MCQs in Quadratic Equation, Binomial Theorem and Logarithms Part II

This is the Multiples Choice Questions Part 2 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 51

If ((log₁₀x)/(1 – log₁₀2)) = 2, what is the value of z?

• A. ¼
• B. 25
• C. 4
• D. 5

Problem 52 (EE October 1992)

Solve for x: log 6 + x log 4 = log 4 + log (32 + 4^x)

• A. 1
• B. 2
• C. 3
• D. 4

Problem 53

Which of the following cannot be used as a base of a system of logarithm?

• A. e
• B. 10
• C. 2
• D. 1

Problem 54

If log_5.21000 = x, what is the value of x?

• A. 4.19
• B. 5.23
• C. 3.12
• D. 4.69

Problem 55

Find the value of a in the equation log_a2187 = 7/2.

• A. 3
• B. 6
• C. 9
• D. 12

Problem 56

If log 2 = x and log 3 = y, find log 1.2.

• A. 2x + y
• B. 2xy/10
• C. 2x + y – 1
• D. xy - 1

Problem 57

((logx^y)/logy^x)) is equal to:

• A. x^y/y^x
• B. y log x – x log y
• C. (y log x)/(x log y)
• D. 1

Problem 58

If 10^ax+b = P, what is the value of x?

• A. (1/a)(log P-b)
• B. (1/a) log ( P-b)
• C. (1/a) P^10-b
• D. (1/a) log P¹⁰

Problem 59

Find the value of log(a^a)^a.

• A. 2a log a
• B. a² log a
• C. a log a²
• D. (a log a)^a

Problem 60

Solve for x: x = log_b a ∙ log_c d ∙ log_d c

• A. log_b a
• B. log_a c
• C. log_b c
• D. log_d a

Problem 61

Find the positive value of x if log_x 36 = 2.

• A. 2
• B. 4
• C. 6
• D. 8

Problem 62

Find x if log_x 27 + log_x 3 = 2.

• A. 9
• B. 12
• C. 8
• D. 7

Problem 63

Find a if log₂ (a+2) + log₂ (a-2) = 5

• A. 2
• B. 4
• C. 6
• D. 8

Problem 64

Solve for x if log₅ x = 3.

• A. 115
• B. 125
• C. 135
• D. 145

Problem 65

Find log P if ln P = 8.

• A. 2980.96
• B. 2542.33
• C. 3.47
• D. 8.57

Problem 66

If log₈ x = -n, then x is equal to:

• A. 8ⁿ
• B. 1/8^-n
• C. 1/8ⁿ
• D. 81/n

Problem 67

If 3 log₁₀ x – log₁₀ y = 0, find y in terms of x.

• A. y = ³√x
• B. y = √x³
• C. y = x³
• D. y = x

Problem 68

Which of the following is correct?

• A. -2 log 7 = 1/49
• B. log₇ (-2) = 1/49
• C. log₇ (1/49) = -2
• D. log₇ (1/49) = 2

Problem 69 (ME April 1996)

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

• A. (log (x))/n
• B. n log (x)
• C. (log (x)^1/n)/n
• D. (n-1) log (x)

Problem 70 (ME April 1996)

What is the natural logarithm of e to the xy power?

• A. 1/xy
• B. 2.718/xy
• C. xy
• D. 2.718xy

Problem 71 (ME April 1997)

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)

Problem 72 (ME April 1997)

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

• A. 9.9
• B. 99.9
• C. 10.9
• D. 9.5

Problem 73

If log_x 2 + log² x = 2, then the value of x is:

• A. 1
• B. 2
• C. 3
• D. 4

Problem 74 (CE November 1997)

Log₆ 845 =?

• A. 4.348
• B. 6.348
• C. 5.912
• D. 3.761

Problem 75 (CE May 1998, similar with November 1998)

The logarithms of the quotient and the product of two numbers are 0.352182518 and 1.556302501, respectively. Find the first number?

• A. 9
• B. 10
• C. 11
• D. 12

Problem 76

The sum of two logarithms of two numbers is 1.748188 and the difference of their logarithms is -0.0579919. One of the numbers is:

• A. 9
• B. 6
• C. 8
• D. 5

Problem 77 (CE November 199)

Solve for y: y = ln (e^x/e^{x – 2}).

