Completing Statements MCQs for Sub-Topics of Topic 1: Numbers & Numeriacal Applications

Question 1. The set of counting numbers $\lbrace 1, 2, 3, \dots \rbrace$ is known as the set of _____ numbers.

(A) Whole

(B) Natural

(C) Integer

(D) Rational

Question 2. When zero is included with the natural numbers, the collection is called the set of _____ numbers.

(A) Integer

(B) Rational

(C) Whole

(D) Real

Question 3. The set $\lbrace \dots, -2, -1, 0, 1, 2, \dots \rbrace$ represents the _____.

(A) Natural Numbers

(B) Whole Numbers

(C) Integers

(D) Rational Numbers

Question 4. A number that can be expressed in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q \neq 0$, is called a _____ number.

(A) Irrational

(B) Real

(C) Integer

(D) Rational

Question 5. Numbers whose decimal expansion is non-terminating and non-recurring are called _____ numbers.

(A) Rational

(B) Irrational

(C) Integer

(D) Whole

Question 6. The collection of all rational and irrational numbers together is called the set of _____ numbers.

(A) Integer

(B) Natural

(C) Real

(D) Complex

Question 7. A number that has exactly two distinct factors (1 and itself) is called a _____ number.

(A) Composite

(B) Even

(C) Prime

(D) Odd

Question 8. A number that has more than two factors is called a _____ number.

(A) Prime

(B) Composite

(C) Natural

(D) Whole

Question 9. The smallest natural number is _____.

(A) 0

(B) 1

(C) -1

(D) 2

Question 10. The smallest whole number is _____.

(A) 1

(B) -1

(C) 0

(D) 2

Question 11. The smallest prime number is _____.

(A) 1

(B) 2

(C) 3

(D) 0

Question 12. The smallest composite number is _____.

(A) 2

(B) 3

(C) 4

(D) 6

Question 1. In the Indian System of Numeration, commas are placed after the hundreds place, then after every _____ digits.

(A) Three

(B) Two

(C) Four

(D) One

Question 2. In the International System of Numeration, commas are placed after every _____ digits from the right.

(A) Two

(B) Three

(C) Four

(D) Five

Question 3. In the decimal number system, the place value of a digit is ten times the place value of the digit to its _____.

(A) Right

(B) Left

(C) Above

(D) Below

Question 4. The face value of a digit in a number is the _____ of the digit itself.

(A) Place value

(B) Position

(C) Value

(D) Sum

Question 5. One lakh is equal to _____ thousand.

(A) 10

(B) 100

(C) 1000

(D) 10000

Question 6. One crore is equal to _____ million.

(A) 1

(B) 10

(C) 100

(D) 1000

Question 7. The Roman numeral XL represents _____.

(A) 60

(B) 40

(C) 90

(D) 110

Question 8. The general form of a 2-digit number with tens digit $a$ and units digit $b$ is _____.

(A) $a+b$

(B) $ab$

(C) $10a+b$

(D) $a \times b$

Question 9. The place value of the digit 3 in 12.345 is _____.

(A) Units

(B) Tenths

(C) Hundredths

(D) Thousandths

Question 10. In the number 5,555, the value of the leftmost 5 is _____ times the value of the rightmost 5.

(A) 10

(B) 100

(C) 1000

(D) 5000

Question 1. On a standard number line, negative numbers are located to the _____ of zero.

(A) Right

(B) Left

(C) Above

(D) Below

Question 2. To represent $\frac{2}{3}$ on the number line between 0 and 1, the segment must be divided into _____ equal parts.

(A) 2

(B) 3

(C) 5

(D) 6

Question 3. Representing irrational numbers like $\sqrt{2}$ on the number line often involves using the _____ theorem.

(A) Thales'

(B) Pythagoras'

(C) Euclid's

(D) Fundamental

Question 4. The technique of successively magnifying parts of the number line is used to visualize the location of numbers with _____ decimal expansions.

(A) Terminating

(B) Recurring

(C) Non-terminating non-recurring

(D) Any (for closer inspection)

Question 5. The point representing $-2.5$ on the number line is located between _____ and _____.

(A) -3 and -2

(B) -2 and -1

(C) 2 and 3

(D) 0 and -1

Question 6. To represent $\sqrt{5}$ on the number line starting from 0, you can construct a right triangle with legs of length 1 and _____.

