Test

Step 1: Start from the next even number after 58, which is 60.

Step 2: Go up to the even number before 80, which is 78.

So the even numbers between 58 and 80 are:

60, 62, 64, 66, 68, 70, 72, 74, 76, 78

Count: 10 numbers

Wait! Let's recheck the question wording:
It says "between 58 and 80" — so 58 and 80 are excluded ✅

Let’s list again carefully:

• 60

• 62

• 64

• 66

• 68

• 70

• 72

• 74

• 76

• 78

? Total = 10 even numbers

✅ Final Answer: 10 (Option 1)

From 17 to 80:

Prime numbers between 16 and 80 are:
17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79
→ 16 primes

? From 90 to 100:

Prime numbers are:
97
→ 1 prime

✅ Total primes = 16 + 1 = 17

✅ Final Answer: 17 (Option 3)

Step 1: Prime factorization of 1729

Let’s divide 1729 by smallest prime numbers:

• 1729 ÷ 7 = 247 ✅

• 247 ÷ 13 = 19 ✅

• 19 is a prime number ✅

So, the prime factors of 1729 are:

$$7,\ 13,\ 19$$

Step 2: Add the prime factors

$$7 + 13 + 19 = \boxed{39}$$

✅ Final Answer: 39 (Option 4)

Sixty five thousand five hundred twenty two means:

• Sixty five thousand = 65,000

• Five hundred twenty two = 522

Now add:

$$65,000 + 522 = \boxed{65,522}$$

✅ Final Answer: 65,522 (Option 1)

Eighty nine thousand seventy eight means:

• Eighty nine thousand = 89,000

• Seventy eight = 78

Now add them:

$$89,000 + 78 = \boxed{89,078}$$

✅ Final Answer: 89,078 (Option 2)

"Seven lakh two hundred" means:

• Seven lakh = 700,000

• Two hundred = 200

Now add them:

$$700,000 + 200 = 700,200$$

✅ Final Answer: 700,200 (Option 1)

• 1 lakh = 100,000

• 20 thousand = 20,000

• Forty six = 46

Now add them:

$$100,000 + 20,000 + 46 = 120,046$$

✅ Final Answer: 120,046 (Option 3)

• 1 million = 1,000,000

• The successor of a number means the number that comes right after it, i.e., add 1.

$$1,000,000 + 1 = 1,000,001$$

So, the successor of 1 million is 1,000,001

✅ Final Answer: 1000001 (Option 2)

Step-by-step:

1. Original number: 6 3 5 0 9 4 7

   • Fix the 6 in place.

2. Digits to rearrange: 3, 5, 0, 9, 4, 7

3. Arrange these digits in ascending order to get the smallest number:

   • Ascending: 0, 3, 4, 5, 7, 9

4. Place them after the fixed 6:

   • Result = 6 0 3 4 5 7 9 → 6034579

✅ Final Answer: 6034579

Let's look at each option:

1. 5 + 0 = 5
   ✔️ Defined — Adding zero to any number gives the number itself.

2. 5 – 0 = 5
   ✔️ Defined — Subtracting zero from a number leaves it unchanged.

3. 5 × 0 = 0
   ✔️ Defined — Multiplying any number by zero results in zero.

4. 5 ÷ 0 = ?
   ❌ Not defined — Division by zero is undefined in mathematics. There's no number that you can multiply by 0 to get 5.

✅ Correct answer: 5 ÷ 0 is not defined

Let the non-zero whole number be n.
Its successor is n + 1.

The product of the number and its successor is:
n × (n + 1)

Now, among any two consecutive numbers, one of them is always even, meaning the product will always be divisible by 2.

Let’s test with a few examples:

• $1 \times 2 = 2$ → divisible by 2 ✔️

• $2 \times 3 = 6$ → divisible by 2 ✔️

• $3 \times 4 = 12$ → divisible by 2 ✔️

• $4 \times 5 = 20$ → divisible by 2 ✔️

Thus, the product is always divisible by 2, not necessarily by 3, 4, or 5.

✅ Correct answer: 2

• The greatest 7-digit number is:
  9,999,999

• If we add 1 to it:
  9,999,999 + 1 = 10,000,000

• 10,000,000 is written as 1 crore in the Indian number system.

