Matching Items MCQs for Sub-Topics of Topic 1: Numbers & Numeriacal Applications

(i) Natural Number

(ii) Integer

(iii) Rational Number

(iv) Irrational Number

(v) Whole Number

(a) $\frac{-3}{4}$

(b) $\sqrt{5}$

(c) 7

(d) -2

(e) 0

(i) Existence of 0

(ii) Closure under subtraction

(iii) Existence of additive inverse

(iv) Closure under division (excluding division by zero)

(v) Representation on a continuous number line

(a) Rational Numbers

(b) Real Numbers

(c) Whole Numbers

(d) Integers

(e) Rational Numbers

(i) Smallest prime number

(ii) Smallest composite number

(iii) Neither prime nor composite

(iv) Example of a non-terminating non-recurring decimal

(v) Example of a non-terminating recurring decimal

(a) 0.101101110...

(b) 0.777...

(c) 2

(d) 4

(e) 1

(i) Natural Numbers

(ii) Integers

(iii) Rational Numbers

(iv) Even Numbers

(v) Odd Numbers

(a) $2n$ (where $n \in \mathbb{Z}$)

(b) $n$ (where $n \in \lbrace 1, 2, 3, \dots \rbrace$)

(c) $2n+1$ (where $n \in \mathbb{Z}$)

(d) $z$ (where $z \in \lbrace \dots, -1, 0, 1, \dots \rbrace$)

(e) $\frac{p}{q}$ (where $p, q \in \mathbb{Z}, q \neq 0$)

(i) Natural Numbers are a subset of

(ii) Whole Numbers are a subset of

(iii) Integers are a subset of

(iv) Rational Numbers are a subset of

(v) Irrational Numbers are a subset of

(a) Rational Numbers

(b) Whole Numbers

(c) Real Numbers

(d) Integers

(e) Real Numbers

(i) Value of digit 6 in 1,26,345 (Indian System)

(ii) Value of digit 6 in 126,345 (International System)

(iii) Value of digit 6 in 1.2367

(iv) Value of digit 6 in 6,54,321 (Indian System)

(v) Value of digit 6 in 654,321 (International System)

(a) 6000

(b) 600000

(c) 0.006

(d) 6000

(e) 600000

(i) Indian System

(ii) International System

(iii) Decimal System

(iv) Roman Numerals

(v) General Form of a Number

(a) Base 10 and Place Value

(b) Symbols and their values based on position

(c) Grouping in powers of 10 (thousands, millions)

(d) Representation using symbols like I, V, X, L, C, D, M

(e) Representation using powers of 10 ($100a+10b+c$)

(i) XL

(ii) XC

(iii) CM

(iv) CD

(v) LIV

(a) 90

(b) 400

(c) 900

(d) 40

(e) 54

(i) 1 Lakh

(ii) 1 Crore

(iii) 10 Crore

(iv) 100 Crore

(v) 1 Thousand

(a) 100 Million

(b) 1 Million

(c) 1 Billion

(d) 100 Thousand

(e) 1 Thousand

(i) Smallest 3-digit number

(ii) Largest 2-digit number

(iii) Value of $4 \times 100 + 5 \times 10 + 6 \times 1$

(iv) Smallest 4-digit number using 1, 0, 2, 3

(v) Roman numeral for 50

(a) 1023

(b) L

(c) 100

(d) 99

(e) 456

(i) -5

(ii) $\frac{1}{2}$

(iii) 2.75

(iv) $\sqrt{2}$

(v) -1.8

(a) Between -2 and -1

(b) Between 2 and 3

(c) Between 1 and 2

(d) To the left of 0

(e) Between 0 and 1

(i) $\frac{3}{5}$ (between 0 and 1)

(ii) $\frac{7}{4}$ (between 1 and 2)

(iii) $1 \frac{2}{3}$ (between 1 and 2)

(iv) $\frac{11}{6}$ (between 1 and 2)

(v) $0.25$ (between 0 and 1)

