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# MCQ in System of Numbers and Conversion Part 3 | ECE Board Exam

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

• MCQ in Systems of Numbers | MCQ in Cardinal and Ordinal Numbers | MCQ in Numerals and Digit | MCQ in Real Numbers | MCQ in Imaginary Number | MCQ in Complex Number | MCQ in Fractions | MCQ in Composite Numbers | MCQs in Prime Numbers | MCQ in Perfect Number | MCQs in Defective and Abundant Numbers | MCQ in Amicable Numbers | MCQ in Factorial | MCQ in Significant Figures | MCQ in Rounding and Truncation

#### Continue Practice Exam Test Questions Part 3 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. 104.04ยฐ
• B. 14.04ยฐ
• C. 345.96ยฐ
• D. 165.96ยฐ

Problem 103

(6 cis 120ยฐ)(4 cis 30ยฐ) is equal to:

• A. 10 cis 150ยฐ
• B. 24 cis 150ยฐ
• C. 10 cis 90ยฐ
• D. 24 cis 90ยฐ

Problem 104

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

• A. 20 cis 30ยฐ
• B. 3 cis 130ยฐ
• C. 3 cis 30ยฐ
• D. 20 cis130ยฐ

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 + 3i)/(2 โ i)).

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

Problem 108

Find the value of i9.

• A. i
• B. โi
• C. 1
• D. -1

Problem 109 (ECE April 1999)

Simplify i1997+ i1999, where I is an imaginary number.

• A. 1 + i
• B. I
• C. 1 โ i
• D. 0

Problem 110

Expand (2 + โ-9)3

• A. 46 + 9i
• B. 46 – 9i
• C. โ46 – 9i
• D. โ46 + 9i

Problem 111

Write โ4 + 3i in polar form.

• A. 5ิผ36.87ยฐ
• B. 5ิผ216.87ยฐ
• C. 5ิผ323.13ยฐ
• D. 5ิผ143.13ยฐ

Problem 112

Simplify: i30 โ 2i25 + 3i17.

• A. I + 1
• B. โ1 – 2i
• C. โ1 + i
• D. โ1 + 5i

Problem 113 (ME April 1997)

Evaluate the value of โ(-10) โ โ(-7).

• A. Imaginary
• B. -โ70
• C. โ17
• D. โ70

Problem 114 (EE April 1994)

Perform the indicated operation: โ(-9) โ 3โ(-343).

• A. 21
• B. 21i
• C. -21i
• D. -21

Problem 115 (ECE April 1999)

What is the quotient when 4 + 8i is divided by i3?

• A. 8 + 4i
• B. โ8 + 4i
• C. 8 โ 4i
• D. โ8 – 4i

Problem 116

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

• A. 5ei53.13ยฐ
• B. 5ei36.87ยฐ
• C. 7ei53.13ยฐ
• D. 7ei36.87ยฐ

Problem 117

What is the algebraic form of the complex number 13ei67.38ยฐ?

• A. 12 + 5i
• B. 5 โ 12i
• C. 12 โ 5i
• D. 5 + 12i

Problem 118 (ME April 1998)

Solve for x that satisfy the equation x2 + 36 = 9 โ 2×2.

• A. ยฑ6i
• B. ยฑ3i
• C. 9i
• D. -9i

Problem 119

Evaluate ln (5 + 12i).

• A. 2.565 + 1.176i
• B. 2.365 โ 0.256i
• C. 5.625 + 2.112i
• D. 3.214 โ 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. โ17
• B. โ21
• C. โ20
• D. โ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

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 Moivreโ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, โฆ) is called:

• A. Fourier series
• B. Fermatโs series
• C. Eulerโ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, 30โฆ Is called:

• A. Triangular number
• B. Pyramidal number
• C. Tetrahedral number
• D. Eulerโ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 0.123123123โฆ. 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 (2.718281828โฆ) 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. Argandโ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
• 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

Problem 159

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

• A. a conditional equation
• B. an identity
• C. a parametric equation

Problem 160 (ME April 1996)

The logarithm of 1 to any base is:

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

### 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
PART 1: MCQs from Number 1 โ 50ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  Answer key: PART I
PART 2: MCQs from Number 51 โ 100ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  Answer key: PART II
PART 3: MCQs from Number 101 โ 150ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย ย  Answer key: PART III

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