✅ Final Answer: 1 crore

The number 9578 is a 4-digit number, and we break it down by place value:

• 9 is in the thousands place → 9 × 1000

• 5 is in the hundreds place → 5 × 100

• 7 is in the tens place → 7 × 10

• 8 is in the ones place → 8 × 1

✅ Correct Expanded Form:

9578 = 9 × 1000 + 5 × 100 + 7 × 10 + 8 × 1

❌ Incorrect Options:

• 9 × 10000... → Too big (10000 is for 5-digit numbers)

• 9 × 100 + 5 × 100... → Adds 9 × 100 and 5 × 100, which is not correct

• 9 × 1000 + 57 × 10... → 57 × 10 is invalid; we don't group digits like that in expanded form

So, the correct answer is: 9 × 1000 + 5 × 100 + 7 × 10 + 8 × 1 ✅

We are given the digits: 5, 9, 2, 6
We must form the largest 4-digit number using these digits, and one of them can be used twice.

Let’s try each option:

1. 9652 → uses 9, 6, 5, 2 (all digits once) ✅

2. 9562 → uses 9, 5, 6, 2 (all digits once) ✅

3. 9659 → uses 9 twice ✅

4. 9965 → uses 9 twice ✅

Now compare the numbers:

• 9652

• 9562

• 9659

• 9965 ← This is the greatest

✅ Answer: 9965

In the Indian System of Numeration, commas are placed according to the following pattern:

• The first comma comes after 3 digits from the right (for thousands),

• After that, commas are placed after every 2 digits (for lakhs and crores).

So, for the number 58695376:

• Start from the right:
  → 376 (first 3 digits)
  → next 2 digits: 95 → for lakhs
  → next 2 digits: 86 → for crores
  → leftmost digit: 5 → added before crores

So it becomes: 5,86,95,376

Final Answer: 5,86,95,376 ✅

In the Indian System of Numeration:

• 1 lakh = 1,00,000

• 10 lakh = 10 × 1,00,000 = 10,00,000

• 1 crore = 1,00,00,000

In the International System of Numeration:

• 1 million = 1,000,000

Now compare:

• 1,000,000 = 10,00,000 → This is 10 lakh

✅ So, 1 million = 10 lakh.

We are asked to find the greatest number that rounds off to 5000 when rounded to the nearest thousand.

? Rounding Rules for Nearest Thousand:

• If the hundreds digit is 0–499, round down to the previous thousand.

• If the hundreds digit is 500–999, round up to the next thousand.

So:

• All numbers from 4500 to 5499 round to 5000 when rounded to the nearest thousand.

Hence, the greatest such number is 5499.

✅ Correct answer: 5499.

1 billion (in the international number system) = 1,000,000,000

Now, let's convert this into lakhs (Indian number system):

• 1 lakh = 100,000

• So,

  $$\frac{1,000,000,000}{100,000}=10,000\text{lakhs}$$

Therefore:

✔️ 1 billion = 10,000 lakhs ✅

• 1 lakh = 100,000

• The predecessor of a number is the number that comes just before it.

So,

$$\text{Predecessor of }1,00,000=1,00,000-1=99,999$$

✅ Correct Option: 99999

We need the largest 5-digit number that has three different digits.

Let’s break this down:

• The largest 5-digit number is 99999, but it has only 1 unique digit.

• So, to keep the number large and still use only three different digits, we should:

  • Start with 9 (the largest possible digit),

  • Use other large digits like 8 and 7 as needed,

  • And arrange them in descending order to make the number as big as possible.

Now let’s look at the options:

1. 98978 → digits = 8, 9, 7 (✔ three different digits)

2. 99897 → digits = 9, 8, 7 (✔ three different digits)

3. 99987 → digits = 9, 8, 7 (✔ three different digits) ✅ This is the largest

4. 98799 → digits = 9, 8, 7 (✔ three different digits)

Among these, 99987 is the greatest number and meets the condition of having three different digits.

✅ Final Answer: 99987

Step-by-step:

1. The smallest 4-digit number is 1000.

2. But 1000 has only two different digits: 1 and 0.

Let’s now look for the next smallest number with:

• Four digits

• Exactly three different digits

Option analysis:

• 1002 → Digits: 1, 0, 0, 2 → ✅ Has three different digits → ✔ Valid

• 1012 → Digits: 1, 0, 1, 2 → Only three different digits → But 1012 > 1002

• 1020 → Digits: 1, 0, 2, 0 → Three different digits → But 1020 > 1002

• 1102 → Digits: 1, 1, 0, 2 → Three different digits → But 1102 > 1002

So, among all, 1002 is the smallest 4-digit number with three different digits.

✅ Correct answer: 1002

• First whole number after 38 = 39

• Last whole number before 68 = 67

Now, find how many whole numbers are there from 39 to 67 (inclusive):

$$67-39+1=29$$

✅ Final Answer: 29

We are asked to find the product of the successor and predecessor of 999.

• Successor of 999 = 999 + 1 = 1000

• Predecessor of 999 = 999 − 1 = 998

Now, multiply the successor and predecessor:

$$998\times 1000=998000$$

✅ Final Answer: 998000

Let the non-zero whole number be n.
Its successor is n + 1.
So, the product is:

$$n\times (n+1)$$

Among any two consecutive numbers, one is always even.
So, their product is always even.

