This is the Multiples Choice Questions Part 3 of the Series in System of Numbers and Conversion 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 Systems of Numbers | MCQs in Cardinal and Ordinal Numbers | MCQs in Numerals and Digit | MCQs in Real Numbers | MCQs in Imaginary Number | MCQs in Complex Number | MCQs in Fractions | MCQs in Composite Numbers | MCQs in Prime Numbers | MCQs in Perfect Number | MCQs in Defective and Abundant Numbers | MCQs in Amicable Numbers | MCQs in Factorial | MCQs in Significant Figures | MCQs in Rounding and Truncation

### Online Questions and Answers in System of Numbers and Conversion Series

Following is the list of multiple choice questions in this brand new series:

**System of Numbers and Conversion MCQs**

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

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART II**

**MCQs from Number 101 – 150**Answer key:

**PART III**

### Continue Practice Exam Test Questions Part III of the Series

**Choose the letter of the best answer in each questions.**

**Problem 101 (CE May 1994)**

In the complex number 3 + 4i, the absolute value is:

- A. 10
- B. 7.211
- C. 5
- D. 5.689

**Problem 102**

In the complex number 8-21, the amplitude is:

- A. 104.04°
- B. 14.04°
- C. 345.96°
- D. 165.96°

**Problem 103**

(6 cis 120°)(4 cis 30°) is equal to:

- A. 10 cis 150°
- B. 24 cis 150°
- C. 10 cis 90°
- D. 24 cis 90°

**Problem 104**

((20 cis 80°)/(10 cis 50°)) is equal to:

- A. 20 cis 30°
- B. 3 cis 130°
- C. 3 cis 30°
- D. 20 cis130°

**Problem 105**

The value of x + y in the complex equation 3 + xi = y + 2i is:

- A. 5
- B. 1
- C. 2
- D. 3

**Problem 106**

Multiply (3-2i)(4+3i).

- A. 12 + i
- B. 18 + i
- C. 6 + i
- D. 20 + i

**Problem 107 (EE October 1997)**

Divide ((4 + 3*i*)/(2 – *i*)).

- A. ((11 + 10
*i*)/5) - B. 1 + 2
*i* - C. ((5 + 2
*i*)/5) - D. 2 + 2
*i*

**Problem 108**

Find the value of i^{9}.

- A. i
- B. –i
- C. 1
- D. -1

**Problem 109 (ECE April 1999)**

Simplify i^{1997}+ i^{1999}, where I is an imaginary number.

- A. 1 + i
- B. I
- C. 1 – i
- D. 0

**Problem 110**

Expand (2 + √-9)^{3}

- A. 46 + 9i
- B. 46 - 9i
- C. –46 - 9i
- D. –46 + 9i

**Problem 111**

Write –4 + 3i in polar form.

- A. 5Ô¼36.87°
- B. 5Ô¼216.87°
- C. 5Ô¼323.13°
- D. 5Ô¼143.13°

**Problem 112**

Simplify: i^{30} – 2i^{25 }+ 3i^{17}.

- A. I + 1
- B. –1 - 2i
- C. –1 + i
- D. –1 + 5i

**Problem 113 (ME April 1997)**

Evaluate the value of √(-10) ● √(-7).

- A. Imaginary
- B. -√70
- C. √17
- D. √70

**Problem 114 (EE April 1994)**

Perform the indicated operation: √(-9) ● ^{3}√(-343).

- A. 21
- B. 21i
- C. -21i
- D. -21

**Problem 115 (ECE April 1999)**

What is the quotient when 4 + 8i is divided by i^{3}?

- A. 8 + 4i
- B. –8 + 4i
- C. 8 – 4i
- D. –8 - 4i

**Problem 116**

What is the exponential form of the complex number 4 + 3i?

- A. 5e
^{i53.13°} - B. 5e
^{i36.87°} - C. 7e
^{i53.13°} - D. 7e
^{i36.87°}

**Problem 117**

What is the algebraic form of the complex number 13e^{i67.38°}?