(A) 1

(B) $\sqrt{2}$

(C) 2

(D) $\sqrt{3}$

Question 7. The number line is a complete representation of the _____ numbers.

(A) Rational

(B) Integer

(C) Real

(D) Irrational

Question 8. Between any two distinct rational numbers on the number line, there are infinitely many _____ numbers.

(A) Integer

(B) Natural

(C) Rational

(D) Whole

Question 9. Between any two distinct real numbers on the number line, there is always a _____ number.

(A) Integer

(B) Natural

(C) Real

(D) Whole

Question 10. To represent $\frac{-7}{4}$ on the number line, you would locate it between _____ and _____.

(A) -1 and 0

(B) -2 and -1

(C) 1 and 2

(D) -2 and 0

Question 1. For any two integers $a$ and $b$, if $a$ is to the right of $b$ on the number line, then $a$ is _____ $b$.

(A) Less than

(B) Greater than

(C) Equal to

(D) Opposite of

Question 2. The absolute value of a number is its _____ from zero on the number line.

(A) Position

(B) Sign

(C) Distance

(D) Value

Question 3. The value of $|-10|$ is _____.

(A) -10

(B) 10

(C) 0

(D) -|10|

Question 4. To compare two fractions with different denominators, one method is to find a _____ denominator.

(A) Numerator

(B) Common

(C) Smallest

(D) Largest

Question 5. Between 0 and 1, there are infinitely many _____ numbers.

(A) Integer

(B) Natural

(C) Rational

(D) Whole

Question 6. When comparing $0.45$ and $0.450$, they are _____.

(A) Equal

(B) Not equal

(C) $0.45$ is greater

(D) $0.450$ is greater

Question 7. For two negative integers, the one with the smaller value is the one located further to the _____ on the number line.

(A) Right

(B) Left

(C) Top

(D) Bottom

Question 8. To find a rational number between $\frac{1}{2}$ and $\frac{3}{4}$, you can calculate their _____.

(A) Sum

(B) Difference

(C) Product

(D) Average

Question 9. The inequality $|x| < 5$ represents all numbers $x$ whose distance from zero is less than _____.

(A) -5

(B) 0

(C) 5

(D) $|-5|$

Question 10. When comparing numbers written in scientific notation like $a \times 10^m$ and $b \times 10^n$, the primary factor to compare is the _____.

(A) Base ($a, b$)

(B) Exponent ($m, n$)

(C) Sign

(D) Sum of digits

Question 1. The result of adding 5 and -3 is _____.

(A) -2

(B) 2

(C) 8

(D) -8

Question 2. Subtracting a negative integer is equivalent to _____ a positive integer.

(A) Subtracting

(B) Multiplying

(C) Dividing

(D) Adding

Question 3. The product of $\frac{2}{5}$ and $\frac{1}{3}$ is _____.

(A) $\frac{3}{8}$

(B) $\frac{1}{5}$

(C) $\frac{2}{15}$

(D) $\frac{6}{5}$

Question 4. Dividing by a fraction is equivalent to multiplying by its _____.

(A) Numerator

(B) Denominator

(C) Reciprocal

(D) Inverse

Question 5. The sum of two irrational numbers can be either rational or _____.

(A) Integer

(B) Whole

(C) Irrational

(D) Natural

Question 6. According to the order of operations (BODMAS/PEMDAS), operations inside _____ are performed first.

(A) Exponents

(B) Multiplication

(C) Addition

(D) Brackets (Parentheses)

Question 7. The result of $10 \div 2 + 3 \times 4$ is _____.

(A) 17

(B) 23

(C) 19

(D) 32

Question 8. When multiplying decimals, the number of decimal places in the product is the _____ of the number of decimal places in the factors.

(A) Difference

(B) Product

(C) Sum

(D) Quotient

Question 9. The reciprocal of $\frac{-3}{7}$ is _____.

(A) $\frac{3}{7}$

(B) $\frac{7}{3}$

(C) $-\frac{7}{3}$

(D) $-\frac{3}{7}$

Question 10. The result of $5.25 \div 0.25$ is _____.

(A) 21

(B) 2.1

(C) 0.21

(D) 210

Question 1. The property $a+b = b+a$ is known as the _____ property of addition.

(A) Associative

(B) Commutative

(C) Distributive

(D) Identity

Question 2. The property $a(b+c) = ab + ac$ is known as the _____ property.