Example:

• $2 \times 3 = 6$ → even

• $3 \times 4 = 12$ → even

• $5 \times 6 = 30$ → even

So, the product is always an even number. ✅

Why not the other options?

• Odd number? ❌ No — because the product of consecutive numbers is never odd.

• Prime number? ❌ No — the product of two numbers is never prime (except 1×2 = 2).

• Divisible by 3? ❌ Not always — e.g., $2 \times 3 = 6$ ✅, but $4 \times 5 = 20$ ❌

✅ Correct option: "an even number".

Step 1: Add x to 25

$$25+x$$

Step 2: Subtract x from 25

$$25-x$$

Step 3: Add the results

$$(25+x)+(25-x)=25+x+25-x=50$$

✅ Final Answer: 50

1. (7 + 8) + 9 = 7 + (8 + 9)

This is true because addition is associative.

• Left side: (7 + 8) + 9 = 15 + 9 = 24

• Right side: 7 + (8 + 9) = 7 + 17 = 24
  ✅ True

2. (7 × 8) × 9 = 7 × (8 × 9)

This is true because multiplication is associative.

• Left side: (7 × 8) × 9 = 56 × 9 = 504

• Right side: 7 × (8 × 9) = 7 × 72 = 504
  ✅ True

3. 7 + 8 × 9 = (7 + 8) × (7 + 9)

Let's evaluate both sides:

• Left side:
  According to order of operations, multiplication before addition:
  → 7 + (8 × 9) = 7 + 72 = 79

• Right side:
  (7 + 8) × (7 + 9) = 15 × 16 = 240

❌ Not equal → False

4. 7 × (8 + 9) = (7 × 8) + (7 × 9)

This is true because of the distributive property of multiplication over addition.

• Left side: 7 × (8 + 9) = 7 × 17 = 119

• Right side: (7 × 8) + (7 × 9) = 56 + 63 = 119
  ✅ True

✅ Correct answer:

7 + 8 × 9 = (7 + 8) × (7 + 9) is not true.

Let's look at each statement:

1. 0 + 0 = 0 → ✅ True. Adding zero to zero gives zero.

2. 0 – 0 = 0 → ✅ True. Subtracting zero from zero is also zero.

3. 0 × 0 = 0 → ✅ True. Zero multiplied by zero is zero.

4. 0 ÷ 0 = 0 → ❌ Not true. Division by zero is not defined in mathematics.

? 0 ÷ 0 is an undefined expression because there is no single number that satisfies it. Any number multiplied by 0 gives 0, so there's no unique solution.

Final Answer: 0 ÷ 0 = 0 is not true ✅

Original number: 6350947

• The digit 6 is in the first position (index 0).

• We must keep 6 fixed in its place.

• Remaining digits to rearrange: 3, 5, 0, 9, 4, 7

We need to arrange these remaining digits in ascending order to get the smallest possible number.

Ascending order of the digits: 0, 3, 4, 5, 7, 9

Now place these after 6:

✅ 6034579 ← This is the smallest possible number with 6 at the start and the rest in ascending order.

✅ Correct Answer: 6034579

• A three-digit number is any number from 100 to 999.

• Among the given options:

  • 900 → three-digit

  • 100 → three-digit

  • 999 → three-digit

  • 990 → three-digit

Now, compare them:

• 100 is the smallest among 100, 900, 990, and 999.

✅ Correct answer: 100

The set of whole numbers includes all non-negative integers:
0, 1, 2, 3, 4, 5, ... and so on without end.

This means:

• There is no largest whole number because you can always add 1 to get a bigger number.

• For example: If you say 1, then 2 is bigger. If you say 1000, then 1001 is bigger.

? Therefore, the largest whole number is indeterminable (cannot be determined).

Answer: Indeterminable

• The number 10,00,000 is read as ten lakh.

• The predecessor of a number is the number that comes just before it.
  → That means:

  $$\text{Predecessor of 10,00,000}=10,00,000-1=9,99,999$$

✅ Correct Option: 9,99,999

The number 95,876 is read in the following way:

• 95 in the thousands place → Ninety five thousand

• 876 in the units/hundreds place → Eight hundred seventy six

Putting them together:
Ninety five thousand eight hundred seventy six

Correct answer:
Ninety five thousand eight hundred seventy six

The number "seventy thousand three hundred sixty four" can be broken down as:

• Seventy thousand = 70,000

• Three hundred = 300

• Sixty four = 64

Now, add them all:

70,000 + 300 + 64 = 70,364

So, the number in figures is 70364.

