This is the Multiple Choice Questions Part 2 of the Series in Algebra and General Mathematics topics in Engineering Mathematics. 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 Algebraic functions | MCQs in theory of Equations | MCQs in Factorization and Algebraic functions | MCQs in Ratio, Proportion and Variation | MCQs in Matrix theory | MCQs in Arithmetic and Geometric Progression | MCQs in Equations and Inequalities | MCQs in Linear and Quadratic Equations | MCQs in Complex Number System | MCQs in Polynomials | MCQs in Mathematical Induction | MCQs in Logic and Probability | MCQs in Statistics| MCQs in System of Numbers and Conversion | MCQs in Fundamentals in Algebra | MCQS in Binomial Theorems and Logarithms | MCQs in Age Problems | MCQs in Work Problems | MCQS in Mixture Problems | MCQs in Digit Problems | MCQs in Motion Problems | MCQs in Clock Problems | MCQs in Variation | MCQs in Progression | MCQs in Miscellaneous Problems

### Continue Practice Exam Test Questions Part II of the Series

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

51. If 16 is 4 more than 4x. Find 5x – 1.

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

52. Find the value of x in (x + 1)/3 + 2x/4 = 47 – 2x

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

53. Find the value of x in the equations:

10[A/x + A/y] = A

2[3(A/x) – 4(A/y)] = A

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

54. Find the values of x and y from the equations:

x – 4y +2 = 0

2x + y -4 = 0

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

55. 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

56. 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

57. 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

58. Solve the value of x.

2x – y + z =6

x – 3y – 2z = 13

2x – 3y – 3z = 16

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

59. Solve simultaneous equation:

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

60. 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

61.Determine the sum of the positive valued solution to the simultaneous equations:

xy = 15 , yz = 35 , zx = 21

- A. 15
- B. 13
- C. 17
- D. 19

62. Simplify:

((x^2y^3z^-2)^-3(x^-3yz^3)^(-1/2))/(xyz^-3)^(-5/2)

- A. 1/(x^2y^7z^5)
- B. 1/ (x^2 y^7 z^3)
- C. 1/ (x^2 y^5 z^7)
- D. 1/ (x^5 y^7 z^2)

63. Simplify the following equation:

(5x/(2x^2 + 7x +3)) – ((x + 3)/(2x^2 – 3x – 20) + ((2x + 1)/(x62 + x – 6))

- A. 4/(x + 3)
- B. 2/(x – 3)
- C. 4/(x + 3)
- D. 2/(x+3)

64. Simplify:

{x^(2/3)[x^(-1/3)y^(-1/2)(x^2y^(-2))^(-2/3)]^(1/2)}^6

- A. y^(5/2) / x
- B. y^(3/2) / x
- C. y^(5/2) / x^2
- D. y^(3/2) / x^2

65. Simplify:

7^(a + 2) – 8*7^(a + 1) + 5*7^a + 49*7^(a – 2)

- A. -5a
- B. -3a
- C. -7a
- D. -4a

66. Solve for x:

x = ((b^2 – 4b + 16)(b^2 – 16)/(b^3 + 64))

- A. b + 4
- B. (b – 4) / (b + 2)
- C. (b^2 – 4 )/ (b+2)
- D. b – 4

67. Solve for y:

x/(b – c) = y/(a – c) = z/(a – b) = 1

- A. x – z
- B. x + z
- C. a + b
- D. a – b

68. Resolve (x + 2)/(x^2 – 7x + 12) into partial fraction.

- A. (6/(x – 4)) – (2/(x – 3))
- B. (2/(x – 4)) – (5/(x – 3))
- C. (6/(x – 4)) – (5/(x – 3))
- D. (7/(x – 4)) – (5/(x – 3))

69. 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. 1/2
- C. -1/2
- D. 2

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

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

71. Evaluate: 64^x . 4^y

- A. 256^(xy)
- B. 4^(x +3y)
- C. 64^(x +3y)
- D. 4^(3x + y)

72. 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

73. Evaluate: y = (((4*5^(2n+1))-3)-10*5^(2n-1))/2*5^(2n)

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

74. Given: (a^n) (a^m) = 100,000

a^n / a^m = 10^1

Find a:

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

75. Give the factors of a^2 – x^2

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

76. Factor the expression x^2 + 6x + 8 as completely as possible

- A. (x + 4)(x + 2)
- B. (x – 4)(x + 2)
- C. (x – 4)(x – 2)
- D. (x + 6)(x + 2)

77. (a – b)^3= ?

- A. a^3 – 3(a^2)b + 3ab^2 + b^3
- B. a^3 – 3(a^2)b – 3ab^2 – b^3
- C. a^3 + 3(a^2)b + 3ab^2 – b^3
- D. a^3 – 3(a^2)b + 3ab^2 – b^3

78. Find the value of k so that 4x^2 + 6x + k is a perfect square

- A. 36
- B. 2.5
- C. 9
- D. 2.25

79. 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)

80. If *p – q = 5* and pq = (k/2), then *p^2 + q^2* equals

- A. k
- B. 25k
- C. 25 + k
- D. k/25

81. Simplify: b^(m/n)

- A. (sqrt(b^m))/n
- B. b^(m+n)
- C. (b^m)^(1/n)
- D. b^m/n

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

sqrt(x-2) = sqrt(x+2)

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

83. Simplify: sqrt(ab/(ab)^(1/3))

- A. (ab)^(1/3)
- B. (ab)^1(1/2)
- C. ab/(ab)^(1/2)
- D. (ab)/(ab)^(1/3)

84. If x to the 3/4 power equals 8, x equals

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

85. Solve for x: sqrt((x+2)(sqrt(2x+3)))-3 = 0

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

86. Solve for x for the given equation:

(8^(1/4)(((2)^(1/3))(sqrt(8x))))

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

87. If f(x) = 2x^2+ 2x + 4, What is f(2)?

- A. 4x + 2
- B. 16
- C. x^2 + x + 2
- D. 8

88. If n is any possible integer, when (n – 1)(n – 2)(n – 3)……(3)(2)(1) = ?

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

89. What is the least common multiple of 15 and 18?

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

90. What is the lowest common factor of 10 and 32?

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

91. The numbers 12 and 16 has the greatest common divisor of

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

92. The polynomial x^3+ 4x^2 – 3x + 8 is divided by x – 5, then the remainder is,

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

93. 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 – 6x – 8
- D. 3x^2 + 6x – 8

94. Find the remainder if we divide 4y^3+ 16y^ 2+ 6y -4 by (2y + 3)

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

95. 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

96. 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

97. 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?

- A. (a + b + c)/3
- B. (a + b + c)/2
- C. (a + b + c)/(a*b*c)
- D. (a*b*c)/(a + b + c)

98. Find the mean proportional of 4 and 36

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

99. 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

100. 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 four?

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

### Online Questions and Answers in Algebra and General Mathematics Series

Following is the list of multiple choice questions in this brand new series:

**Algebra and General Mathematics MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

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

**PART II**

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

**PART III**

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

**PART IV**

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

**PART V**

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

**PART VI**