- A. 12 + 5i
- B. 5 – 12i
- C. 12 – 5i
- D. 5 + 12i

**Problem 118 (ME April 1998)**

Solve for x that satisfy the equation x^{2 }+ 36 = 9 – 2x^{2}.

- A. ±6i
- B. ±3i
- C. 9i
- D. -9i

**Problem 119**

Evaluate ln (5 + 12i).

- A. 2.565 + 1.176i
- B. 2.365 – 0.256i
- C. 5.625 + 2.112i
- D. 3.214 – 1.254i

**Problem 120 (EE April 1994)**

Add the given vectors: (-4, 7) + (5, -9)

- A. (1, 16)
- B. (1, -2)
- C. (9, 2)
- D. (1, 2)

**Problem 121 (EE April 1994)**

Find the length of vector (2, 1,1).

- A. √17
- B. √21
- C. √20
- D. √19

**Problem 122 (ECE November 1997)**

Find the length of the vector (2, 4, 4).

- A. 8.75
- B. 6.00
- C. 7.00
- D. 5.18

**Problem 123**

If a = b and b = c, then a = c. This property of real numbers is known as:

- A. Reflexive Property
- B. Symmetric Property
- C. Transitive Property
- D. Addition Property

**Problem 124**

If a = b, then b = a. This property of real numbers is known as:

- A. Reflexive Property
- B. Symmetric Property
- C. Transitive Property
- D. Multiplication Property

**Problem 125**

A statement the truth of which is admitted without proof is called:

- A. An axiom
- B. A postulate
- C. A theorem
- D. A corollary

**Problem 126**

In a proportion of four quantities, the first and the fourth terms are referred to:

- A. means
- B. denominators
- C. extremes
- D. numerators

**Problem 127 (ECE November 1997)**

Convergent series is a sequence of decreasing numbers or when the succeeding term is ____ than the preceding term.

- A. ten times more
- B. greater
- C. equal
- D. lesser

**Problem 128 (ECE November 1997)**

It is the characteristics of a population which is measurable.

- A. Frequency
- B. Distribution
- C. Sample
- D. Parameter

**Problem 129 (ECE November 1997)**

The quartile deviation is a measure of:

- A. Division
- B. Central tendency
- C. Certainty
- D. Dispersion

**Problem 130 (ECE November 1995, 1997)**

In complex algebra, we use a diagram to represent a complex plane commonly called:

- A. De Moivre’s Diagram
- B. Funicular Diagram
- C. Argand Diagram
- D. Venn Diagram

**Problem 131**

A series of numbers which are perfect square numbers (i.e. 1, 4, 9, 16, …) is called:

- A. Fourier series
- B. Fermat’s series
- C. Euler’s series
- D. Fibonacci numbers

**Problem 132**

A sequence of numbers where every term is obtained by adding all the preceding terms such as 1, 5, 14, 30… Is called:

- A. Triangular number
- B. Pyramidal number
- C. Tetrahedral number
- D. Euler’s number

**Problem 133 (ECE November 1995)**

The graphical representation of the commulative frequency distribution in a set of statistical data is called:

- A. Ogive
- B. Histogram
- C. Frequency polyhedron
- D. Mass diagram

**Problem 134 (ECE March 1996)**

A sequence of numbers where the succeeding term is greater than the preceding term is called:

- A. Dissonant series
- B. Convergent series
- C. Isometric series
- D. Divergent series

**Problem 135 (ECE March 1996)**

The number 0.123123123…. is

- A. Irrational
- B. Surd
- C. Rational
- D. Transcendental

**Problem 136 (ECE November 1996)**

An array of m x n quantities which represent a single number system composed of elements in rows and columns is know as:

- A. Transpose of a matrix
- B. Determinant
- C. Co-factor of a matrix
- D. Matrix

**Problem 137**

If equals are added to equals, the sum is equal.