(A) Commutative

(B) Associative

(C) Distributive

(D) Closure

Question 3. The identity element for addition in real numbers is _____.

(A) 1

(B) -1

(C) 0

(D) Undefined

Question 4. The identity element for multiplication in real numbers is _____.

(A) 0

(B) -1

(C) 1

(D) Undefined

Question 5. For any non-zero real number $a$, its multiplicative inverse is _____.

(A) $-a$

(B) $\frac{1}{a}$

(C) $a^2$

(D) $-\frac{1}{a}$

Question 6. A number is divisible by 9 if the sum of its digits is divisible by _____.

(A) 3

(B) 6

(C) 9

(D) 18

Question 7. A number is divisible by 4 if the number formed by its last two digits is divisible by _____.

(A) 2

(B) 4

(C) 8

(D) 10

Question 8. The square of an odd number is always _____.

(A) Even

(B) Odd

(C) Prime

(D) Composite

Question 9. The sum of the first $n$ odd natural numbers is equal to _____.

(A) $n$

(B) $2n$

(C) $n^2$

(D) $n(n+1)$

Question 10. A number is divisible by 10 if its units digit is _____.

(A) 5

(B) 0

(C) Even

(D) Odd

Question 1. In the fraction $\frac{a}{b}$, $a$ is the numerator and $b$ is the _____.

(A) Denominator

(B) Quotient

(C) Remainder

(D) Dividend

Question 2. A fraction where the numerator is less than the denominator is called a _____ fraction.

(A) Improper

(B) Proper

(C) Mixed

(D) Unit

Question 3. Fractions that have the same value are called _____ fractions.

(A) Proper

(B) Improper

(C) Like

(D) Equivalent

Question 4. To reduce a fraction to its lowest terms, you divide the numerator and denominator by their _____.

(A) LCM

(B) Product

(C) Sum

(D) HCF

Question 5. Decimals that have a finite number of digits after the decimal point are called _____ decimals.

(A) Recurring

(B) Non-terminating

(C) Terminating

(D) Irrational

Question 6. Decimals that have the same number of digits after the decimal point are called _____ decimals.

(A) Unlike

(B) Equivalent

(C) Proper

(D) Like

Question 7. To convert a fraction to a decimal, you _____ the numerator by the denominator.

(A) Add

(B) Subtract

(C) Multiply

(D) Divide

Question 8. The mixed number $2 \frac{3}{4}$ is equivalent to the improper fraction _____.

(A) $\frac{9}{4}$

(B) $\frac{11}{4}$

(C) $\frac{6}{4}$

(D) $\frac{10}{4}$

Question 9. The decimal equivalent of $\frac{3}{5}$ is _____.

(A) 0.3

(B) 0.5

(C) 0.6

(D) 0.8

Question 10. The fraction form of 0.25 is _____ in simplest terms.

(A) $\frac{25}{100}$

(B) $\frac{1}{4}$

(C) $\frac{5}{20}$

(D) $\frac{1}{25}$

Question 1. The decimal expansion of a rational number is either terminating or non-terminating and _____.

(A) Non-recurring

(B) Recurring

(C) Finite

(D) Infinite

Question 2. The decimal expansion of an irrational number is always non-terminating and _____.

(A) Recurring

(B) Repeating

(C) Non-recurring

(D) Terminating

Question 3. The fraction $\frac{1}{7}$ has a _____ decimal expansion.

(A) Terminating

(B) Non-terminating recurring

(C) Non-terminating non-recurring

(D) Integer

Question 4. The decimal expansion of $\frac{3}{8}$ is _____.

(A) $0.375$ (terminating)

(B) $0.38$ (terminating)

(C) $0.\overline{375}$ (recurring)

(D) $0.83$ (terminating)

Question 5. To express a non-terminating recurring decimal in $\frac{p}{q}$ form, you typically use equations involving powers of _____ and subtraction.

(A) 2

(B) 5

(C) 10

(D) Any integer

Question 6. The $\frac{p}{q}$ form of $0.\overline{6}$ is _____.

(A) $\frac{6}{10}$

(B) $\frac{6}{9} = \frac{2}{3}$

(C) $\frac{6}{100}$

(D) $\frac{1}{6}$

Question 7. The process of converting a denominator with a radical (like $\sqrt{3}$) into a rational number is called _____ the denominator.