? Correct option: 70364

? Face Value:

• The face value of a digit is the digit itself, regardless of its position.

• So, the face value of 3 is 3.

? Place Value:

• The place value depends on the position of the digit in the number.

• In 53974, the digit 3 is in the thousands place.

? So, place value of 3 = 3 × 1000 = 3000

✅ Final Answer: 3000, 3 ✅

✅ Step 1: Use all digits exactly once

We are told to use the digits: 3, 5, 1, 2, 2, 7, 0, 4
This is 8 digits → perfect for an 8-digit number.

✅ Step 2: Arrange digits in descending order

To get the greatest number, arrange the digits from largest to smallest:

Given digits: 7, 5, 4, 3, 2, 2, 1, 0

So, the greatest number = 75432210

✅ Step 3: Ensure number doesn't start with 0

It doesn’t — it starts with 7 → valid 8-digit number.

✅ Final Answer: 75432210 ✅

• 1 lakh = 100,000

• 1 crore = 1,00,00,000

Now divide:

$$1\, \text{crore} \div 1\, \text{lakh} = \frac{1,00,00,000}{1,00,000} = 100$$

Oops! That shows 100 lakhs, but that's incorrect.

Wait — let's recheck:

Actually:

$$1\, \text{crore} = 100\, \text{lakhs} \text{ ❌ (Incorrect)}$$

$$1\, \text{crore} = 10,000,000$$

$$1\, \text{lakh} = 100,000$$

$$10\, \text{lakh} = 1,000,000$$

$$\therefore \boxed{10\, \text{lakh} = 1\, \text{crore}} \text{ ❌ Again incorrect}$$

10lakh= 1crore​ ❌ Again incorrect

Wait — correction:

Real values:

• 1 lakh = 1,00,000

• 10 lakh = 10,00,000

• 1 crore = 1,00,00,000

So,

$$\frac{1,00,00,000}{1,00,000} = 100$$

✅ Correct Answer: 3. 100 lakhs

✅ Final Answer: 3. 100 lakhs

(100 lakhs make 1 crore)

Descending order means numbers arranged from largest to smallest.

Let’s check Option 2:

• 160 → largest

• 159 → next

• 158 → smaller

• 154 → smallest

All numbers are arranged from highest to lowest, so this is correct ✅

❌ Why not the others?

• Option 1: 154 < 159 < 160 → goes up and down → ❌

• Option 3: Ends with 159 which is larger than 154 → ❌

• Option 4: 154 before 158 → out of order → ❌

✅ Final Answer: 2. 160, 159, 158, 154

Ascending order means from smallest to largest.

Let’s check Option 3 step-by-step:

• 172803 → smallest

• 372108 → middle

• 723108 → largest

So this option is correctly arranged in ascending order ✅

❌ Why not the others?

• Option 1: 372108 comes before 172803 → ❌

• Option 2: Starts with the largest number → ❌

• Option 4: Middle number is the smallest → ❌

✅ Final Answer: 3. 172803, 372108, 723108

Ascending order means arranging numbers from smallest to largest.

Let’s look at the numbers in Option 3:

• 163982 → smallest

• 192136 → middle

• 363281 → largest

This is correct ascending order.

❌ Why not the others?

• Option 1: 192136, 163982, 363281 → 192136 > 163982 → ❌

• Option 2: 363281, 192136, 163982 → Largest comes first → ❌

• Option 4: 192136, 363281, 163982 → Last number is smaller → ❌

✅ Final Answer: 3. 163982, 192136, 363281

1. 100002 > 100000 → ✅ True

2. 58479 < 58947 → ✅ True

3. 1100101 > 1010011 → ✅ True (You can verify by comparing digit by digit)

4. 479011 > 479011 → ❌ False, because:

• A number cannot be greater than itself

• 479011 = 479011, so the statement is not correct

✅ Final Answer: 4. 479011 > 479011

• 700,000

• • 60,000 → 760,000

• • 3,000 → 763,000

• • 200 → 763,200

• • 90 → 763,290

• • 8 → 763,298

✅ Final Answer: 763,298

• Natural numbers are the counting numbers:
  1, 2, 3, 4, ...

• They do not include 0 or any negative numbers.

• -1 is not natural.

• Infinity is not a number — it's a concept.

✅ Final Answer: 1 is the smallest natural number.

Explanation:

• Whole numbers are: 0, 1, 2, 3, 4, 5, ...

• The smallest whole number is 0
  (It includes 0 and all positive integers)

❌ Why not others?

