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

MCQs in Quadratic Equation, Binomial Theorem and Logarithms Part 1

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 1996

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

  • A. 5×2 + 3x – 2 = 0
  • B. 2×2 + 3x – 5 = 0
  • C. 3×2 – 3x +2 = 0
  • D. 2×2 + 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 = 9

  • A. ± 2
  • B. ± 3
  • C. ± 4
  • D. ± 5

Problem 4: ME Board October 1996

Solve for x that satisfies the equation 6×2 – 7x – 5 = 0

  • A. clip_image002[13]
  • B. clip_image004[12]
  • C. clip_image006[12]
  • D. clip_image008[12]

Problem 5: EE Board October 1997

Find the values of x in the equation 24×2 + 5x – 1 = 0

  • A. clip_image002[15]
  • B. clip_image004[14]
  • C. clip_image006[14]
  • D. clip_image008[14]

Problem 6: EE Board October 1990

Determine k so that the equation 4×2 + 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: 10×2 + 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. 6×2 + 7x – 3 = 0
  • B. 6×2 – 7x + 3 = 0
  • C. 6×2 – 7x – 3 = 0
  • D. 6×2 – 7x + 1 = 0

Problem 9:

Which of the following is a root of this quadratic equation 30×2 + 49x + 20 = 0

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

Problem 10:

What is the discriminant of the equation 4×2 = 8x – 5?

  • A. 8
  • B. -16
  • C. 16
  • D. -8

Problem 11:

Given the equation 3×2 + 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

Problem 12:

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

  • A. 8064 x10y5
  • B. 8046 x5y5
  • C. 8046 x10y5
  • D. 4680 x5y5

Problem 13:

Find the 5th term of expansion of

clip_image018[4].

  • A. 260 x8
  • B. 5040 x8
  • C. 210 x8
  • D. 420 x8

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. 1650 x103
  • B. 161700 x103
  • C. 167100 x103
  • D. 167100 x100

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 expansion of

clip_image020[4].

  • A. clip_image002[17]
  • B. clip_image004[16]
  • C. clip_image006[16]
  • D. clip_image008[16]

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 10003.3?

  • 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

clip_image030[4]

  • A. 1/n
  • B. n
  • C. -1/n
  • D. –n

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

If loga 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 logb y = 2x + logb x. Which of the following is true.

  • A. clip_image002
  • B. clip_image004
  • C. clip_image006
  • D. clip_image008

Problem 130: 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. clip_image002[4]
  • B. clip_image004[4]
  • C. clip_image006[4]
  • D. clip_image008[4]

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: x3logx = 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 + 4x). 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:

clip_image048

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