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 Pascalโs 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 Eulerโs 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**

**MCQs from Number 1 โ 50**Answer key:

**PART I**

**MCQs from Number 51 โ 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 โ 3x โ 5 = 0** is,

- A. 5×2 + 3x โ 2 = 0
- B. 2×2 + 3x โ 5 = 0
- C. 3×2 โ 3x +2 = 0
- D. 2×2 + 5x โ 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. ยผ
- D. none of these

**Problem 3: ECE Board April 1990**

Solve for the value of โ**a**โ in the equation **a8 โ 17a4 + 16 = 9**

- A. ยฑ 2
- B. ยฑ 3
- C. ยฑ 4
- D. ยฑ 5

**Problem 4: ME Board October 1996**

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

**Problem 5: EE Board October 1997**

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

**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 โ 3 = 0
- B. 6×2 โ 7x + 3 = 0
- C. 6×2 โ 7x โ 3 = 0
- D. 6×2 โ 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 โ 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

- 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

**Problem 18:**

What is the coefficient of the term free of x of the expansion of **(2x โ 5y)4**?

- A. 256
- B. 526
- C. 265
- D. 625

**Problem 19:**

Find the **6th** term of **(3x โ 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 โ 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 โ 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

- A. 1/n
- B. n
- C. -1/n
- D. โn

**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.

**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

**Problem 32: ECE Board November 1990**

Log (MN) is equal to:

- a. Log M โ 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) โ log (y + z)**?

- A. log x + log y + log z
- B. log [x/(y + z)]
- C. log x โ log y โ 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 โ 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.
- 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:

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

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