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:
2x2 – 3y2 = 6
3x2 + 2y2 = 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. 10x2 – 21xy + 10y2
B. -10x2 + 21xy + 10y2
C. 10x2 + 21xy – 10y2
D. -10x2 – 21xy – 10y2
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
81y3 – 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 a2 – x2
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. a3 – 3a2b + 3ab2 + b3
B. a3 – 3a2b – 3ab2 – b3
C. a3 + 3a2b + 3ab2 – b3
D. a3 – 3a2b + 3ab2 – b3
Answer: Option D
Solution:Review Solution for Number 27
Problem 28:
Find the value of k so that 4x2 + 6x + k is a perfect square.
A. 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 3x3 – 3x2 – 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 p2 + q2 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) = 2x2 + 2x + 4, what is f(2)?
A. 4x + 2
B. 16
C. x2 + 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 3x5 – 4x3 + 2x2 + 36x + 48 divided by x3 – 2x2 + 6.
A. 3x2 – 4x – 8
B. 3x2 + 4x + 8
C. 3x2 – 6x – 8
D. 3x2 + 6x + 8
Answer: Option D
Solution:Review Solution for Number 43
Problem 44: CE Board November 1997
Find the remainder if we divide 4y3 + 18y2 + 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 x4 + ax3 + 5x2 + 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:
Online Questions and Answers in Algebra and General Mathematics Series
Following is the list of multiple choice questions in this brand new series:
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