• A. 2
• B. x
• C. -2
• D. x – 2

Problem 78 (ECE April 1998)

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

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

Problem 79 (ME October 1997)

The logarithm of negative number is:

• A. irrational number
• B. real number
• C. imaginary number
• D. complex number

Problem 80 (ME April 1998)

38.5 to the x power = 6.5 to the x – 2 power, solve for x using logarithms.

• A. 2.70
• B. 2.10
• C. -2.10
• D. -2.02

Problem 81 (CE November 1996)

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

• A. –(22113/256a¹¹)
• B. –(66339/128a¹¹)
• C. –(22113/128a¹¹)
• D. –(66339/256a¹¹)

Problem 82 (ECE April 1998)

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

• A. 253440
• B. 126720
• C. 63360
• D. 506880

Problem 83

The middle term in the expansion of (x² – 3)⁸ is:

• A. -70x⁸
• B. 70x⁸
• C. -5760x⁸
• D. 5760x⁸

Problem 84

The term involving x⁹ in the expansion of (x² + 2/x)¹² is:

• A. 25434x⁹
• B. 52344x⁹
• C. 25344x⁹
• D. 23544x⁹

Problem 85

The constant term in the expansion of ( x + (1/x^3/2)¹⁵ is:

• A. 3003
• B. 5005
• C. 6435
• D. 7365

Problem 86

Find the sum of the coefficients in the expansion of (x + 2y – z)⁸.

• A. 256
• B. 1024
• C. 1
• D. 6

Problem 87

Find the sum of the coefficients in the expansion of (x + 2y + z) ⁴ (x + 3y) ⁵ is:

• A. 524288
• B. 65536
• C. 131072
• D. 262 144

Problem 88 (ECE April 1995)

What is the sum of the coefficients in the expansion of (x + y -z) ⁸ is:

• A. less than 2
• B. above 10
• C. from 2 to 5
• D. from 5 to 10

Problem 89 (ECE November 1995)

What is the sum of the coefficients of the expansion of (2x -1)²⁰?

• A. 1
• B. 0
• C. 215
• D. 225

Problem 90

In the quadratic equation Ax² + Bx + C = 0, the product of the roots is:

• A. C/A
• B. –B/A
• C. –C/A
• D. B/A

Problem 91

If ¼ and -7/2 are the roots of the quadratic equation Ax² + Bx + C = 0, what is the value of B?

• A. -28
• B. 4
• C. -7
• D. 26

Problem 92

In the equation 3x² + 4x + (2h – 5) = 0, find h if the product of the roots is 4.

• A. -7/2
• B. -10/2
• C. 17/2
• D. 7/2

Problem 93

If the roots of ax² + bx + c = 0, are u and v, then the roots of cx² + bx + a = 0 are:

• A. u and v
• B. –u and v
• C. 1/u and 1/v
• D. -1/u and -1/v

Problem 94

If the roots of the quadratic equation ax² + bx + c = 0 are 3 and 2 and a, b, and c are all whole numbers, find a + b + c.

• A. 12
• B. -2
• C. 2
• D. 6

Problem 95 (ECE March 1996)

The equation whose roots are the reciprocals of the roots of 2x² – 3x – 5 = 0 is:

• A. 5x² + 3x – 2 = 0
• B. 3x² – 5x – 3 = 0
• C. 5x² – 2x – 3 = 0
• D. 2x² – 5x -3 = 0

Problem 96 (ECE November 1997)

The roots of a quadratic equation are 1/3 and ¼. What is the equation?

• A. 12x² + 7x + 1 = 0
• B. 12x² + 7x – 1 = 0
• C. 12x² – 7x + 1 = 0
• D. 12x² – 7x – 1 = 0

Problem 97

Find k so that the expression kx² – 3kx + 9 is a perfect square.

• A. 3
• B. 4
• C. 12
• D. 6

Problem 98 (EE October 1990)

Find k so that 4x² + kx + 1 = 0 will only have one real solution.

• A. 1
• B. 4
• C. 3
• D. 2

Problem 99

The only root of the equation x² – 6x + k = 0 is:

• A. 3
• B. 2
• C. 6
• D. 1

Problem 100

Two engineering students are solving a problem leading to a quadratic equation. One student made a mistake in the coefficient of the first-degree term, got roots of 2 and -3. The other student made a mistake in the coefficient of the constant term got roots of -1 and 4. What is the correct equation?

• A. x² – 6x – 3 = 0
• B. x² + 6x + 3 = 0
• C. x² + 3x + 6 = 0
• D. x² – 3x – 6 = 0

---