(a) 4

(b) 5

(c) 3

(d) 6

(e) 4

(i) Marking points at equal intervals

(ii) Dividing a segment into equal parts

(iii) Using Pythagorean theorem (right triangle)

(iv) Successive Magnification

(v) Representing negative numbers

(a) Locating integers

(b) Locating fractions

(c) Locating irrational numbers like $\sqrt{2}$

(d) Locating numbers with decimal expansions (terminating or non-recurring)

(e) Locating numbers to the left of zero

(i) -3

(ii) -0.5

(iii) 1.414

(iv) 3.14

(v) -2.7

(a) Approximately at $\sqrt{2}$

(b) Approximately at $\pi$

(c) Midway between -1 and 0

(d) To the left of -2

(e) At the integer point -3

(i) Natural Numbers

(ii) Integers

(iii) Rational Numbers

(iv) Real Numbers

(v) Irrational Numbers

(a) A dense set of points, but with 'gaps'

(b) A set of discrete points on the positive side

(c) A complete, continuous line

(d) A set of discrete points on both sides of zero and at zero

(e) A set of points that fill the 'gaps' left by rational numbers

(i) 5 vs 8

(ii) -5 vs -8

(iii) $\frac{1}{2}$ vs $\frac{1}{3}$

(iv) 0.2 vs 0.20

(v) $\sqrt{2}$ vs 1.4

(a) Equal

(b) First is greater

(c) Second is greater

(d) First is greater

(e) First is greater

(i) $|-7|$

(ii) $|3.5|$

(iii) $|0|$

(iv) $|-\frac{2}{5}|$

(v) $| \sqrt{3} |$

(a) 0

(b) 7

(c) 3.5

(d) $\frac{2}{5}$

(e) $\sqrt{3}$

(i) $x > 3$

(ii) $x \leq -1$

(iii) $|x| < 2$

(iv) $|x| \geq 4$

(v) $0 < x < 1$

(a) All numbers greater than 3

(b) All numbers less than or equal to -1

(c) Numbers between -2 and 2 (exclusive)

(d) Numbers less than or equal to -4 or greater than or equal to 4

(e) Numbers strictly between 0 and 1

(i) 1 and 2

(ii) 0 and 1

(iii) -2 and -1

(iv) $\sqrt{2}$ and $\sqrt{3}$

(v) $\frac{1}{4}$ and $\frac{1}{2}$

(a) 0.3

(b) -1.5

(c) 1.5

(d) 1.7

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

(i) Comparing $\frac{3}{7}$ and $\frac{2}{5}$

(ii) Comparing 1234567 and 1234657

(iii) Comparing $10^{-4}$ and $10^{-6}$

(iv) Comparing $3.14$ and $\pi$

(v) Comparing -10 and -5

(a) Cross-multiplication or common denominator

(b) Comparing digits from left to right

(c) Comparing exponents

(d) Using the known value of $\pi$ or subtracting

(e) Position on the number line (further left is smaller)

(i) $15 + (-7)$

(ii) $-15 - (-7)$

(iii) $(-3) \times (-4)$

(iv) $-20 \div 5$

(v) $0 \times 100$

(a) -4

(b) 0

(c) 8

(d) -8

(e) 12

(i) $\frac{1}{2} + \frac{1}{4}$

(ii) $\frac{3}{4} - \frac{1}{4}$

(iii) $\frac{2}{3} \times \frac{3}{4}$

(iv) $\frac{1}{5} \div \frac{2}{5}$

(v) $\frac{1}{3} + \frac{1}{6}$

(a) $\frac{1}{2}$

(b) $\frac{1}{2}$

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

(d) $\frac{3}{4}$

(e) $\frac{1}{2}$

(i) $2.5 + 1.3$

(ii) $4.0 - 1.5$

(iii) $0.6 \times 0.2$

(iv) $1.2 \div 0.3$

(v) $10.5 + 2.31$

(a) 4

(b) 12.81

(c) 3.8

(d) 2.5

(e) 0.12

(i) $5 + 2 \times 3$

(ii) $(5+2) \times 3$

(iii) $10 - 4 \div 2$

(iv) $(10-4) \div 2$

(v) $10 \div 5 \times 2$

(a) $6 \div 2 = 3$

(b) $2 \times 2 = 4$

(c) $5 + 6 = 11$

(d) $7 \times 3 = 21$

(e) $10 - 2 = 8$

(i) Closure under addition

(ii) Closure under subtraction

(iii) Closure under multiplication

(iv) Closure under division (excluding by zero)

