# MCQs in Algebra and General Mathematics Part III

Compiled MCQs in Algebra and General Mathematics Part 3 of the series as one topic in Engineering Mathematics in the ECE Board Exam.

This is the Multiple Choice Questions Part 3 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

### 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
PART 1: MCQs from Number 1 – 50                        Answer key: PART I
PART 2: MCQs from Number 51 – 100                        Answer key: PART II
PART 3: MCQs from Number 101 – 150                        Answer key: PART III
PART 4: MCQs from Number 151 – 200                        Answer key: PART IV
PART 5: MCQs from Number 201 – 250                        Answer key: PART V
PART 6: MCQs from Number 251 – 300                        Answer key: PART VI

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

Choose the letter of the best answer in each questions.

101. The equation of whose roots are the reciprocal of the roots of 2x^2 – 3x – 5  = 0 is,

• A. 5x^2 + 3x – 2 = 0
• B. 2x^2 + 3x – 5 = 0
• C. 3x^2 - 3x + 2 = 0
• D. 2x^2 + 5x – 3 = 0

102. In the equation x^2 + x = 0, one root is x equal to

• A. 1
• B. 5
• C. 1/4
• D. None of these

103. Solve the value of “a” in the equation a^8 – 17a^4 + 16 = 0.

• A. ± 2
• B. ± 3
• C. ± 4
• D. ± 5

104. Solve for x that satisfies the equation 6x^2 – 7x – 5 = 0.

• A. 5/3 or -1/2
• B. 3/2 or 3/8
• C. 7/5 or -7/15
• D. 3/5 or 3/4

105. Find the values of x in the equation 24x^2 + 5x – 1 = 0.

• A. (1/6 , 10
• B. (1/6 , 1/5)
• C. (1/2 , 1/5)
• D. (1/8, 1/3)

106. Determine k so that the equation 4x^2 + kx + 1 = 0 will have just one real solution.

• A. 3
• B. 4
• C. 5
• D. 6

107. Solve for x: 10x^2 + 10x +1 = 0

• A. -0.113, -0.887
• B. -0.331, -0.788
• C. -0.113, -0.788
• D. -0.311, -0.887

108. If 1/3 and -3/2 are the roots of a quadratic equation, then the equation is

• A. 6x^2 + 7x – 3 = 0
• B. 6x^2 - 7x + 3 = 0
• C. 6x^2- 7x – 3 = 0
• D. 6x^2- 7x + 1 = 0

109. Which of the following is a root of this quadratic equation, 30x^2 + 49x + 20 = 0?

• A. 0.6
• B. -0.6
• C. -0.8
• D. 0.75

110. What is the discriminant of the equation 4x^2 = 8x – 5?

• A. 8
• B. -16
• C. 16
• D. -8

111. Given the equation 3x^2 + Bx + 12 = 0. What is the value of B so that the roots of the equation are equal?

• A. 4
• B. 8
• C. 10
• D. -12

112. Find the term involving y5 in the expansion of (2x^2+ y)^10.

• A. 8064x^10 y^5
• B. 8046 x^5 y^5
• C. 8046 x^10 y^5
• D. 4680 x^5 y^5

113. Find the 5th term of the expansion of (x^2 + 1/x)^10

• A. 260x^6
• B. 5040x^6
• C. 210x^6
• D. 420x^6

114. In the expression of (x + 4y)^12, the numerical coefficient of the 5th term is,

• A. 63,360
• B. 126,720
• C. 506,880
• D. 253,440

115. What is the fourth term of the expansion of (x + x^2)^1000?

• A. 1650x^103
• B. 161700x^103
• C. 167100x^103
• D. 167100x^103

116. What is the numerical coefficient of the next term next to 495x^8y^4?

• A. 660
• B. 792
• C. 990
• D. 1100

117. Find the 6th term of the expression of ((1/2a) – 3)^16

• A. -66939/256a^11
• B. -66339/128a^11
• C. -33669/256a^11
• D. -39396/128^11

118. What is the coefficient of the term free of x of the expression of (2x – 5y)^4?

• A. 256
• B. 526
• C. 265
• D. 625

119. Find the 6th term of (3x – 4y)^6.

• A. -148,288x^3y^5
• B. -548x^3y^5
• C. -154,288x^3y^5
• D. -1,548,288x^3y^5

120. What is the sum of the coefficients of the expansion of (2x – 1)^20?

• A. 0
• B. 1
• C. 2
• D. 3

121. What is the sum of the coefficients of the expansion of (x + y – z)^8

• A. 0
• B. 1
• C. 2
• D. 3

122. Find the value of log848

• A. 1.86
• B. 1.68
• C. 1.78
• D. 1.98

123.Evaluate the log6 845 = x.

