MCQ in Fundamentals in Algebra Part 2 | ECE Board Exam

(Last Updated On: March 17, 2020)

MCQs in Fundamentals in Algebra Part 2

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 – 4×2 –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 3×3+3×2-18x as completely as possible.

  • A. 3x(x+2)(x-3)
  • B. 3x(x-2)(x+3)
  • C. 3x(x-3)(x+6)
  • D. (3×2-6x)(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+2×2+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)) – ((4×2)/(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:

4×2 + 7y2 = 32

11y2 – 3×2 = 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

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 4×2 + 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 3×3 – 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 + 4×2 -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 3×5 – 4×3 + 2×2 + 36x + 48 divided by x3 – 2×2 + 6.

  • A. -3×2 – 4x + 8
  • B. 3×2 + 4x + 8
  • C. 3×2 – 4x – 8
  • D. 3×2 + 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)/(2×2 + 7x + 3)) – ((x + 3)/(2×2 – 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 ((3×2)/(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 +2×2 – 8x + 4
  • C. x4 – 2×3 + 4×2 – 8x + 16
  • D. x4 + 2×3 + 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 + 2×2 + 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
DOWNLOAD PDF / PRINT
Print Friendly, PDF & Email
Please do Subscribe on YouTube!

P inoyBIX educates thousands of reviewers and students a day in preparation for their board examinations. Also provides professionals with materials for their lectures and practice exams. Help me go forward with the same spirit.

“Will you subscribe today via YOUTUBE?”

Subscribe

Add Comment

PinoyBIX Engineering. © 2014-2020 All Rights Reserved | How to Donate? | Follow me on Blogarama DMCA.com Protection Status

Math Solution

Advanced Math problem age work mixture digit motion Analytic Geometry 01 problem Analytic Geometry 02 problem clock variation progression misc Combination problem Differential Calculus 01 Problem Differential Calculus 02 Problem Differential Equations Problem Fundamentals in Algebra Fundamentals in Algebra Problem Integral Calculus problem Permutation problem Plane Geometry problem Plane Trigonometry problem Probability problem quadratic equation binomial theorem logarithms Solid Geometry problem Spherical Trigonometry problem System of Numbers Problem Venn Diagram Problem

Questions and Answers in Mathematics

Advanced Math Age Work Mixture Digit Motion Algebra and General Mathematics Analytic Geometry 01 Analytic Geometry 02 Calculus Clock Variation Progression Misc Differential Calculus 01 Differential Calculus 02 Differential Equations Engineering Mathematics Geometry Integral Calculus Plane Geometry Plane Trigonometry Probability and Statistics Quadratic Equation Binomial Theorem Logarithms Solid Geometry Spherical Trigonometry System of Numbers Trigonometry

video

Pre-board in Electronics Engineering

Answers Pre-board in Electronics Engineering - Answers

Questions and Answers

Basic Television - Grob TV Boylestad Questions and Answers Computer Principles Electrical Circuit Electricity and Magnetism Fundamentals Electronic Circuits Floyd Questions and Answers Floyd Self-test Gibilisco Questions and Answers Grob Questions and Answers Industrial Electronics Principles and Applications Malvino Questions and Answers Microelectronics Power Generators / Sources / Principles and Applications Solid State Devices Tests and Measurements Vacuum Tubes

Pre-board in Communications Engineering

Answers

Questions and Answers

Acoustics Antennas Blake Questions and Answers Broadcasting and Cable TV System Digital Communication Networks Forouzan Frenzel Self-test Kennedy Questions and Answers Microwave Communications Miscellaneous Questions in Communications Modulation Navigational Aids and Radar Systems Noise Optical Fiber Communications Radiation and Wave Propagation Satellite Communications Transmission Fundamentals Wire and Wireless Communications

GEAS Solution

Dynamics problem Economics problem Physics problem Statics problem Strength problem Thermodynamics problem

Pre-board in GEAS

Questions and Answers in GEAS

Engineering Economics Engineering Laws and Ethics Engineering Management Engineering Materials Engineering Mechanics General Chemistry Giancoli Physics Physics Strength of Materials Thermodynamics
Online Tool: Electrical Charge Conversions
Online Tool: Electrical Charge Conversions
Online Tool: Color Code Conversions
Online Tool: Color Code Conversions
Online Tool: Weight Measurement Conversions
Online Tool: Weight Measurement Conversions
Online Tool: Temperature Measurement Conversions
Online Tool: Temperature Measurement Conversions