This is the Multiples Choice Questions Part 1 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**### Start Practice Exam Test Questions Part I of the Series

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

**Problem 1: ECE Board April 1999**

If 16 is 4 more than 4x, find 5x – 1.

- A. 14
- B. 3
- C. 12
- D. 5

**Problem 2: EE Board October 1992**

Find the value of x in

- A. 16.47
- B. 12.87
- C. 18.27
- D. 20.17

**Problem 3: EE Board October 1991**

Find the value of x in the equations:

- A. 50/9
- B. 80/9
- C. 70/9
- D. 60/9

**Problem 4: EE Board October 1997**

Find the values of x and y from the equations:

x - 4y + 2 = 0

2x + y – 4 = 0

- A. 11/7, -5/7
- B. 14/9, 8/9
- C. 4/9, 8/9
- D. 3/2, 5/3

**Problem 5: ME Board October 1995**

Solve for the value of x and y.

4x + 2y = 5 13x -3y = 2

- A. y = 1/2, x = 3/2
- B. y = 3/2, x = 1/2
- C. y = 2, x = 1
- D. y = 3, x =1

**Problem 6: ME Board October 1996**

Solve the simultaneous equations:

2x

^{2}- 3y

^{2}= 6

3x

^{2}+ 2y

^{2}= 35

- A. x = 3 or -3; y = 2 or -2
- B. x = 3 or -3, y = -2 or 1
- C. x = 3 or -3, y = -2 or -1
- D. x = 3 or -3, y = 2 or -3

**Problem 7: CE Board May 1997**

Find the value of w in the following equations:

3x - 2y + w = 11

x + 5y - 2w = -9

2x + y -3w = -6

- A. 3
- B. 2
- C. 4
- D. -2

**Problem 8: EE Board October 1993**

Solve for the value of x.

2x – y + z = 6

x- 3y - 2z = 13

2x - 3y - 3z = 16

- A. 4
- B. 3
- C. 2
- D. 1

**Problem 9: ME Board October 1996**

Solve the simultaneous equations:

x + y = - 4

x + z - 1 = 0

y + z + 1 = 0

- A. x = -1, y = -5, z = 3
- B. x = 1, y = 2, z = -3
- C. x = -1, y = -3, z = 2
- D. x = -2, y = -3, z = -1

**Problem 10: EE Board April 1997**

Multiply the following: (2x + 5y)(5x - 2y)

- A. 10x
^{2}– 21xy + 10y^{2} - B. -10x
^{2}+ 21xy + 10y^{2} - C. 10x
^{2}+ 21xy - 10y^{2} - D. -10x
^{2}- 21xy - 10y^{2}

**Problem 11: EE Board March 1998**

Determine the sum of the positive valued solution

to the simultaneous equations:

xy = 15, yz = 35, zx = 21.

- A. 16
- B. 13
- C. 17
- D. 19

**Problem 12: ECE Board April 1991**

Simplify:

**Problem 13: ECE Board November 1993**

Simplify the following equation

**Problem 14: ECE Board April 1991**

Simplify:

**Problem 15: ECE Board April 1991**

Simplify:

A. -5a

B. -3a

C. -7a

D. -4a

**Problem 16:**

Solve for x:

A. b + 4

B.

C.

D.

**b – 4**

**Problem 17: ECE Board April 1993**

Solve for y:

A. x – z

B. x + z

C. a + b

D. a – b

**Problem 18: ME Board October 1996**

Resolve into partial fraction.

**Problem 19: CE Board May 1996**

Find the value of A in the equation:

- A. -2
- B. 1/2
- C. -1/2
- D. 2

**Problem 20: ME Board October 1996**

The value of (3 to 2.5 power) square is equal to:

- A. 729
- B. 140
- C. 243
- D. 81

**Problem 21:**

Evaluate: 64

^{x}• 4

^{y}

- A. 256
^{xy} - B. 4
^{x + 3y} - C. 64
^{x + 3y} - D. 4
^{3x + y}

**Problem 22: ECE Board April 1993**

Solve for x in the following equations.

27

^{x}= 9

^{y}

81

^{y}3

^{-x}= 243

- A. 1
- B. 1.5
- C. 2
- D. 2.5

**Problem 23: ECE Board April 1993**

Evaluate:

- A. y = 5
^{n} - B. y = 9
- C. y = 5
^{2n} - D. y = 18

**Problem 24: ECE Board April 1990**

Given: (a

^{n})( a

^{m}) = 100,000 a

^{nm}= 1000000

Find a:

- A. 12
- B. 9
- C. 11
- D. 10

**Problem 25: ECE Board November 1991**

Give the factors of a

^{2 }– x

^{2}

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

**Problem 26: ME Board October 1996**

Factor the expression

**x**as completely possible.

^{2 }+ 6x + 8- A. (x + 4)(x + 2)
- B. (x – 4)(x + 2)
- C. (x – 4)(x – 2)
- D. (x + 6)(x + 2)

**Problem 27: ECE Board November 1990**

Expand:

**(a – b)**= ?

^{3}- A. a
^{3}– 3a^{2}b + 3ab^{2}+ b^{3} - B.
^{ }a^{3}– 3a^{2}b – 3ab^{2}– b^{3} - C. a
^{3}+ 3a^{2}b + 3ab^{2}– b^{3} - D. a
^{3}– 3a^{2}b + 3ab^{2}– b^{3}

**Problem 28:**

Find the value of

**so that**

*k***4x**is a perfect square.

