MCQ in Quadratic Equation, Binomial Theorem and Logarithms Part 1 | Math Board Exam

MASTER YOUR MATH BOARD EXAM: Power Through Quadratic Equations, Binomial Theorem & Logarithms

DOMINATE these critical Engineering Mathematics topics with our comprehensive MCQ collection!

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Multiple Choice Questions Topic Outline

MCQ in Basic Rules in Quadratic Formula | MCQ in Nature of Roots | MCQ 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 | MCQ in Sum of Exponents | MCQ in Common and Natural Logarithms | MCQ in Euler’s Number | MCQ in Binary Logarithms | MCQ in Properties of Logarithms

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each question.

Problem 1: ECE Board March 1996

The equation whose roots are the reciprocals 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

Problem 2: EE Board October 1993

In the equation x² + x = 0, one root is x equal to

A. 1

B. 5

C. ¼

D. None of these

Problem 3: ECE Board April 1990

Solve for the value of “a” in the equation a⁸ – 17a⁴ + 16 = 0

A. ± 2

B. ± 3

C. ± 4

D. ± 5

Problem 4: ME Board October 1996

Solve for x that satisfies the equation 6x² – 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

Problem 5: EE Board October 1997

Find the values of x in the equation 24x² + 5x – 1 = 0

A. (1/6, 1)

B. (1/6, 1/5)

C. (1/2, 1/5)

D. (1/8, -1/3)

Problem 6: EE Board October 1990

Determine k so that the equation 4x² + kx + 1 = 0 will have just one real solution.

A. 3

B. 4

C. 5

D. 6

Problem 7: ME Board April 1996

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

Problem 8:

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

Problem 9:

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

Problem 10:

What is the discriminant of the equation 4x² = 8x – 5?

A. 8

B. -16

C. 16

D. -8

Problem 11:

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

Problem 12:

Find the term involving y⁵ in the expansion of (2x² + y)¹⁰.

A. 8064x¹⁰y⁵

B. 8046x⁵y⁵

C. 8046x¹⁰y⁵

D. 4680x⁵y⁵

Problem 13:

Find the 5th term of the expansion of (x² +1/x)¹⁰

A. 260x⁸

B. 5040x⁸

C. 210x⁸

D. 420x⁸

Problem 14: ECE Board April 1998

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

Problem 15:

What is the fourth term of the expansion of (x + x²)¹⁰⁰?

A. 1650x¹⁰³

B. 161700x¹⁰³

C. 167100x¹⁰³

D. 167100x¹⁰⁰

Problem 16:

What is the numerical coefficient of the term next to 495x⁸y⁴?

A. 660

B. 792

C. 990

D. 1100

Problem 17: CE Board November 1996

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

A. – 66939/256a¹¹

B. – 66339/128a¹¹

C. – 33669/256a¹¹

D. – 39396/128a¹¹

Problem 18:

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

Problem 19:

Find the 6th term of (3x – 4y)⁸?

A. -148,288 x³y⁵

B. -548 x²y⁵

C. -154,288 x³y⁵

D. -1,548,288 x³y⁵

Problem 20: ECE Board November 1995

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

A. 0

B. 1

C. 2

D. 3

Problem 21: ECE Board April 1995

What is the sum of the coefficients in the expansion (x + y – z)⁸?

A. 0

B. 1

C. 2

D. 3

Problem 22: CE Board November 1993, ECE Board November 1993

Find the value of log₈ 48.

A. 1.86

B. 1.68

C. 1.78

D. 1.98

Problem 23: CE Board November 1997

Evaluate the log₆ 845 = x

A. 3.76

B. 5.84

C. 4.48

D. 2.98

Problem 24: ME Board April 1997

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

A.10.9

B. 99.9

C. 9.9

D. 9.5

Problem 25: ECE Board April 1998

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

Problem 26:

Find the value of log₄ (log₃ 5).

A.1.460

B. 0.275

C. 1.273

D. 0.165

Problem 27:

Given: log₄ 7 = n. Find log₄ 1/7.

A. 1/n

B. n

C. -1/n

D. –n

Problem 28: CE Board November 1992, CE Board May 1994

If log_a 10 = 0.25, what is the value of log₁₀ a?

A. 2

B. 4

C. 6

D. 8

Problem 29: ECE Board November 1995

Given log_b y = 2x + log_b x. Which of the following is true?

A. y = b^2x

B. y = 2xb

C. y = 2x/b

D. y = xb^2x

Problem 30: ME Board October 1996

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

Problem 31: ME Board April 1996

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

A. (log x)/n

B. nlog x

C. {log (x to the 1/n power)}/n

D. (n -1) log x

Problem 32: ECE Board November 1990

Log (MN) is equal to:

a. Log M – N

B. Log M + N

C. N log M

D. Log M + Log N

Problem 33: ME Board 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 34: ECE Board November 1991

Given: logb 1024 = 5/2. Find b.

A. 2560

B. 16

C. 4

D. 2

Problem 35:

Given: log₃ (x² – 8x) = 2. Find x.

A. -1

B. 9

C. -1 and 9

D. 1 and -9

Problem 36: ECE Board November 1991

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

A. 12

b. 8

C. 30

D. 10

Problem 37: EE Board October 1992

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

A. 2

B. 3

C. 4

D. 6

Problem 38: ECE Board November 1998

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

Problem 39: ME Board October 1997

Find the value of x if log₁₂ x = 2

A. 144

B. 414

C. 524

D. 425

Problem 40:

Solve for the value of x:

log 2x³ + log 6/x = 6.278

A. 379.65

B. 365.97

C. 397.56

D. 356.79

Online Questions and Answers in Quadratic Equation, Binomial Theorem and Logarithms Series

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