(v) Commutativity of multiplication

(a) Natural Numbers

(b) Integers

(c) Rational Numbers

(d) Real Numbers

(e) Natural Numbers, Integers, Rational Numbers, Real Numbers

(i) Additive Identity

(ii) Multiplicative Identity

(iii) Additive Inverse

(iv) Multiplicative Inverse

(v) Closure Property

(a) For a number $a$, its inverse is $-a$ such that $a+(-a)=0$.

(b) The element 0.

(c) The element 1.

(d) For a non-zero number $a$, its inverse is $\frac{1}{a}$ such that $a \times \frac{1}{a}=1$.

(e) Performing an operation on two numbers in a set results in a number still within that set.

(i) Divisibility by 2

(ii) Divisibility by 3

(iii) Divisibility by 5

(iv) Divisibility by 6

(v) Divisibility by 10

(a) The sum of its digits is divisible by 3.

(b) Its units digit is 0 or 5.

(c) Its units digit is 0.

(d) Its units digit is an even number (0, 2, 4, 6, or 8).

(e) It is divisible by both 2 and 3.

(i) Square Numbers

(ii) Triangular Numbers

(iii) Cube Numbers

(iv) Even Numbers

(v) Odd Numbers

(a) 1, 3, 6, 10, 15, ...

(b) 1, 4, 9, 16, 25, ...

(c) ..., -4, -2, 0, 2, 4, ...

(d) 1, 8, 27, 64, 125, ...

(e) ..., -3, -1, 1, 3, 5, ...

(i) $5 + 7 = 7 + 5$

(ii) $3 \times (2+4) = 3 \times 2 + 3 \times 4$

(iii) $(2+3)+4 = 2+(3+4)$

(iv) $8 \times 1 = 8$

(v) $6 + (-6) = 0$

(a) Additive Inverse

(b) Commutative Property of Addition

(c) Associative Property of Addition

(d) Multiplicative Identity

(e) Distributive Property

(i) Natural Numbers

(ii) Integers

(iii) Rational Numbers (excluding 0)

(iv) Real Numbers (excluding 0)

(v) Whole Numbers

(a) Division

(b) Subtraction

(c) Division

(d) Subtraction

(e) Division

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

(ii) $\frac{1}{2}$

(iii) $\frac{3}{4}$

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

(v) $\frac{1}{10}$

(a) 0.5

(b) 0.25

(c) 0.75

(d) 0.1

(e) 0.2

(i) 0.6

(ii) 0.125

(iii) 0.8

(iv) 0.01

(v) 0.5

(a) $\frac{1}{2}$

(b) $\frac{3}{5}$

(c) $\frac{1}{8}$

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

(e) $\frac{1}{100}$

(i) Proper Fraction

(ii) Improper Fraction

(iii) Mixed Number

(iv) Unit Fraction

(v) Equivalent Fraction (to 1/3)

(a) $2 \frac{1}{4}$

(b) $\frac{7}{5}$

(c) $\frac{2}{6}$

(d) $\frac{1}{7}$

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

(i) Terminating Decimal

(ii) Non-terminating Recurring Decimal

(iii) Non-terminating Non-recurring Decimal

(iv) Like Decimals (with 1.25)

(v) Unlike Decimals (with 1.25)

(a) 0.333...

(b) 4.7

(c) 0.121221222...