• 1 → It's a whole number, but not the smallest

• -1 → It's a negative number (not a whole number)

• Infinitive → Not a valid number in this context

✅ Final Answer: 0

• 1 million = 1,000,000

Now convert it to the Indian number system:

• 1 lakh = 100,000

• So, 1,000,000 ÷ 100,000 = 10 lakh

✅ Final Answer: 10 lakh

Explanation (Descending Order):

Descending order means arranging numbers from largest to smallest.

Let's compare the numbers in each option:

Option 3:

• 826188 → largest

• 682818 → second largest

• 188826 → smallest

Since the numbers are listed from largest to smallest,
➡️ Option 3 is in descending order.

❌ Why not the others?

Option 1:

• 682818 < 826188 → wrong order
  ➡️ Not descending

Option 2:

• Starts with 188826 (smallest)
  ➡️ Definitely not descending

Option 4:

• 826188 > 188826 ✅

• But 188826 < 682818 ❌
  ➡️ Not descending overall

✅ Final Answer:

Option 3: 826188, 682818, 188826 is the correct descending order.

In Roman numerals, some symbols can be repeated, but V, L, and D are not among them.

Here’s a breakdown:

✅ Symbols that can be repeated:

• I, X, C, and M
  These can be repeated up to three times in a row.

  • Example:

    • III = 3

    • XXX = 30

    • CCC = 300

    • MMM = 3000

❌ Symbols that cannot be repeated:

• V (5)

• L (50)

• D (500)
  These symbols are never repeated in Roman numeral notation.

Summary:

Since V, L, and D cannot be repeated, the statement is False.

In Roman numerals, certain rules must be followed. Let's examine each option:

1. VX ❌

   • This is not valid.

   • The numeral "V" (5) cannot be subtracted from "X" (10), because "V" is not a subtractive numeral.

   • Valid subtractive combinations include:

     • I before V or X → IV (4), IX (9)

     • X before L or C → XL (40), XC (90)

     • C before D or M → CD (400), CM (900)

   • VX breaks these rules, so it is meaningless.

2. III ✅

   • Valid Roman numeral = 3

   • "I" can be repeated up to 3 times.

3. XX ✅

   • Valid Roman numeral = 20

   • "X" can be repeated up to 3 times.

4. XC ✅

   • Valid Roman numeral = 90

   • "X" can be placed before "C" to subtract 10 from 100.

✅ Correct Answer: VX is meaningless

Let’s analyze each option:

1. LXII

   • L = 50

   • X = 10

   • II = 2

   • Total = 50 + 10 + 2 = 62 ✅ (Correct)

2. XCI

   • XC = 90

   • I = 1

   • Total = 90 + 1 = 91 ✅ (Correct)

3. LC

   • L = 50

   • C = 100

   • "LC" is invalid because you cannot subtract 50 (L) from 100 (C) in Roman numeral rules. Only I, X, or C can be subtracted from larger values, and only in specific combinations (like IV, IX, XL, XC, etc.). ❌ (Incorrect)

4. XLIV

   • XL = 40

   • IV = 4

   • Total = 40 + 4 = 44 ✅ (Correct)

✅ Correct Answer: LC

In Roman numerals, if a symbol is repeated, its value is added as many times as it occurs—not multiplied.

For example:

• III = 1 + 1 + 1 = 3, not 1 × 3.

• XX = 10 + 10 = 20, not 10 × 2.

So, repetition results in addition, not multiplication. Therefore, the statement is False.

In Roman numerals, if a symbol is repeated, its value is added each time it appears.

For example:

• II = 1 + 1 = 2

• XXX = 10 + 10 + 10 = 30

However, there are some rules:

• Only the symbols I (1), X (10), C (100), and M (1000) can be repeated, and they can be repeated up to three times.

• Symbols like V (5), L (50), and D (500) are never repeated.

So, the statement is True — if a Roman numeral symbol is repeated (and it's allowed), its value is added as many times as it occurs.

Answer: True

In Roman numerals, if a symbol is repeated, its value is added as many times as it occurs (with some restrictions).

For example:

• III = 1 + 1 + 1 = 3

• XX = 10 + 10 = 20

Important Rules:

• Only I, X, C, and M can be repeated up to three times in a row.

• Symbols like V, L, and D are never repeated.

So, the statement "its value is not added as many times as it occurs" is False

In Roman numerals, a symbol is not repeated more than three times in a row. This is one of the basic rules of Roman numeral notation.

For example:

• III = 3 (I is repeated 3 times — valid)

• But IIII is not valid for 4. Instead, 4 is written as IV (which means 5 - 1).

Symbols like:

• I, X, C, M can be repeated (but not more than 3 times in a row).

• V, L, D are never repeated, even once.

So, the statement is True ✅.