- A. theorem
- B. postulate
- C. axiom
- D. corollary

**Problem 138 (ECE November 1996)**

Terms that differ only in numeric coefficients are known as:

- A. unequal terms
- B. unlike terms
- C. like terms
- D. equal terms

**Problem 139 (ECE November 1996)**

______ is a sequence of terms whose reciprocals are in arithmetic progression.

- A. Geometric progression
- B. Harmonic progression
- C. Algebraic Progression
- D. Ratio and proportion

**Problem 140 (ECE November 1996)**

The logarithm of a number to the base e (2.718281828…) is called:

- A. Naperian logarithm
- B. Characteristic
- C. Mantissa
- D. Briggsian logarithm

**Problem 141 (ECE November 1996)**

The ratio or product of two expressions in direct or inverse relation of the other is called:

- A. Ratio and proportion
- B. Constant variation
- C. Means
- D. Extremes

**Problem 142 (ECE November 1996)**

In any square matrix, when the elements of any two rows are the same the determinant is:

- A. Zero
- B. Positive integer
- C. Negative integer
- D. Unity

**Problem 143 (ECE November 1996)**

Two or more equations are equal if and only if they have the same

- A. Solution set
- B. Degree
- C. Order
- D. Variable set

**Problem 144**

What is the possible outcome of an experiment called?

- A. a sample space
- B. a random point
- C. an event
- D. a finite set

**Problem 145**

If the roots of an equation are zero, then they are classified as:

- A. Trivial solutions
- B. Extraneous roots
- C. Conditional solutions
- D. Hypergolic Solutions

**Problem 146**

A complex number associated with a phase-shifted sine wave in polar form whose magnitude is in RMS and angle is equal to the angle of the phase-shifted sine wave is known as:

- A. Argand’s number
- B. Imaginary number
- C. Phasor
- D. Real number

**Problem 147**

In raw data, the term, which occurs most frequently, is known as:

- A. Mean
- B. Median
- C. Mode
- D. Quartile

**Problem 148**

Infinity minus infinity is:

- A. Infinity
- B. Zero
- C. Indeterminate
- D. None of these

**Problem 149**

Any number divided by infinity is equal to:

- A. I
- B. Infinity
- C. Zero
- D. Indeterminate

**Problem 150**

The term in between any two terms of an arithmetic progression is called:

- A. Arithmetic mean
- B. Median
- C. Middle terms
- D. Mean

**Problem 151**

Any equation which, because of some mathematical process, has acquired an extra root is sometimes called a:

- A. Redundant equation
- B. Literal equation
- C. Linear equation
- D. Defective equation

**Problem 152**

A statement that one mathematical expression is greater than or less than another is called:

- A. inequality
- B. non-absolute condition
- C. absolute condition
- D. conditional expression

**Problem 153**

A relation, in which every ordered pair (x, y) has one and only one value of y that corresponds to the values of x, is called:

- A. Function
- B. Range
- C. Domain
- D. Coordinates

**Problem 154**

An equation in which a variable appears under the radical sign is called:

- A. Literal equation
- B. Radical equation
- C. Irradical equation
- D. Irrational equation

**Problem 155**

The number of favorable outcomes divided by the number of possible outcomes:

- A. Permutations
- B. Probability
- C. Combination
- D. Chance

**Problem 156**

Two factors are considered essentially the same if:

- A. One is merely the negative of the other
- B. One is exactly the same of the other
- C. Both of them are negative
- D. Both of them are positive

**Problem 157**

An integer is said to be prime if:

- A. It is factorable by any value
- B. It is an odd integer
- C. It has no other integer as factor excepts itself or 1
- D. It is an even integer

**Problem 158**

Equations in which the members are equal for all permissible values of integer are called:

- A. a conditional equation
- B. an identity
- C. a parametric equation
- D. a quadratic equation

**Problem 159**

Equations which satisfy only for some values of unknown are called:

- A. a conditional equation
- B. an identity
- C. a parametric equation
- D. a quadratic equation

**Problem 160 (ME April 1996)**

The logarithm of 1 to any base is:

- A. indeterminate
- B. zero
- C. infinity
- D. one

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