(d) 0.78

(e) 3.456

(i) Fraction to Decimal

(ii) Decimal to Fraction

(iii) Reducing a fraction

(iv) Mixed number to Improper fraction

(v) Improper fraction to Mixed number

(a) Divide numerator by denominator.

(b) Write the decimal as a fraction with a power of 10 denominator and simplify.

(c) Divide numerator and denominator by their HCF.

(d) Multiply the whole number by the denominator and add the numerator.

(e) Divide the numerator by the denominator to get the whole number part and the remainder.

(i) $\frac{1}{8}$

(ii) $\frac{1}{3}$

(iii) $\sqrt{2}$

(iv) $\frac{3}{5}$

(v) $\frac{2}{7}$

(a) Terminating

(b) Non-terminating Recurring

(c) Non-terminating Non-recurring

(d) Terminating

(e) Non-terminating Recurring

(i) $0.\overline{3}$

(ii) $0.\overline{6}$

(iii) $0.\overline{1}$

(iv) $0.\overline{9}$

(v) $0.\overline{12}$

(a) $\frac{1}{9}$

(b) 1

(c) $\frac{1}{3}$

(d) $\frac{2}{3}$

(e) $\frac{12}{99} = \frac{4}{33}$

(i) $\sqrt{2}$

(ii) $\sqrt{3}$

(iii) $\pi$

(iv) $e$

(v) $\phi$ (Golden Ratio)

(a) Approximately 1.732

(b) Approximately 3.14159

(c) Approximately 2.718

(d) Approximately 1.414

(e) Approximately 1.618

(i) $\frac{1}{\sqrt{3}}$

(ii) $\frac{1}{2+\sqrt{5}}$

(iii) $\frac{1}{\sqrt{7}-\sqrt{2}}$

(iv) $\frac{1}{\sqrt{a}}$

(v) $\frac{1}{\sqrt{a}+\sqrt{b}}$

(a) $\sqrt{a}$

(b) $2-\sqrt{5}$

(c) $\sqrt{7}+\sqrt{2}$

(d) $\sqrt{3}$

(e) $\sqrt{a}-\sqrt{b}$

(i) 4.56

(ii) 1.212121...

(iii) 0.101001000...

(iv) $\frac{7}{11}$ (as a decimal)

(v) $\sqrt{16}$ (as a decimal)

(a) Terminating

(b) Non-terminating Recurring

(c) Non-terminating Non-recurring

(d) Non-terminating Recurring

(e) Terminating

(i) 18

(ii) 25

(iii) 36

(iv) 100

(v) 7

(a) 1

(b) 5

(c) 6

(d) 4

(e) 7

(i) 3

(ii) 5

(iii) 8

(iv) 11

(v) 15

(a) 25

(b) 24

(c) 33

(d) 30

(e) 12

(i) 29

(ii) 4

(iii) 1

(iv) 51

(v) 2

(a) Smallest prime number

(b) Prime number

(c) Composite number

(d) Neither prime nor composite

(e) Composite number ($51 = 3 \times 17$)

(i) 14

(ii) 21

(iii) 35

(iv) 30

(v) 77

(a) 5

(b) 2

(c) 7

(d) 3

(e) 11

(i) 144

(ii) 123

(iii) 450

(iv) 221

(v) 120

(a) Divisible by 5 and 10

(b) Divisible by 3

(c) Divisible by 4 and 9

(d) Divisible by 13 (since $221 = 13 \times 17$)

(e) Divisible by 2, 3, 4, 5, 6, 8, 10, 12

(i) HCF(12, 18)

(ii) HCF(20, 30)

(iii) HCF(7, 14)

(iv) HCF(8, 12)

(v) HCF(25, 35)

(a) 4

(b) 5

(c) 6

(d) 10

(e) 7

(i) LCM(12, 18)

(ii) LCM(20, 30)

(iii) LCM(7, 14)

(iv) LCM(8, 12)

(v) LCM(25, 35)

