MCQ in Quadratic Equation, Binomial Theorem and Logarithms Part 2 | ECE Board Exam

(Last Updated On: February 6, 2020)

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

• MCQ in Basic Rules in Quadratic Formula | MCQ in Nature of Roots | MCQs in Properties of Roots | MCQ in Binomial Theorem | MCQ in Properties of Expansion | MCQ in Pascal’s Triangle | MCQ in Coefficient of any term | MCQ in Formula for rth term | MCQ in Sum of Coefficients | MCQs in Sum of Exponents | MCQs in Common and Natural Logarithms | MCQ in Euler’s Number | MCQs in Binary Logarithms | MCQ in Properties of Logarithms

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 + 4x)

• 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 log5.21000 = 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 loga2187 = 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

((logxy)/logyx)) is equal to:

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

Problem 58

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

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

Problem 59

Find the value of log(aa)a.

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

Problem 60

Solve for x: x = logb a ∙ logc d ∙ logd c

• A. logb a
• B. loga c
• C. logb c
• D. logd a

Problem 61

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

• A. 2
• B. 4
• C. 6
• D. 8

Problem 62

Find x if logx 27 + logx 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 10003.3?

• A. 9.9
• B. 99.9
• C. 10.9
• D. 9.5

Problem 73

If logx 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 (ex/ex – 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 6th 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 5th term is.

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

Problem 83

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

• A. -70×8
• B. 70×8
• C. -5760×8
• D. 5760×8

Problem 84

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

• A. 25434×9
• B. 52344×9
• C. 25344×9
• D. 23544×9

Problem 85

The constant term in the expansion of ( x + (1/x3/2)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 3×2 + 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 2×2 – 3x – 5 = 0 is:

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

Problem 96 (ECE November 1997)

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

• A. 12×2 + 7x + 1 = 0
• B. 12×2 + 7x – 1 = 0
• C. 12×2 – 7x + 1 = 0
• D. 12×2 – 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 4×2 + 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

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