(A) Simplifying

(B) Reducing

(C) Rationalizing

(D) Multiplying

Question 8. The rationalized form of $\frac{1}{\sqrt{5}}$ is _____.

(A) $\frac{1}{5}$

(B) $\frac{\sqrt{5}}{5}$

(C) $\sqrt{5}$

(D) $\frac{5}{\sqrt{5}}$

Question 9. For a fraction in simplest form, its decimal expansion is terminating if the prime factors of the denominator are only _____ and/or _____.

(A) 2, 3

(B) 3, 5

(C) 2, 5

(D) Any prime numbers

Question 10. The number $0.232332333...$ is an example of a non-terminating _____ decimal.

(A) Recurring

(B) Repeating

(C) Non-recurring

(D) Terminating

Question 1. A number that divides another number exactly, leaving no remainder, is called a _____.

(A) Multiple

(B) Factor

(C) Quotient

(D) Divisor

Question 2. A number obtained by multiplying a given number by an integer is called a _____ of the given number.

(A) Factor

(B) Prime

(C) Multiple

(D) Composite

Question 3. A number is divisible by 6 if it is divisible by both 2 and _____.

(A) 3

(B) 4

(C) 5

(D) 8

Question 4. A prime number has exactly _____ factors.

(A) One

(B) Two

(C) Three

(D) More than two

Question 5. A composite number has _____ than two factors.

(A) Less

(B) Exactly

(C) More

(D) Equal

Question 6. The process of expressing a composite number as a product of its prime factors is called _____.

(A) Divisibility

(B) Factoring

(C) Prime factorization

(D) Multiplying

Question 7. The number 1 is neither prime nor _____.

(A) Even

(B) Odd

(C) Composite

(D) Natural

Question 8. To check if a number is divisible by 5, you check if its units digit is 0 or _____.

(A) 2

(B) 5

(C) Any odd digit

(D) Any even digit

Question 9. The sum of the digits of 126 is 9. Therefore, 126 is divisible by _____ and _____.

(A) 3, 6

(B) 3, 9

(C) 2, 3

(D) 2, 9

Question 10. Factors of a number are always _____ than or equal to the number itself.

(A) Greater

(B) Less

(C) Equal

(D) Twice

Question 1. The largest common factor of two or more numbers is called their _____.

(A) LCM

(B) HCF

(C) Product

(D) Sum

Question 2. The smallest common multiple of two or more numbers is called their _____.

(A) HCF

(B) LCM

(C) Factor

(D) Multiple

Question 3. The HCF of 15 and 25 is _____.

(A) 5

(B) 15

(C) 25

(D) 75

Question 4. The LCM of 6 and 8 is _____.

(A) 2

(B) 12

(C) 24

(D) 48

Question 5. For any two positive integers $a$ and $b$, $HCF(a, b) \times LCM(a, b) = a \times$ _____.

(A) $HCF(a,b)$

(B) $LCM(a,b)$

(C) $b$

(D) $a$

Question 6. If the HCF of two numbers is 1, they are called _____ numbers.

(A) Prime

(B) Composite

(C) Co-prime

(D) Perfect

Question 7. To find the largest possible size of identical items to divide two quantities equally, you find their _____.

(A) Sum

(B) Product

(C) LCM

(D) HCF

Question 8. To find the smallest number of items needed so they can be arranged in groups of different given sizes, you find the _____ of the group sizes.

(A) HCF

(B) LCM

(C) Sum

(D) Product

Question 9. The HCF of two prime numbers is always _____.

(A) The smaller number

(B) The larger number

(C) Their product

(D) 1

Question 10. The LCM of two co-prime numbers is always equal to their _____.

(A) Sum

(B) Difference

(C) Product

(D) HCF

Question 1. According to Euclid's Division Lemma, for any two positive integers $a$ and $b$, there exist unique integers $q$ and $r$ such that $a = bq + r$, where the remainder $r$ satisfies _____.

(A) $0 < r < b$

(B) $0 \leq r < b$

(C) $0 < r \leq b$

(D) $0 \leq r \leq b$

Question 2. Euclid's Division Algorithm is used to find the _____ of two positive integers.

(A) LCM

(B) HCF

(C) Product

(D) Sum

Question 3. The Fundamental Theorem of Arithmetic states that every composite number can be uniquely expressed as a product of _____ numbers.

(A) Even

(B) Odd

(C) Composite

(D) Prime

Question 4. When applying Euclid's Division Algorithm, the HCF is the divisor at the step where the remainder is _____.