(a) 24

(b) 36

(c) 14

(d) 60

(e) 175

(i) HCF of two prime numbers

(ii) LCM of two co-prime numbers

(iii) Relation between HCF and LCM of $a$ and $b$

(iv) HCF of $a$ and $b$ always divides

(v) LCM of $a$ and $b$ is always a multiple of

(a) $a \times b$

(b) HCF(a,b)

(c) 1

(d) $a \times b$

(e) $a$ and $b$ individually

(i) Prime Factorization Method for HCF

(ii) Prime Factorization Method for LCM

(iii) Division Method for HCF (Euclid's Algorithm)

(iv) Common Division Method for LCM

(v) Finding common factors/multiples by listing

(a) Uses the property $HCF(a,b) = HCF(b,r)$.

(b) Involves dividing the numbers simultaneously by common prime factors.

(c) Takes the product of common prime factors with the lowest powers.

(d) Takes the product of all prime factors with the highest powers.

(e) Simple method for small numbers.

(i) Finding the largest number of items to put in each group to divide two sets equally

(ii) Finding the smallest number of items needed so that they can be arranged in groups of different sizes

(iii) Finding when events that repeat at different intervals will happen together next

(iv) Finding the greatest common divisor

(v) Finding the least common multiple

(a) LCM

(b) HCF

(c) HCF

(d) LCM

(e) LCM

(i) $a$

(ii) $b$

(iii) $q$

(iv) $r$

(v) $0 \leq r < b$

(a) Divisor

(b) Quotient

(c) Remainder

(d) Condition for the remainder

(e) Dividend

(i) Euclid’s Division Lemma

(ii) Euclid’s Division Algorithm

(iii) Fundamental Theorem of Arithmetic

(iv) Prime Factorization

(v) HCF

(a) A technique for finding the HCF of two positive integers.

(b) A statement about the existence and uniqueness of quotient and remainder.

(c) Expressing a composite number as a product of prime numbers.

(d) The statement about the unique prime factorization of composite numbers.

(e) The largest positive integer that divides two or more integers without leaving a remainder.

(i) Finding the HCF of 96 and 404

(ii) Showing that the square of any positive integer is of the form $3m$ or $3m+1$

(iii) Proving that $\sqrt{p}$ is irrational for any prime $p$

(iv) Expressing 24 as $2^3 \times 3$

(v) Using $HCF(a, b) \times LCM(a, b) = a \times b$ after finding prime factors

(a) Fundamental Theorem of Arithmetic

(b) Euclid’s Division Lemma

(c) Euclid’s Division Algorithm

(d) Fundamental Theorem of Arithmetic

(e) Fundamental Theorem of Arithmetic

(i) First division: $100 = 60 \times 1 + r_1$

(ii) Second division: $60 = r_1 \times q_2 + r_2$

(iii) Third division: $r_1 = r_2 \times q_3 + r_3$

(iv) Value of HCF(60, 100)

