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# MCQ in Algebra and General Mathematics Part 2 | ECE Board Exam

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.

#### MCQ Topic Outline included in Mathematics Board Exam Syllabi

• MCQ in Algebraic functions | MCQ in theory of Equations | MCQ in Factorization and Algebraic functions | MCQ in Ratio, Proportion and Variation | MCQ in Matrix theory | MCQ in Arithmetic and Geometric Progression | MCQ in Equations and Inequalities | MCQ in Linear and Quadratic Equations | MCQ in Complex Number System | MCQ in Polynomials | MCQ in Mathematical Induction | MCQ in Logic and Probability | MCQ in Statistics| MCQ in System of Numbers and Conversion | MCQ in Fundamentals in Algebra | MCQ in Binomial Theorems and Logarithms | MCQ in Age Problems | MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Motion Problems | MCQ in Clock Problems | MCQ in Variation | MCQ in Progression | MCQ in Miscellaneous Problems

#### Continue Practice Exam Test Questions Part 2 of the Series

Choose the letter of the best answer in each questions.

51. If 16 is 4 more than 4x. Find 5x โ 1.

A. 14

B. 3

C. 12

D. 5

Solution:

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

A. 16.47

B. 12.87

C. 18.27

D. 20.17

Solution:

53. Find the value of x in the equations:

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

2[3(A/x) โ 4(A/y)] = A

A. 50/9

B. 80/9

C. 70/9

D. 60/9

Solution:

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

Solution:

55. Solve for the value of x and y,

4x + 2y = 5

13x โ 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

Solution:

56. Solve the simultaneous equations:

2x^2 โ 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

Solution:

57. Find the value of w in the following equations:

3x โ 2y + w = 11

x + 5y โ 2w = -9

2x + y โ 3w = -6

A. 3

B. 2

C. 4

D. -2

Solution:

58. Solve the value of x.

2x โ y + z =6

x โ 3y โ 2z = 13

2x โ 3y โ 3z = 16

A. 4

B. 3

C. 2

D. 1

Solution:

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

Solution:

60. Multiply the following:

(2x + 5y)(5x โ 2y)

A. 10x^2 โ 21xy + 10y^2

B. -10x^2 + 21xy + 10y^2

C. 10x^2 + 21xy – 10y^2

D. – 10x^2 โ 21xy – 10y^2

Solution:

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

Solution:

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)

Solution:

63. Simplify the following equation:

(5x/(2x^2 + 7x +3)) โ ((x + 3)/(2x^2 โ 3x โ 20) + ((2x + 1)/(x62 + x โ 6))

A. 4/(x + 3)

B. 2/(x โ 3)

C. 4/(x + 3)

D. 2/(x+3)

Solution:

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

Solution:

65. Simplify:

7^(a + 2) โ 8*7^(a + 1) + 5*7^a + 49*7^(a โ 2)

A. -5a

B. -3a

C. -7a

D. -4a

Solution:

66. Solve for x:

x = ((b^2 โ 4b + 16)(b^2 โ 16)/(b^3 + 64))

A. b + 4

B. (b โ 4) / (b + 2)

C. (b^2 โ 4 )/ (b+2)

D. b โ 4

Solution:

67. Solve for y:

x/(b โ c) = y/(a โ c) = z/(a โ b) = 1

A. x โ z

B. x + z

C. a + b

D. a โ b

Solution:

68. Resolve (x + 2)/(x^2 โ 7x + 12) into partial fraction.

A. (6/(x โ 4)) โ (2/(x โ 3))

B. (2/(x โ 4)) โ (5/(x โ 3))

C. (6/(x โ 4)) โ (5/(x โ 3))

D. (7/(x โ 4)) โ (5/(x โ 3))

Solution:

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

Solution:

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

A. 729

B. 140

C. 243

D. 81

Solution:

71. Evaluate: 64^x . 4^y

A. 256^(xy)

B. 4^(x +3y)

C. 64^(x +3y)

D. 4^(3x + y)

Solution:

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

Solution:

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

Solution:

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

a^n / a^m = 10^1

Find a:

A. 12

B. 9

C. 11

D. 10

Solution:

75. Give the factors of a^2 โ x^2

A. 2a โ 2x

B. (a + x)(a โ x)

C. (a +x)(a + x)

D. 2x โ 2a

Solution:

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

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

B. (x โ 4)(x + 2)

C. (x โ 4)(x โ 2)

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

Solution:

77. (a โ b)^3= ?

A. a^3 โ 3(a^2)b + 3ab^2 + b^3

B. a^3 โ 3(a^2)b – 3ab^2 – b^3

C. a^3 + 3(a^2)b + 3ab^2 – b^3

D. a^3 โ 3(a^2)b + 3ab^2 – b^3

Solution:

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

Solution:

79. Factor the expression:

3x^3 โ 3x^2 โ 18x

A. 3x (x โ 3)(x + 2)

B. 3x (x + 3)(x + 2)

C. 3x (x + 3)(x – 2)

D. 3x (x โ 3)(x – 2)

Solution:

80. If p โ q = 5 and pq = (k/2), then p^2 + q^2 equals

A. k

B. 25k

C. 25 + k

D. k/25

Solution:

81. Simplify: b^(m/n)

A. (sqrt(b^m))/n

B. b^(m+n)

C. (b^m)^(1/n)

D. b^m/n

Solution:

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

Solution:

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)

Solution:

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

A. -9

B. 6

C. 9

D. 16

Solution:

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

A. 3

B. 23

C. 3 and 23

D. 20

Solution:

86. Solve for x for the given equation:

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

A. 4

B. 2

C. 3

D. 5

Solution:

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

A. 4x + 2

B. 16

C. x^2 + x + 2

D. 8

Solution:

88. If n is any possible integer, when (n โ 1)(n โ 2)(n โ 3)โฆโฆ(3)(2)(1) = ?

A. e^(n โ 1)

B. (n โ 1)!

C. n!

D. (n โ 1)^n

Solution:

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

A. 3

B. 5

C. 90

D. 270

Solution:

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

A. 320

B. 2

C. 180

D. 90

Solution:

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

A. 2

B. 4

C. 6

D. 192

Solution:

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

A. 175

B. 140

C. 218

D. 200

Solution:

93. Find the quotient of 3x^5 โ 4x^3+ 2x^2+ 36x + 48 divided by x^3 โ 2x^2 + 6

A. 3x^2 โ 4x โ 8

B. 3x^2 + 4x + 8

C. 3x^2 โ 6x โ 8

D. 3x^2 + 6x โ 8

Solution:

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

A. 10

B. 11

C. 15

D. 13

Solution:

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

Solution:

96. The expression x^4 + ax^3 +5x^2 + bx + 6 when divided by (x โ 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

Solution:

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)

Solution:

98. Find the mean proportional of 4 and 36

A. 72

B. 24

C. 12

D. 20

Solution:

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

Solution:

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

Solution:

### 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
PART 1: MCQ from Number 1 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                          Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                        Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                         Answer key: PART 5
PART 6: MCQ from Number 251 โ 300                         Answer key: PART 6
PART 7: MCQ from Number 301 โ 350                         Answer key: PART 7
PART 8: MCQ from Number 351 โ 400                         Answer key: PART 8
PART 9: MCQ from Number 401 โ 450                         Answer key: PART 9
PART 10: MCQ from Number 451 โ 500                        Answer key: PART 10

### 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
PART 1: MCQ from Number 1 โ 50                           Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                      Answer key: PART 2

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