(A) 1

(B) 0

(C) Prime

(D) The HCF itself

Question 5. The Fundamental Theorem of Arithmetic is also known as the _____.

(A) Division Lemma

(B) Division Algorithm

(C) Unique Factorization Theorem

(D) Remainder Theorem

Question 6. One application of the Fundamental Theorem of Arithmetic is in finding the _____ and _____ of numbers using their prime factorizations.

(A) Sum, Difference

(B) Product, Quotient

(C) HCF, LCM

(D) Numerator, Denominator

Question 7. The step-by-step process in Euclid's Division Algorithm continues until the remainder becomes _____.

(A) 1

(B) A prime number

(C) 0

(D) Negative

Question 8. The uniqueness in the Fundamental Theorem of Arithmetic is apart from the _____ in which the prime factors occur.

(A) Sum

(B) Product

(C) Order

(D) Power

Question 9. When applying Euclid's Division Algorithm to find HCF(a, b), the next step after $a = bq + r$ (where $r \neq 0$) is to apply the lemma to $b$ and _____.

(A) $a$

(B) $q$

(C) $r$}

(D) $b$

Question 10. The property that in the prime factorization of a perfect square, the exponents of all prime factors are even, is a consequence of the _____.

(A) Euclid's Division Lemma

(B) Euclid's Division Algorithm

(C) Fundamental Theorem of Arithmetic

(D) Properties of prime numbers

Question 1. In the expression $7^4$, 7 is the base and 4 is the _____.

(A) Power

(B) Product

(C) Exponent (or index)

(D) Value

Question 2. According to the law of exponents, $a^m \times a^n = a^{_____}$.

(A) $m+n$

(B) $m-n$

(C) $m \times n$

(D) $m/n$

Question 3. The value of any non-zero number raised to the power of zero is _____.

(A) 0

(B) The number itself

(C) 1

(D) Undefined

Question 4. The expression $a^{-n}$ is equivalent to $\frac{1}{_____}$ for $a \neq 0$.

(A) $a^n$

(B) $-a^n$

(C) $a^{-n}$

(D) $a \times (-n)$

Question 5. The standard form of a number is written as $a \times 10^n$, where $a$ is a number such that _____.

(A) $0 < |a| < 10$

(B) $1 \leq |a| < 10$

(C) $|a| > 10$

(D) $a$ is any integer

Question 6. The standard form of 5,000,000 is _____.

(A) $5 \times 10^5$

(B) $5 \times 10^6$

(C) $5 \times 10^7$

(D) $5 \times 10^8$

Question 7. The standard form of 0.0008 is _____.

(A) $8 \times 10^{-3}$

(B) $8 \times 10^{-4}$

(C) $8 \times 10^{-5}$

(D) $0.8 \times 10^{-3}$

Question 8. When comparing $2 \times 10^5$ and $3 \times 10^4$, the larger number is _____.

(A) $2 \times 10^5$

(B) $3 \times 10^4$

(C) They are equal

(D) Cannot compare

Question 9. The value of $(\frac{1}{4})^{-3}$ is _____.

(A) $\frac{1}{12}$

(B) $\frac{1}{64}$

(C) 64

(D) 12

Question 10. Exponents are also known as _____.

(A) Bases

(B) Powers

(C) Indices

(D) Radicals

Question 1. A number obtained by multiplying an integer by itself is called a _____.

(A) Cube

(B) Square

(C) Prime

(D) Composite

Question 2. The symbol $\sqrt{}$ represents the _____ root.

(A) Cube

(B) Fourth

(C) Square

(D) Any

Question 3. The value of $\sqrt{81}$ is _____.

(A) 9

(B) 8

(C) 81

(D) 64

Question 4. A set of three positive integers $(a, b, c)$ such that $a^2 + b^2 = c^2$ is called a _____ triplet.

(A) Euclidean

(B) Prime

(C) Pythagorean

(D) Composite

Question 5. The square of an even number is always _____.

(A) Odd

(B) Even

(C) Prime

(D) Composite

Question 6. The number of zeros at the end of a perfect square is always _____.

(A) Odd

(B) Even

(C) One

(D) Zero

Question 7. The units digit of a perfect square cannot be _____.

(A) 1

(B) 4

(C) 7

(D) 9

Question 8. The square root of 0.16 is _____.