(v) The divisor when the remainder is 0

(a) 20

(b) 0

(c) 20

(d) 40

(e) 20

(i) 24

(ii) 36

(iii) 100

(iv) 144

(v) 210

(a) $2 \times 3 \times 5 \times 7$

(b) $2^4 \times 3^2$

(c) $2^2 \times 5^2$

(d) $2^2 \times 3^2$

(e) $2^3 \times 3$

(i) $a^5 \times a^3$

(ii) $\frac{a^7}{a^2}$

(iii) $(a^4)^2$

(iv) $(ab)^3$

(v) $(\frac{a}{b})^4$

(a) $a^8$

(b) $a^5$

(c) $a^8$

(d) $a^3 b^3$

(e) $\frac{a^4}{b^4}$

(i) $2^{-1}$

(ii) $3^{-2}$

(iii) $10^{-3}$

(iv) $a^{-n}$

(v) $(\frac{1}{5})^{-2}$

(a) $\frac{1}{a^n}$

(b) $\frac{1}{2}$

(c) $\frac{1}{9}$

(d) $\frac{1}{1000}$

(e) $5^2 = 25$

(i) $4^2$

(ii) $2^4$

(iii) $(-3)^3$

(iv) $(1.5)^2$

(v) $(\frac{-1}{2})^3$

(a) 16

(b) -27

(c) 2.25

(d) 16

(e) $-\frac{1}{8}$

(i) 5000

(ii) 0.005

(iii) 1,23,000

(iv) 0.0000123

(v) 70,00,000

(a) $1.23 \times 10^5$

(b) $5 \times 10^{-3}$

(c) $7 \times 10^6$

(d) $5 \times 10^3$

(e) $1.23 \times 10^{-5}$

(i) $10^5$ vs $10^3$

(ii) $10^{-2}$ vs $10^{-4}$

(iii) $2 \times 10^3$ vs $20 \times 10^2$

(iv) $3 \times 10^{-5}$ vs $0.3 \times 10^{-4}$

(v) $1 \times 10^0$ vs $0$

(a) Equal

(b) First is larger

(c) First is larger

(d) Equal

(e) First is larger

(i) 7

(ii) 11

(iii) 15

(iv) 20

(v) -6

(a) 225

(b) 400

(c) 49

(d) 121

(e) 36

(i) 81

(ii) 169

(iii) 196

(iv) 0.04

(v) $\frac{25}{49}$

(a) 9

(b) 13

(c) 14

(d) 0.2

(e) $\frac{5}{7}$

(i) Ends in 1

(ii) Ends in 4

(iii) Ends in 5

(iv) Ends in 6

(v) Ends in 9

(a) 5

(b) 1 or 9

(c) 2 or 8

(d) 4 or 6

(e) 3 or 7

(i) (3, 4, c)

(ii) (5, 12, c)

(iii) (8, 15, c)

(iv) (7, 24, c)

(v) (20, 21, c)

(a) 13

(b) 17

(c) 25

(d) 29

(e) 5

(i) 36 (by repeated subtraction)

(ii) 1024 (by long division)

(iii) 225 (by prime factorization)

(iv) 50 (by estimation)

(v) 0.81 (by decimal square root)

(a) Lies between 7 and 8

(b) Result is 6

(c) Result is 32

(d) Result is 15

(e) Result is 0.9

(i) 3

(ii) 5

(iii) -2

(iv) 10

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

(a) -8

(b) 1000

(c) 27

(d) 125

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

(i) 64

(ii) 343

(iii) 512

(iv) 1728

(v) -27

(a) 8

(b) -3

(c) 4

(d) 7

(e) 12

(i) 0

(ii) 1

(iii) 2

(iv) 3

(v) 4

(a) 8

(b) 7

(c) 4

(d) 0

(e) 1

(i) $\sqrt[3]{0.008}$

(ii) $\sqrt[3]{\frac{1}{125}}$

(iii) $\sqrt[3]{-1000}$

(iv) $\sqrt[3]{64 \times 27}$

(v) $\sqrt[3]{2.744}$

(a) $\sqrt[3]{64} \times \sqrt[3]{27} = 4 \times 3 = 12$

(b) 1.4

(c) 0.2

(d) $\frac{1}{5} = 0.2$

(e) -10

(i) Smallest number to multiply 32 to get a perfect cube

(ii) Smallest number to divide 81 to get a perfect cube

(iii) Smallest number to multiply 72 to get a perfect cube

(iv) Smallest number to divide 192 to get a perfect cube ($192 = 2^6 \times 3$)

(v) Smallest number to multiply 100 to get a perfect cube ($100 = 2^2 \times 5^2$)

(a) 3

(b) 2 ($32 = 2^5$)

(c) 3 ($81 = 3^4$)

(d) 2 ($72 = 2^3 \times 3^2$)