In Roman numerals, no symbol is repeated more than three times in a row. This is one of the key rules of Roman numeral formation. For example:

• Correct: III = 3

• Incorrect: IIII (should be written as IV)

This rule helps maintain clarity and avoids confusion in reading large numbers. Therefore, a symbol cannot be repeated more than three times.

Answer: False

In Roman numerals, the symbols V (5), L (50), and D (500) are never repeated. This is one of the core rules of Roman numeral formation.

• Symbols like I (1), X (10), and C (100) can be repeated up to three times in a row (e.g., III = 3, XXX = 30, CCC = 300).

• However, V, L, and D are never repeated because they represent "half" of the next higher base (e.g., V is half of X, L is half of C, and D is half of M).

So, repeating V, L, or D would violate the rules of Roman numeral notation.

✅ Correct Answer: True

1. IXX

• This is incorrect.

• The correct way to write 19 in Roman numerals is XIX (10 + 9).

• IXX would imply 1 before 20, which is not a valid formation.

2. VVII

• This is incorrect.

• Roman numeral rule: V is never repeated.

• Also, this expression is not valid structurally. VII (7) is valid, but VVII has two Vs, which is wrong.

3. IVC

• This is incorrect.

• Roman numeral rule: A smaller numeral can only be placed before the next two higher denominations to indicate subtraction.

  • I can precede V and X.

  • So, IV = 4 is valid.

  • But IVC implies 4 before 100, which is not valid Roman numeral format.

  • 96 should be written as XCVI.

✅ Therefore, the correct answer is: All of these

The Roman numeral LXXX can be broken down as:

• L = 50

• X = 10

• X = 10

• X = 10

So:

L + X + X + X = 50 + 10 + 10 + 10 = 80

✅ Correct Answer: 80

Roman numeral rules state:

• The symbols V (5), L (50), and D (500) are never repeated.

• Valid combinations build numbers using addition (left to right) and sometimes subtraction (if a smaller numeral comes before a larger one).

Let’s evaluate each option:

• LXXX = 50 + 10 + 10 + 10 = 80 ✅ Correct

• LXX = 50 + 10 + 10 = 70 ✅ Correct

• LX = 50 + 10 = 60 ✅ Correct

• LLX ❌ Incorrect — The symbol L (50) is repeated, which is not allowed in Roman numerals.

✅ Correct Answer: LLX

To write 92 in Roman numerals:

1. Break 92 into parts:
   90 + 2

2. Roman numeral for 90 = XC
   (Because 100 is C, and 10 is X, so 90 is written as 100 - 10 = XC)

3. Roman numeral for 2 = II

4. Combine them:
   XC + II = XCII

Why the others are incorrect:

• IIXC – Invalid order of symbols. Subtractive notation like XC must come before smaller values.

• CIIX – Incorrect and meaningless; placing "C" (100) before "IIX" makes no logical Roman numeral sense.

• XIIC – Invalid structure; 12 is XII and cannot be followed by C (100) in this form.

✅ Correct Roman numeral for 92 is: XCII

We need to write 73 in Roman numerals.

Break 73 into Roman numeral parts:

• 70 = LXX
  (L = 50, X = 10, X = 10 → 50 + 10 + 10 = 70)

• 3 = III
  (I + I + I = 3)

So,
73 = LXX + III = LXXIII

Let's examine the options:

1. XXXCIII – ❌ Incorrect

   • "XC" = 90, "XXX" = 30 → 30 + 90 = 120 → This is invalid and misused.

2. XLXXXIII – ❌ Incorrect

   • "XL" = 40, "XXX" = 30, "III" = 3 → 40 + 30 + 3 = 73, but "XLXXX" is not valid Roman numeral format. You should not combine subtractive and additive parts improperly. "XLXXX" is not a standard format.

3. LXXIII – ✅ Correct Roman numeral for 73

4. All of these – ❌ Only LXXIII is valid.

✅ Final Answer: LXXIII

1. CIV < 56

• CIV = 100 + 4 = 104

• 56 is just 56

➡️ 104 < 56 is False
✅ This is NOT correct

2. XLIV < LXIX

• XLIV = 40 + 4 = 44

• LXIX = 60 + 9 = 69

➡️ 44 < 69 is True

3. L - IX = 41

• L = 50

• IX = 9

• 50 - 9 = 41

➡️ This is True

4. LXX + IX < 85

• LXX = 70

• IX = 9

• 70 + 9 = 79

• 79 < 85 → True

✅ Final Answer: CIV < 56

Roman numeral LXXIV can be broken down as:

• L = 50

• X = 10

• X = 10

• IV = 4 (since I before V means 5 - 1)

Now add the values:

50 + 10 + 10 + 4 = 74

So, the correct Hindu-Arabic number is 74 ✅

Roman numeral: XCIX

We break this down:

• XC = 90 (because X before C means 100 - 10 = 90)

• IX = 9 (because I before X means 10 - 1 = 9)

Now add them:

• XC (90) + IX (9) = 99

✅ Correct answer: 99

The Roman numeral XCV can be broken down as:

• X = 10

• C = 100

• V = 5

In Roman numerals, when a smaller numeral appears before a larger one, it is subtracted.

