This is the Multiples Choice Questions Part 1 of the Series in Quadratic Equation, Binomial Theorem and Logarithms 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.
Multiple Choice Questions Topic Outline
- MCQs in Basic Rules in Quadratic Formula | MCQs in Nature of Roots | MCQs in Properties of Roots | MCQs in Binomial Theorem | MCQs in Properties of Expansion | MCQs in Pascal’s Triangle | MCQs in Coefficient of any term | MCQs in Formula for rth term | MCQs in Sum of Coefficients | MCQs in Sum of Exponents | MCQs in Common and Natural Logarithms | MCQs in Euler’s Number | MCQs in Binary Logarithms | MCQs in Properties of Logarithms
Online Questions and Answers in Quadratic Equation, Binomial Theorem and Logarithms Series
Quadratic Equation, Binomial Theorem and Logarithms MCQs
PART 1: MCQs from Number 1 – 50 Answer key: PART I
PART 2: MCQs from Number 51 – 100 Answer key: PART II
Start Practice Exam Test Questions Part I of the Series
Choose the letter of the best answer in each questions.
Problem 1: ECE Board March 1996The equation whose roots are the reciprocal of the roots of 2x2 – 3x – 5 = 0 is,
- A. 5x2 + 3x – 2 = 0
- B. 2x2 + 3x – 5 = 0
- C. 3x2 – 3x +2 = 0
- D. 2x2 + 5x – 3 = 0
In the equation x2 + x = 0, one root is x equal to
- A. 1
- B. 5
- C. ¼
- D. none of these
Solve for the value of “a” in the equation a8 – 17a4 + 16 = 9
- A. ± 2
- B. ± 3
- C. ± 4
- D. ± 5
Solve for x that satisfies the equation 6x2 – 7x – 5 = 0
- A.
- B.
- C.
- D.
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Find the values of x in the equation 24x2 + 5x – 1 = 0
- A.
- B.
- C.
- D.
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Determine k so that the equation 4x2 + kx + 1 = 0 will have just one real solution.
- A. 3
- B. 4
- C. 5
- D. 6
Solve for x: 10x2 + 10x + 1 = 0
- A. -0.113, -0.887
- B. -0.331, -0.788
- C. -0.113, -0.788
- D. -0.311, -0.887
If 1/3 and -3/2 are roots of a quadratic equation, then the equation is
- A. 6x2 + 7x – 3 = 0
- B. 6x2 – 7x + 3 = 0
- C. 6x2 – 7x – 3 = 0
- D. 6x2 – 7x + 1 = 0
Which of the following is a root of this quadratic equation 30x2 + 49x + 20 = 0
- A. 0.6
- B. -0.6
- C. -0.8
- D. 0.75
What is the discriminant of the equation 4x2 = 8x – 5?
- A. 8
- B. -16
- C. 16
- D. -8
Given the equation 3x2 + 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
Find the term involving y5 in the expansion of (2x2 + y)10.
- A. 8064 x10y5
- B. 8046 x5y5
- C. 8046 x10y5
- D. 4680 x5y5
Find the 5th term of expansion of
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.
- A. 260 x8
- B. 5040 x8
- C. 210 x8
- D. 420 x8
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
What is the fourth term of the expansion of (x + x2)100?
- A. 1650 x103
- B. 161700 x103
- C. 167100 x103
- D. 167100 x100
What is the numerical coefficient of the term next to 495x8y4?
- A. 660
- B. 792
- C. 990
- D. 1100
Find the 6th term of expansion of
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.
- A.
- B.
- C.
- D.
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What is the coefficient of the term free of x of the expansion of (2x – 5y)4?
- A. 256
- B. 526
- C. 265
- D. 625
Find the 6th term of (3x – 4y)8?
- A. -148,288 x3y5
- B. -548 x2y5
- C. -154,288 x3y5
- D. -1,548,288 x3y5
What is the sum of the coefficients of the expansion (2x – 1)20?
- A. 0
- B. 1
- C. 2
- D. 3
What is the sum of the coefficients in the expansion (x + y – z)8?
- A. 0
- B. 1
- C. 2
- D. 3
Find the value of log8 48.
- A. 1.86
- B. 1.68
- C. 1.78
- D. 1.98
Evaluate the log6 845 = x
- A. 3.76
- B. 5.84
- C. 4.48
- D. 2.98
What is the value of log to base 10 of 10003.3?
- A.10.9
- B. 99.9
- C. 9.9
- D. 9.5
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
Find the value of log4 (log3 5).
- A.1.460
- B. 0.275
- C. 1.273
- D. 0.165
Given: log4 7 = n. Find
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- A. 1/n
- B. n
- C. -1/n
- D. –n
If loga 10 = 0.25, what is the value of log10 a?
- A. 2
- B. 4
- C. 6
- D. 8
Given logb y = 2x + logb x. Which of the following is true.
- A.
- B.
- C.
- D.
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
Log of the nth root of x equals log of x to 1/n power and also equal to
- A.
- B.
- C.
- D.
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Log (MN) is equal to:
- a. Log M – N
- B. Log M + N
- C. N log M
- D. Log M + Log N
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)
Given: logb 1024 = 5/2. Find b.
- A. 2560
- B. 16
- C. 4
- D. 2
Given: log3 (x2 – 8x) = 2. Find x.
- A. -1
- B. 9
- C. -1 and 9
- D. 1 and -9
Solve for the value of x in the following equation: x3logx = 100x
- A. 12
- b. 8
- C. 30
- D. 10
Given: log 6 + x log 4 = log 4 + log (32 + 4x). Find x.
- A. 2
- B. 3
- C. 4
- D. 6
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
Find the value of x if log12 x = 2
- A. 144
- B. 414
- C. 524
- D. 425
Solve for the value of x:
- A. 379.65
- B. 365.97
- C. 397.56
- D. 356.79
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