(e) $2 \times 5 = 10$

(i) 349

(ii) 350

(iii) 780

(iv) 950

(v) 1020

(a) 400

(b) 1000

(c) 800

(d) 400

(e) 1000

(i) 1.23

(ii) 4.56

(iii) 0.98

(iv) 10.04

(v) 5.05

(a) 1.2

(b) 4.6

(c) 1.0

(d) 10.0

(e) 5.1

(i) Estimating $23 \times 48$ by rounding to nearest ten

(ii) Estimating $345 + 589$ by rounding to nearest hundred

(iii) Estimating $\textsf{₹} 487 \times 9$ by rounding price to nearest hundred

(iv) Estimating $815 \div 19$ by rounding to nearest ten

(v) Rounding $\textsf{₹} 149.75$ to the nearest Rupee

(a) $40 \times 50$

(b) $300 + 600$

(c) $\textsf{₹} 500 \times 9$

(d) $820 \div 20$

(e) $\textsf{₹} 150$

(i) 1,23,456 (nearest thousand)

(ii) 1,23,45,678 (nearest lakh)

(iii) 5,67,890 (nearest ten thousand)

(iv) 10,00,500 (nearest thousand)

(v) 99,999 (nearest ten thousand)

(a) 1,23,000

(b) 1,23,00,000

(c) 5,70,000

(d) 10,01,000

(e) 1,00,000

(i) 123,456 (nearest thousand)

(ii) 1,234,567 (nearest ten thousand)

(iii) 12,345,678 (nearest million)

(iv) 999,999 (nearest hundred thousand)

(v) 54,789,123 (nearest million)

(a) 1,235,000

(b) 1,230,000

(c) 12,000,000

(d) 1,000,000

(e) 55,000,000

(i) $\log_{10} 100 = 2$

(ii) $\log_b A = C$

(iii) $\log_2 8 = 3$

(iv) $\log_e X = Y$

(v) $\log_{10} 0.01 = -2$

(a) $b^C = A$

(b) $10^2 = 100$

(c) $2^3 = 8$

(d) $e^Y = X$

(e) $10^{-2} = 0.01$

(i) Product Rule

(ii) Quotient Rule

(iii) Power Rule

(iv) Logarithm of Base

(v) Logarithm of 1

(a) $\log_b \frac{M}{N} = \log_b M - \log_b N$

(b) $\log_b M^k = k \log_b M$

(c) $\log_b b = 1$

(d) $\log_b 1 = 0$

(e) $\log_b (MN) = \log_b M + \log_b N$

(i) $\log_{10} 1$

(ii) $\log_{10} 10$

(iii) $\log_{10} 1000$

(iv) $\log_{10} 0.1$

(v) $\log_{10} 0.0001$

(a) 1

(b) 3

(c) -1

(d) -4

(e) 0

(i) $\log_{10} 789$

(ii) $\log_{10} 45.6$

(iii) $\log_{10} 3.14$

(iv) $\log_{10} 0.5$

(v) $\log_{10} 0.0012$

(a) 2

(b) 1

(c) 0

(d) -1

(e) -3

(i) Logarithm

(ii) Antilogarithm

(iii) Common Logarithm

(iv) Natural Logarithm

(v) Characteristic

(a) Inverse of logarithm

(b) Integer part of a logarithm

(c) Base is $e$

(d) Base is 10

(e) Exponent or Power

(i) $17 \pmod 5$

(ii) $10 \pmod 2$

(iii) $25 \pmod 8$

(iv) $-10 \pmod 3$

(v) $0 \pmod 7$

(a) 0

(b) 3

(c) 1

(d) 2

(e) 0

(i) $10 \equiv 2 \pmod m$

(ii) $15 \equiv 0 \pmod m$

(iii) $7 \equiv -1 \pmod m$

(iv) $22 \equiv 1 \pmod m$

(v) $30 \equiv 6 \pmod m$

(a) $m=8$

(b) $m=15$

(c) $m=8$

(d) $m=7$

(e) $m=4$

(i) $a \equiv a \pmod m$

(ii) If $a \equiv b \pmod m$, then $b \equiv a \pmod m$

(iii) If $a \equiv b \pmod m$ and $b \equiv c \pmod m$, then $a \equiv c \pmod m$