^{2}+ 6x + k- A. 36
- B. 2.5
- C. 9
- D. 2.25

**Problem 29: ME Board April 1995**

Factor the expression

**3x**

^{3}– 3x^{2}– 18x- A. 3x(x – 3)(x + 2)
- B. 3x(x + 3)(x + 2)
- C. 3x(x + 3)(x – 2)
- D. 3x(x – 3)(x – 2)

**Problem 30:**

If

**p – q = 5**and

**pq = k/2**, then

**p**equals,

^{2}+ q^{2}- A. k
- B. 25k
- C. 25 + k
- D. k/25

**Problem 31: ME Board April 1995**

Simplify:

A.

B.

C.

D.

**Problem 32: ME Board April 1998**

Find the value of x which will satisfy the following expression:

- A. 3/2
- B. 9/4
- C. 18/6
- D. None of these

**Problem 33:**

Simplify:

**Problem 34: ME Board April 1996**

If x to the ¾ power equals 8, x equals

- A. -9
- B. 6
- C. 9
- D. 16

**Problem 35:**

Solve for x:

- A. 3
- B. 23
- C. 3 and 23
- D. 20

**Problem 36: CE Board November 1991**

Solve for x from the given equation:

- A. 4
- B. 2
- C. 3
- D. 5

**Problem 37: EE Board October 1997**

If

**f(x) = 2x**, what is

^{2}+ 2x + 4**f(2)**?

- A. 4x + 2
- B. 16
- C. x
^{2}+ x + 2 - d. 8

**Problem 38: EE Board April 1997**

If

**n**is any positive integer, when

**(n – 1) (n – 2) (n – 3)… (3)(2)(1) =**

- A. e
^{(n – 1)} - B. (n – 1)!
- C. n!
- D. (n – 1)
^{n}

**Problem 39:**

What is the least common multiple of 15 and 18?

- A. 3
- B. 5
- C. 90
- D. 270

**Problem 40: ECE Board April 1998**

What is the lowest common factor of 10 and 32?

- A. 320
- B. 2
- C. 180
- D. 90

**Problem 41:**

The numbers 12 and 16 has the greatest common divisor of

- A. 2
- B. 4
- C. 6
- D. 192

**Problem 42: EE Board April 1996, EE Board March 1998**

The Polynomial

**x**is divided by (

^{3}+ 4x^{2}– 3x + 8**x – 5)**, then the remainder is,

- A. 175
- B. 140
- C. 218
- D. 200

**Problem 43:**

Find the quotient of

**3x**divided by

^{5}– 4x^{3}+ 2x^{2}+ 36x + 48**x**.

^{3}– 2x^{2}+ 6- A. 3x
^{2}– 4x – 8 - B. 3x
^{2}+ 4x + 8 - C. 3x
^{2}– 6x – 8 - D. 3x
^{2}+ 6x + 8

**Problem 44: CE Board November 1997**

Find the remainder if we divide

**4y**by (

^{3}+ 18y^{2}+ 8y – 4**2y + 3**).

- A. 10
- B. 11
- C. 15
- D. 13

**Problem 45: ECE Board November 1999**

Given:

**f(x) = (x + 3)(x – 4) + 4**. When f(x) is divided by (

**x – k**), the remainder is

**k**. Find

**k**.

- A. 2
- B. 4
- C. 6
- D. 8

**Problem 46:**

The expression

**x**when divided by (

^{4}+ ax^{3}+ 5x^{2}+ bx + 6**x – 2**) leaves a remainder of

**16**and when divided by (

**x + 1**) leaves a remainder of

**10**. Find a and

**b**.

- A. a = 5, b = 7
- B. a = -5, b = 7
- C. a = -5, b = -7
- D. a = 5, b = -7

**Problem 47:**

The mean of

**x and y**is

**a**, the mean of

**y and z**is

**b**and the mean of

**x and z**is

**c.**What is the mean of x, y, and z?

**Problem 48: ECE Board April 1999**

Find the mean proportional of

**4 and 36**.

- A. 72
- B. 24
- C. 12
- D. 20

**Problem 49: ECE Board 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. 50
- C. 38.62
- D. 57.12

**Problem 50: ECE Board April 1998**

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

- A. 21, 25
- B. 23, 27
- C. 8, 12
- D. 16, 20

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