(A) 0.04

(B) 0.4

(C) 4

(D) 0.004

Question 9. The square root of $\frac{36}{49}$ is _____.

(A) $\frac{6}{7}$

(B) $\frac{36}{49}$

(C) $\frac{6}{49}$

(D) $\frac{36}{7}$

Question 10. The smallest perfect square greater than 100 is _____.

(A) 101

(B) 121

(C) 100

(D) 110

Question 1. A number obtained by multiplying an integer by itself three times is called a _____.

(A) Square

(B) Cube

(C) Power

(D) Radical

Question 2. The symbol $\sqrt[3]{}$ represents the _____ root.

(A) Square

(B) Third

(C) Fourth

(D) Any

Question 3. The value of $\sqrt[3]{216}$ is _____.

(A) 6

(B) 36

(C) 7

(D) 5

Question 4. The cube of a negative number is always _____.

(A) Positive

(B) Negative

(C) Zero

(D) Even

Question 5. The units digit of the cube of a number ending in 8 is _____.

(A) 2

(B) 8

(C) 4

(D) 6

Question 6. The units digit of the cube root of a number ending in 3 is _____.

(A) 3

(B) 7

(C) 9

(D) 1

Question 7. The cube root of $\frac{64}{125}$ is _____.

(A) $\frac{4}{5}$

(B) $\frac{8}{10}$

(C) $\frac{4}{25}$

(D) $\frac{64}{125}$

Question 8. The smallest number by which 32 must be multiplied to make it a perfect cube is _____.

(A) 2

(B) 4

(C) 8

(D) 16

Question 9. The smallest number by which 24 must be divided to make it a perfect cube is _____.

(A) 2

(B) 3

(C) 4

(D) 6

Question 10. The value of $\sqrt[3]{0.001}$ is _____.

(A) 0.1

(B) 0.01

(C) 1

(D) 0.001

Question 1. Rounding a number means finding a number that is _____ to the original number but is simpler to work with.

(A) Exactly equal

(B) Greater than

(C) Less than

(D) Approximate

Question 2. To round a number to a specific place value, you look at the digit immediately to the _____ of that place.

(A) Left

(B) Right

(C) Above

(D) Below

Question 3. If the digit to be rounded is 5 or greater, you round _____ the previous digit.

(A) Down

(B) Up

(C) Ignore

(D) Double

Question 4. Round 567 to the nearest ten.

(A) 560

(B) 570

(C) 600

(D) 500

Question 5. Round 1.234 to the nearest hundredth.

(A) 1.23

(B) 1.24

(C) 1.2

(D) 1.234

Question 6. Estimate the sum of 28 and 53 by rounding each to the nearest ten. The estimate is _____.

(A) $20 + 50 = 70$

(B) $30 + 50 = 80$

(C) $30 + 60 = 90$

(D) $28 + 53 = 81$

Question 7. Round 999 to the nearest hundred.

(A) 900

(B) 990

(C) 1000

(D) 999

Question 8. Round $\textsf{₹} 456.75$ to the nearest Rupee.

(A) $\textsf{₹} 456$

(B) $\textsf{₹} 457$

(C) $\textsf{₹} 456.80$

(D) $\textsf{₹} 460$

Question 9. Estimation is used to get a value that is reasonably _____ to the exact answer.

(A) Far

(B) Close

(C) Larger

(D) Smaller

Question 10. Round 1,56,789 to the nearest thousand (Indian System).

(A) 1,56,000

(B) 1,57,000

(C) 1,60,000

(D) 1,56,700

Question 1. The logarithm of a number $A$ to the base $b$ is the _____ to which $b$ must be raised to get $A$.

(A) Product

(B) Sum

(C) Difference

(D) Exponent (or power)

Question 2. The statement $\log_{10} 100 = 2$ is equivalent to the exponential statement _____.

(A) $10^2 = 100$

(B) $2^{10} = 100$

(C) $100^2 = 10$

(D) $10^{100} = 2$

Question 3. The logarithm of 1 to any valid base is always _____.

(A) 1

(B) The base itself

(C) 0

(D) Undefined

Question 4. $\log_b b = $ _____.

(A) 0

(B) $b$

(C) 1

(D) Undefined

Question 5. The law of logarithms for multiplication states that $\log_b (MN) = \log_b M$ _____ $\log_b N$.