(iv) If $a \equiv b \pmod m$ and $c \equiv d \pmod m$, then $a+c \equiv b+d \pmod m$

(v) If $a \equiv b \pmod m$ and $c \equiv d \pmod m$, then $ac \equiv bd \pmod m$

(a) Transitivity

(b) Property of Addition

(c) Reflexivity

(d) Symmetry

(e) Property of Multiplication

(i) Last digit of $2^4$

(ii) Last digit of $3^5$

(iii) Remainder of $100 \div 7$

(iv) Day of the week 10 days after Monday (Monday is day 1)

(v) Last digit of $13^{13}$

(a) 2 ($100 = 14 \times 7 + 2$)

(b) Wednesday ($1+10 = 11$, $11 \pmod 7 = 4$, which is Wednesday)

(c) 6 ($2^4 = 16 \equiv 6 \pmod {10}$)

(d) 3 ($3^5 = 243 \equiv 3 \pmod {10}$)

(e) 3 ($13 \equiv 3 \pmod{10}$, $13^{13} \equiv 3^{13} \pmod{10}$; powers of 3 mod 10 cycle: 3, 9, 7, 1; $13 \pmod 4 = 1$, so $3^{13} \equiv 3^1 \equiv 3 \pmod {10}$)

(i) Modulus

(ii) Congruence

(iii) Remainder

(iv) Congruence Class (modulo m)

(v) Modular Inverse (of a mod m)

(a) The number $m$ in $a \equiv b \pmod m$.

(b) A relation between two integers that share the same remainder when divided by a positive integer $m$.

(c) The integer $r$ such that $a = qm + r$, where $0 \leq r < m$.

(d) The set of all integers that are congruent to a given integer $a$ modulo $m$.

(e) An integer $x$ such that $ax \equiv 1 \pmod m$ (if it exists).

(i) Find the total cost of multiple items

(ii) Find the difference between two quantities

(iii) Share a quantity equally among groups

(iv) Find the total when quantities are combined

(v) Find a part of a quantity (e.g., fraction of a whole)

(a) Subtraction

(b) Division

(c) Addition

(d) Multiplication

(e) Multiplication

(i) Kilometers to Meters

(ii) Meters to Centimeters

(iii) Kilograms to Grams

(iv) Litres to Milliliters

(v) Hours to Minutes

(a) Multiply by 100

(b) Multiply by 1000

(c) Multiply by 60

(d) Multiply by 1000

(e) Multiply by 1000

(i) Total cost of 3 pens at $\textsf{₹} 10.50$ each

(ii) Remaining amount from $\textsf{₹} 50$ after spending $\textsf{₹} 23.75$

(iii) Number of $\textsf{₹} 5$ coins in $\textsf{₹} 100$

(iv) Total length of two ropes, one $2 \frac{1}{2}$ m and the other $3.75$ m

(v) Area of a rectangle with length 4 cm and width 2.5 cm

(a) $100 \div 5$

(b) $3 \times 10.50$

(c) $50 - 23.75$

(d) $2.5 + 3.75$

(e) $4 \times 2.5$

(i) Two-digit number; digits reversed when 18 added; sum of digits 8

(ii) Two-digit number; digits reversed when 27 subtracted; sum of digits 9

(iii) Two-digit number; digits reversed when 45 added; sum of digits 11

(iv) A number where reversing digits results in the same number (e.g., 44)

(v) A number whose value is 7 times the sum of its digits (e.g., 21: $2+1=3$, $3 \times 7 = 21$)

(a) Palindrome

(b) 36

(c) Property of numbers divisible by 7

(d) 26

(e) 29

(i) Distance between two cities

(ii) Weight of an apple

(iii) Volume of milk in a bottle

(iv) Area of a room

(v) Cost of a book

(a) Kilometers

(b) Grams

(c) Litres

(d) Square meters

(e) Rupees ($\textsf{₹}$)