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.

#### 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

#### Start Practice Exam Test Questions Part 1 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

Answer: **Option A**

Solution:Review Solution for Number 1

**Problem 2: EE Board October 1992 **

Find the value of x in

A. 16.47

B. 12.87

C. 18.27

D. 20.17

Answer: **Option A**

Solution:Review Solution for Number 2

**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

Answer: **Option C**

Solution:Review Solution for Number 3

**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

Answer: **Option B**

Solution:Review Solution for Number 4

**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

Answer: **Option B**

Solution:Review Solution for Number 5

**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

Answer: **Option A**

Solution:Review Solution for Number 6

**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

Answer: **Option A**

Solution:Review Solution for Number 7

**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

Answer: **Option C**

Solution:Review Solution for Number 8

**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

Answer: **Option C**

Solution:Review Solution for Number 9

**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}

Answer: **Option C**

Solution:Review Solution for Number 10

**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

Answer: **Option A**

Solution:Review Solution for Number 11

**Problem 12: ECE Board April 1991**

Simplify:

Answer: **Option B**

Solution:Review Solution for Number 12

**Problem 13: ECE Board November 1993**

Simplify the following equation

Answer: **Option A**

Solution:Review Solution for Number 13

**Problem 14: ECE Board April 1991**

Answer: **Option A**

Solution:Review Solution for Number 14

**Problem 15: ECE Board April 1991**

Simplify:

A. -5a

B. -3a

C. -7a

D. -4a

Answer: **Option C**

Solution:Review Solution for Number 15

**Problem 16:**

Solve for x:

A. b + 4

D. b – 4

Answer: **Option D**

Solution:Review Solution for Number 16

**Problem 17: ECE Board April 1993**

Solve for y:

A. x – z

B. x + z

C. a + b

D. a – b

Answer: **Option B**

Solution:Review Solution for Number 17

**Problem 18: ME Board October 1996**

Resolve into partial fraction.

Answer: **Option C**

Solution:Review Solution for Number 18

**Problem 19: CE Board May 1996**

Find the value of A in the equation:

A. -2

B. 1/2

C. -1/2

D. 2

Answer: **Option D**

Solution:Review Solution for Number 19

**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

Answer: **Option C**

Solution:Review Solution for Number 20

**Problem 21:**

Evaluate: 64x • 4y

A. 256xy

B. 4x + 3y

C. 64x + 3y

D. 43x + y

Answer: **Option D**

Solution:Review Solution for Number 21

**Problem 22: ECE Board April 1993**

Solve for x in the following equations.

27x = 9y

81y^{3 }– x = 243

A. 1

B. 1.5

C. 2

D. 2.5

Answer: **Option A**

Solution:Review Solution for Number 22

**Problem 23: ECE Board April 1993**

Evaluate:

A. y = 5n

B. y = 9

C. y = 52n

D. y = 18

Answer: **Option B**

Solution:Review Solution for Number 23

**Problem 24: ECE Board April 1990**

Given: (an)( am) = 100,000 anm = 1000000

Find a:

A. 12

B. 9

C. 11

D. 10

Answer: **Option D**

Solution:Review Solution for Number 24

**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

Answer: **Option B**

Solution:Review Solution for Number 25

**Problem 26: ME Board October 1996**

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

A. (x + 4)(x + 2)

B. (x – 4)(x + 2)

C. (x – 4)(x – 2)

D. (x + 6)(x + 2)

Answer: **Option A**

Solution:Review Solution for Number 26

**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}

Answer: **Option D**

Solution:Review Solution for Number 27

**Problem 28: **

Find the value of ** k** so that

**4x**is a perfect square.

^{2}+ 6x + kA. 36

B. 2.5

C. 9

D. 2.25

Answer: **Option D**

Solution:Review Solution for Number 28

**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)

Answer: **Option A**

Solution:Review Solution for Number 29

**Problem 30: **

If **p – q = 5** and **pq = k/2**, then **p ^{2} + q^{2}** equals,

A. k

B. 25k

C. 25 + k

D. k/25

Answer: **Option C**

Solution:Review Solution for Number 30

**Problem 31: ME Board April 1995**

Simplify:

Answer: **Option C**

Solution:Review Solution for Number 31

**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

Answer: **Option D**

Solution:Review Solution for Number 32

**Problem 33: **

Simplify:

Answer: **Option A**

Solution:Review Solution for Number 33

**Problem 34: ME Board April 1996**

If x to the ¾ power equals 8, x equals

A. -9

B. 6

C. 9

D. 16

Answer: **Option D**

Solution:Review Solution for Number 34

**Problem 35: **

Solve for x:

A. 3

B. 23

C. 3 and 23

D. 20

Answer: **Option A**

Solution:Review Solution for Number 35

**Problem 36: CE Board November 1991**

Solve for x from the given equation:

A. 4

B. 2

C. 3

D. 5

Answer: **Option B**

Solution:Review Solution for Number 36

**Problem 37: EE Board October 1997**

If **f(x) = 2x ^{2} + 2x + 4**, what is

**f(2)**?

A. 4x + 2

B. 16

C. x^{2} + x + 2

d. 8

Answer: **Option B**

Solution:Review Solution for Number 37

**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

Answer: **Option A**

Solution:

**Problem 39:**

What is the least common multiple of 15 and 18?

A. 3

B. 5

C. 90

D. 270

Answer: **Option C**

Solution:Review Solution for Number 39

**Problem 40: ECE Board April 1998**

What is the lowest common factor of 10 and 32?

A. 320

B. 2

C. 180

D. 90

Answer: **Option B**

Solution:Review Solution for Number 40

**Problem 41:**

The numbers 12 and 16 has the greatest common divisor of

A. 2

B. 4

C. 6

D. 192

Answer: **Option B**

Solution:Review Solution for Number 41

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

The Polynomial **x3 + 4×2 – 3x + 8** is divided by (**x – 5)**, then the remainder is,

A. 175

B. 140

C. 218

D. 200

Answer: **Option C**

Solution:Review Solution for Number 42

**Problem 43:**

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

**x**.

^{3}– 2x^{2}+ 6A. 3x^{2} – 4x – 8

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

C. 3x^{2} – 6x – 8

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

Answer: **Option D**

Solution:Review Solution for Number 43

**Problem 44: CE Board November 1997**

Find the remainder if we divide **4y ^{3} + 18y^{2} + 8y – 4** by (

**2y + 3**).

A. 10

B. 11

C. 15

D. 13

Answer: **Option B**

Solution:Review Solution for Number 44

**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

Answer: **Option B**

Solution:Review Solution for Number 45

**Problem 46:**

The expression **x ^{4} + ax^{3} + 5x^{2} + bx + 6** when divided by (

**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

Answer: **Option B**

Solution:Review Solution for Number 46

**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?

Answer: **Option A**

Solution:Review Solution for Number 47

**Problem 48: ECE Board April 1999**

Find the mean proportional of **4 and 36**.

A. 72

B. 24

C. 12

D. 20

Answer: **Option C**

Solution:Review Solution for Number 48

**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

Answer: **Option A**

Solution:Review Solution for Number 49

**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

Answer: **Option B**

Solution:Review Solution for Number 50

### 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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