

B. (x + 3)(2x – 2) = 2(x^{2 }+ 2x – 3)

C. x^{2 }– (x – 1)^{2} = 2x – 1

D. 2(x – 1) + 3(x + 1) = 5x + 4

Answer: **Option D**

Solution:

**Problem 69 (ME October 1997)**

Solve for x: 4 + ((x + 3)/(x – 3)) – ((4x^{2})/(x^{2} – 9)) = ((x + 9)/(x + 3)) .

A. -18 = -18

B. 12 = 12 or -3 = -3

C. Any value

D. -27 = -27 or 0 = 0

Answer: **Option C**

Solution:

**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

Answer: **Option B**

Solution:

**Problem 71 (ME April 1998)**

Solve algebraically:

4x^{2} + 7y^{2} = 32

11y^{2} – 3x^{2} = 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

Answer: **Option B**

Solution:

**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

Answer: **Option C**

Solution:

**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

Answer: **Option C**

Solution:

**Problem 74**

Find k in the equation 4x^{2} + kx + 1 = 0 so that it will only have one real root.

A. 1

B. 2

C. 3

D. 4

Answer: **Option D**

Solution:

**Problem 75**

Find the remainder when (x^{12} + 2) is divided by (x – √3)

A. 652

B. 731

C. 231

D. 851

Answer: **Option B**

Solution:

**Problem 76 (CE November 1997)**

If 3x^{3} – 4x^{2}y + 5xy^{2} + 6y^{3} is divided by (x^{2} – 2xy + 3y^{2}), the remainder is

A. 0

B. 1

C. 2

D. 3

Answer: **Option A**

Solution:

**Problem 77 (CE November 1007 & May 1999)**

If (4y^{3} + 8y + 18y^{2} – 4) is divided by (2y + 3), the remainder is:

A. 10

B. 11

C. 12

D. 13

Answer: **Option B**

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

Answer: **Option C**

Solution:

**Problem 79 (EE March 1998)**

The polynomial x^{3} + 4x^{2} – 3x + 8 is divided by x – 5. What is the remainder?

A. 281

B. 812

C. 218

D. 182

Answer: **Option C**

Solution:

**Problem 80**

Find the quotient of 3x^{5} – 4x^{3} + 2x^{2} + 36x + 48 divided by x^{3} – 2x^{2} + 6.

A. -3x^{2} – 4x + 8

B. 3x^{2} + 4x + 8

C. 3x^{2} – 4x – 8

D. 3x^{2} + 6x + 8

Answer: **Option D**

Solution:

**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/(a^{2} – b^{2})

D. 2b/(a^{2} – b^{2})

Answer: **Option D**

Solution:

**Problem 82**

If x-1/x = 1, find the value of x^{3} – 1/x^{3}.

A. 1

B. 2

C. 3

D. 4

Answer: **Option D**

Solution:

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

Answer: **Option C**

Solution:

**Problem 84**

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

A. 2/(x – 3)

B. (x – 3)/5

C. (x + 3)/(x – 1)

D. 4/(x + 3)

Answer: **Option D**

Solution:

**Problem 85**

If 3x = 4y then ((3x^{2})/(4y^{2})) is equal to:

A. ¾

B. 4/3

C. 2/3

D. 3/2

Answer: **Option B**

Solution:

**Problem 86**

Simplify: (a + 1/a)^{2} – (a – 1/a)^{2}.

A. -4

B. 0

C. 4

D. -2/a^{2}

Answer: **Option C**

Solution:

**Problem 87 (ECE November 1996)**

The quotient of (x^{5} + 32) by (x + 2) is:

A. x^{4} – x^{3} + 8

B. x^{3} +2x^{2} – 8x + 4

C. x^{4} – 2x^{3} + 4x^{2} – 8x + 16

D. x^{4} + 2x^{3} + x^{2} + 16x + 8

Answer: **Option C**

Solution:

**Problem 88 (ME April 1996)**

Solve the simultaneous equations:

**y – 3x + 4 = 0**

**y + x ^{2}/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

Answer: **Option C**

Solution:

**Problem 89 (CE May 1996)**

Find the value of A in the equation. ((x^{2} = 4x + 10)/(x^{3} + 2x^{2} + 5x)) = A/x + ((B(2x + 2))/(x^{2} + 2x + 5)) + (C/(x^{2} + 2x + 5))

A. 2

B. -2

C. -1/2

D. ½

Answer: **Option A**

Solution:

**Problem 90**

Find A and B such that ((x + 10)/(x^{2} – 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

Answer: **Option C**

Solution:

**Problem 91 (ME October 1996)**

Resolve ((x + 2)/(x^{2} – 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))

Answer: **Option C**

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

Answer: **Option A**

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

Answer: **Option B**

Solution:

**Problem 94**

If 2x – 3y = x + y, then x^{2} : y^{2} =

A. 1:4

B. 4:1

C. 1:16

D. 16:1

Answer: **Option D**

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

Answer: **Option A**

Solution:

**Problem 96**

Find the mean proportional to 5 and 20.

A. 8

B. 10

C. 12

D. 14

Answer: **Option B**

Solution:

**Problem 97**

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

A. 36

B. 34

C. 32

D. 40

Answer: **Option A**

Solution:

**Problem 98 (ECE November 1997)**

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

A. 1

B. 2

C. 3

D. 4

Answer: **Option C**

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

Answer: **Option B**

Solution:

**Problem 100**

Solve for x: x^{2} + 4x > 12.

A. -6 > x > 2

B. 6 > x > -2

C. -6 > x > -2

D. 6 > x > 2

Answer: **Option A**

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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 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**

**MCQ from Number 1 – 50**Answer key:

**PART 1**

**MCQ from Number 51 – 100**Answer key:

**PART 2**

**MCQ from Number 101 – 150**Answer key:

**PART 3**

**MCQ from Number 151 – 200**Answer key:

**PART 4**

**MCQ from Number 201 – 250**Answer key:

**PART 5**

**MCQ from Number 251 – 300**Answer key:

**PART 6**

**MCQ from Number 301 – 350**Answer key:

**PART 7**

**MCQ from Number 351 – 400**Answer key:

**PART 8**

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

**PART 9**

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

**PART 10**

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