(A) $+$

(B) $-$

(C) $\times$

(D) $\div$

Question 6. The law of logarithms for powers states that $\log_b M^k = $ _____.

(A) $\log_b M + k$

(B) $k \times \log_b M$}

(C) $\log_b (M+k)$

(D) $M^k$

Question 7. The Antilogarithm of a number $C$ to base $b$ is the number $A$ such that $\log_b A = $ _____.

(A) $A$

(B) $b$

(C) $C$

(D) 1

Question 8. Finding the antilog of $C$ to base $b$ is equivalent to calculating _____.

(A) $A^b$

(B) $b^C$

(C) $C^b$}

(D) $b \times C$

Question 9. The base of the common logarithm is _____.

(A) $e$

(B) 2

(C) 10

(D) Any positive number

Question 10. Logarithms are useful for simplifying calculations involving multiplication, division, and _____.

(A) Addition

(B) Subtraction

(C) Powers and roots

(D) Modulo

Question 1. The result of the modulo operation $a \pmod m$ is the _____ when $a$ is divided by $m$, where $0 \leq r < m$.

(A) Quotient

(B) Divisor

(C) Remainder

(D) Dividend

Question 2. The statement $a \equiv b \pmod m$ means that $a$ and $b$ have the same _____ when divided by $m$.

(A) Quotient

(B) Divisor

(C) Remainder

(D) Product

Question 3. The statement $a \equiv b \pmod m$ is equivalent to saying that $m$ divides _____.

(A) $a+b$

(B) $ab$}

(C) $a-b$

(D) $a/b$

Question 4. The last digit of a number can be found by calculating the number modulo _____.

(A) 2

(B) 5

(C) 10

(D) 100

Question 5. If today is Monday, the day of the week after 7 days will be _____.

(A) Tuesday

(B) Monday

(C) Sunday

(D) Thursday

Question 6. If $a \equiv b \pmod m$ and $c \equiv d \pmod m$, then $a+c \equiv$ _____ $\pmod m$.

(A) $a+d$

(B) $c+b$}

(C) $b+d$

(D) $a-c$

Question 7. If $a \equiv b \pmod m$ and $c \equiv d \pmod m$, then $ac \equiv$ _____ $\pmod m$.

(A) $a+c$

(B) $bd$}

(C) $a \times c$

(D) $b \times d$

Question 8. The possible remainders when an integer is divided by 5 are _____.

(A) 0, 1, 2, 3, 4, 5

(B) 1, 2, 3, 4, 5

(C) 0, 1, 2, 3, 4

(D) Any integer

Question 9. The concept of congruence modulo $m$ is fundamental in defining _____ classes.

(A) Remainder

(B) Divisibility

(C) Congruence

(D) All of the above

Question 10. Modulo arithmetic is widely used in the field of _____.

(A) Geometry

(B) Physics

(C) Cryptography

(D) Statistics

Question 1. To find the total number of items when quantities are combined, you perform _____.

(A) Subtraction

(B) Multiplication

(C) Division

(D) Addition

Question 2. If the cost of one item is given, to find the cost of multiple identical items, you perform _____.

(A) Addition

(B) Subtraction

(C) Multiplication

(D) Division

Question 3. To find how much quantity is left after some is removed, you perform _____.

(A) Addition

(B) Subtraction

(C) Multiplication

(D) Division

Question 4. If a total quantity is divided into equal parts, to find the size of each part, you perform _____.

(A) Addition

(B) Subtraction

(C) Multiplication

(D) Division

Question 5. To convert kilometers to meters, you multiply by _____.

(A) 10

(B) 100

(C) 1000

(D) 10000

Question 6. To convert liters to milliliters, you multiply by _____.

(A) 10

(B) 100

(C) 1000

(D) 10000

Question 7. If a car travels a certain distance in a certain time, its average speed is calculated by dividing the total distance by the total _____.

(A) Speed

(B) Distance

(C) Time

(D) Fuel

Question 8. The area of a rectangle is calculated by multiplying its length by its _____.

(A) Perimeter

(B) Width

(C) Diagonal

(D) Height

Question 9. The perimeter of a rectangle is calculated by adding the lengths of all its _____.

(A) Diagonals

(B) Corners

(C) Sides

(D) Areas

Question 10. If you reverse the digits of a two-digit number $10t+u$, the new number is _____.

(A) $10u+t$

(B) $tu$}

(C) $10t-u$

(D) $t+u$