• A. 3.76
• B. 5.84
• C. 4.48
• D. 2.98

124. What is the value of log to the base 10 of 1000^3.3?

• A. 10.9
• B. 99.9
• C. 9.9
• D. 9.5

125. What is the value of (log 5 to the base 2) + (log 5 to the base 3)?

• A. 7.39
• B. 3.79
• C. 3.97
• D. 9.37

126. Find the value of log4 (log3 5)

• A. 1.460
• B. 0.275
• C. 1.273
• D. 0.165

127. Given: log4 7 = n

Find: log4 (1/7)

• A. 1/n
• B. n
• C. -1/n
• D. –n

128. IF loga 10 = 0.25, what is the value of log10 = a?

• A. 2
• B. 4
• C. 6
• D. 8

129. Given: logb y = 2x + logb x. Which of the following is true?

• A. y = b^2x
• B. y = 2xb
• C. y = (2x/b)
• D. y = xb^2x

130. Which value is equal to log to the base e of e to the -7x power?

• A. -7x
• B. 10 to the -7x power
• C. 7
• D. -7 log to the base 10

131. Log of the nth root x equals log of x to 1/n power and also equal to:

• A. log x / n
• B. n log x
• C. log(x to the base 1/n power)/n
• D. (n – 1)log x

132. Log (MN) is equal to:

• A. Log M – N
• B. Log M + N
• C. N Log M
• D. Log M + Log N

133. What expression is equivalent to log(x) – log(y + z)?

• A. log x + log y + log z
• B. log [x / (y + z)]
• C. log x – log y – log z
• D. log y + log (x + z)

134. Given: logb 1024 = 5/2

Find: b

• A. 2560
• B. 16
• C. 4
• D. 2

135. Given: log3 (x2 – 8x) = 2

Find: x

• A. -1
• B. 9
• C. -1 and 9
• D. 1 and -9

136. Solve for the value of x in the following equation: x^3logx = 100x.

• A. 12
• B. 8
• C. 30
• D. 10

137. Given: log 6 + log 4 = log 4 log (32 + 4^x). Find: x

• A. 2
• B. 3
• C. 4
• D. 6

138. If log of 2 to the base 2 plus log of x to the base 2 is equal to 2, then the value of x is,

• A. 4
• B. -2
• C. 2
• D. -1

139. Find the value of x if log12 x = 2.

• A. 144
• B. 414
• C. 524
• D. 425

140. Solve for the value of x:

log 2x^3 + log (6/x) = 6.278

• A. 379.65
• B. 365.97
• C. 397.56
• D. 356.79

141. Mary is 24 years old. Mary is twice as old as Ann was when Mary has as old as ANN is now. How old is Ann now?

• A. 16
• B. 18
• C. 12
• D. 15

142. The sum of Kim’s and Kevin’s ages is 18. In 3 years, Kim will be twice as old as Kevin. What are their ages now?

• A. 4, 14
• B. 5, 13
• C. 7, 11
• D. 6, 12

143. Robert is 15 years older than his brother Stan. However “y” years ago, Robert was twice as old as Stan. If Stan is now “b” years old and b>y, find value of (b – y)?

• A. 15
• B. 16
• C. 17
• D. 18

144. JJ is three times as old as Jan – Jan. Three years ago, JJ was four times as old as Jan – Jan. The sum of their ages is

• A. 20
• B. 24
• C. 28
• D. 36

145. A girl is one-third as old as her brother and 8 years younger than her sister. The sum of their ages is 38 years. How old is the girl?

• A. 4
• B. 5
• C. 6
• D. 7

146. Paula is now 18 yrs. old and her colleague Monica is 14 yrs. old. How many years ago was Paula twice as old as Monica?

• A. 5
• B. 7
• C. 8
• D. 10

147. A father tells his son, “I was your age now when you where born”. If the father is now 38 yrs. old, how old was his son 2 years ago?

• A. 15
• B. 17
• C. 19
• D. 21

148. Six years ago, Karen was five times as old as Gina. In five years, Karen will be three times as old as Gina. What is the present age of Gina?

• A. 17
• B. 16
• C. 15
• D. 14

149. At present, the sum of the parents’ ages is twice the sum of the children’s ages. Five years ago, the sum of the parents’ ages was 4 times the sum of the children’s ages. Fifteen years hence, the sum of the parents’ ages will be equal to the sum of the children’s ages. How may children are there?

• A. 3
• B. 4
• C. 5
• D. 6

150. Nhicole is now twice as old as Vryan. Four years ago, Nhicole was three times as old as Vryan then. How old is Nhicole?

• A. 14
• B. 16
• C. 18
• D. 24

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