So:

• XC = 100 - 10 = 90

• V = 5

Now add them:

• 90 + 5 = 95

✅ Final Answer: 95

To understand why, let's break down each option:

1. LXII = L (50) + X (10) + II (2) = 62 → ✅ Correct

2. XCI = XC (90) + I (1) = 91 → ✅ Correct

3. LC ❌ Incorrect

   • L = 50, C = 100

   • In Roman numerals, a smaller numeral cannot precede a numeral more than 10 times greater, except in standard cases like:

     • IV = 4

     • IX = 9

     • XL = 40

     • XC = 90

     • CD = 400

     • CM = 900

   • LC (50 before 100) is not a valid subtraction rule. So this is incorrect.

4. XLIV = XL (40) + IV (4) = 44 → ✅ Correct

✅ Final Answer: LC

To convert 2°C to Fahrenheit, use the formula:

$$\mathrm{°}F=(\mathrm{°}C\times \frac{9}{5})+32$$

Step-by-step calculation:

$$\mathrm{°}F=(2\times \frac{9}{5})+32=\left(\frac{18}{5}\right)+32=3.6+32=35.6\mathrm{°}F$$

✅ Correct Answer: (A) 35.6° F

Step-by-step calculation:

$$\mathrm{°}C=\frac{5}{9}(66-32)=\frac{5}{9}\times 34=\frac{170}{9}\approx 18.89\mathrm{°}C$$

Final Answer:

$$\boxed{{\displaystyle {18.89}^{\circ }\mathrm{C<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}}$$

So, the closest correct option is:

(A) 18.8°F — But this is labeled incorrectly, because 18.8°F is still in Fahrenheit.

Corrected Answer:

The value of 66°F in degree Celsius is approximately 18.8°C, not Fahrenheit.

✅ Correct option text should be:
(A) 18.8°C

If "Answer A" is required as correct, the label should be fixed.

✅ Correct Answer: (A)

To convert 45°F to degrees Celsius, we use the Fahrenheit to Celsius formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Substitute 45°F into the formula:

$$\mathrm{°}C=\frac{5}{9}(45-32)=\frac{5}{9}\times 13=\frac{65}{9}\approx 7.22\mathrm{°}C$$

Final Answer:

(B) 7°C

Explanation:

• Subtract 32 from 45: 45 − 32 = 13

• Multiply 13 by 5: 13 × 5 = 65

• Divide 65 by 9: 65 ÷ 9 ≈ 7.22°C

• Rounded to the nearest whole number: 7°C

✅ Correct Option: (B)

To convert Fahrenheit (°F) to Celsius (°C), we use the formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Given:

$$\mathrm{°}F=20$$

Now substitute into the formula:

$$\mathrm{°}C=\frac{5}{9}(20-32)=\frac{5}{9}\times (-12)=\frac{-60}{9}=-6.66\bar{6}$$

So the value in Celsius is approximately:

$$-6.67\mathrm{°}C$$

Correct Answer:

(A) -6.66° C

Explanation:

• Subtracted 32 from 20 → $20 - 32 = -12$

• Multiplied by $\frac{5}{9}$ → $\frac{5}{9} \times -12 = -6.66...$

• Result: $-6.66\overline{6} \approx -6.66°C$

✅ Option A is correct.

To convert temperature from Fahrenheit (°F) to Celsius (°C), use the formula:

$${}^{\circ }C=\frac{5}{9}{(}^{\circ }F-32)$$

Given:

$${}^{\circ }F=114$$

Now apply the formula:

$${}^{\circ }C=\frac{5}{9}(114-32)=\frac{5}{9}\times 82=\frac{410}{9}\approx {45.56}^{\circ }C$$

✅ Correct Answer: D. 45.6° C

To convert Fahrenheit (°F) to Celsius (°C), use the formula:

$$\mathrm{°}C=\frac{5}{9}\times (\mathrm{°}F-32)$$

Given:

$$\mathrm{°}F=58$$

Step-by-step calculation:

$$°C = \frac{5}{9} \times (58 - 32)$$
$$°C = \frac{5}{9} \times 26$$
$$\mathrm{°}C=\frac{130}{9}\approx 14.44$$

Final Answer:

14.4° C

Correct Option:

(C) 14.4° C ✅

To convert temperature from Celsius to Fahrenheit, use the formula:

$$F=(\frac{9}{5}\times C)+32$$

Given:

$C = -18^\circ$

C=−18∘

Substitute into the formula:

$$F=(\frac{9}{5}\times -18)+32=(-32.4)+32=-{0.4}^{\circ }F$$

✅ Correct Answer: A. -0.4° F

To convert Celsius (°C) to Fahrenheit (°F), use the formula:

$$\mathrm{°}F=(\frac{9}{5}\times \mathrm{°}C)+32$$

Given:

$$°C = 210$$

$$\mathrm{°}F=(\frac{9}{5}\times 210)+32=378+32=\boxed{{\displaystyle {410}^{\circ }\mathrm{F<span\; style="font-size:\; 16px;\; font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"></span>}}}$$

✅ Correct Answer: B. 410° F

To convert Celsius to Fahrenheit, we use the formula:

$$F=(\frac{9}{5}\times C)+32$$

Given:

$C = 17^\circ$

C=17∘

Step-by-step Calculation:

$$F=(\frac{9}{5}\times 17)+32=(30.6)+32={62.6}^{\circ }F$$

✅ Correct Answer: B. 62.6° F

Step-by-step Conversion:

Given:

$$\mathrm{°}F=58$$

Apply the formula:

$$°C = \frac{5}{9} (58 - 32) = \frac{5}{9} \times 26$$
$$\mathrm{°}C=\frac{130}{9}\approx 14.4\mathrm{°}C$$

So, 58°F = 14.4°C, not any of the options listed like 167°C, 134°C, etc.

Conclusion:

The correct conversion of 58°F is 14.4°C, so none of the given options (A–D) are correct. If the question says "Answer C" and "Explanation", then either the question is incorrect or the temperature value is wrong. Possibly, the Fahrenheit value was meant to be 350°F, which gives:

$$\mathrm{°}C=\frac{5}{9}(350-32)=\frac{5}{9}\times 318=176.6\mathrm{°}C$$

That matches option (C) 176.6°C

To convert temperature from Fahrenheit to Celsius, we use the formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Given:

$$°F = 62$$

Substitute into the formula:

$$\mathrm{°}C=\frac{5}{9}(62-32)=\frac{5}{9}\times 30=\frac{150}{9}\approx 16.7\mathrm{°}C$$

✅ Correct Answer: C. 16.7° C

To convert Fahrenheit (°F) to Celsius (°C), we use the formula:

$$°C = \frac{5}{9} (°F - 32)$$

Given:

°F = 10

Step-by-step calculation:

$$°C = \frac{5}{9} (10 - 32)$$
$$°C = \frac{5}{9} (-22)$$
$$°C = -\frac{110}{9} ≈ -12.2° C$$

✅ Correct answer: D. -12.2°C

$$°C=35$$

Apply the formula:

$$\mathrm{°}F=(35\times \frac{9}{5})+32=(35\times 1.8)+32=63+32=95\mathrm{°}F$$

✅ Correct Answer: (A) 95°F

To convert Fahrenheit to Celsius, we use the formula:

$${}^{\circ }C=\frac{5}{9}({}^{\circ }F-32)$$

Given:

$$^\circ F = 95$$

$${}^{\circ }C=\frac{5}{9}(95-32)=\frac{5}{9}\times 63={35}^{\circ }C$$

✅ Correct Answer: A. 35° C

To convert 140°F to degrees Celsius, we use the Fahrenheit to Celsius conversion formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Substitute 140°F into the formula:

$$°C = \frac{5}{9}(140 - 32) = \frac{5}{9}(108)$$
$$°C = \frac{540}{9} = 60°C$$

✅ Correct Answer: (A) 60° C

To convert temperature from Fahrenheit (°F) to Celsius (°C), use the formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Given:

$$°F = 46$$

Calculation:

$$\mathrm{°}C=\frac{5}{9}(46-32)=\frac{5}{9}\times 14=\frac{70}{9}\approx 7.78\mathrm{°}C$$

✅ Correct Answer: C. 7.8° C

To convert temperature from Fahrenheit (°F) to Celsius (°C), use the formula:

$$\mathrm{°}C=\frac{5}{9}(\mathrm{°}F-32)$$

Given:

$$°F = 140$$

Substitute into the formula:

$$\mathrm{°}C=\frac{5}{9}(140-32)=\frac{5}{9}\times 108={60}^{\circ }C$$

✅ Correct Answer: A. 60° C

We are given the temperature in Fahrenheit (°F) as:

$${83}^{\circ }\text{F}$$

We need to convert it into Celsius (°C) using the formula:

$${}^{\circ }\text{C}=\frac{5}{9}{(}^{\circ }\text{F}-32)$$

Step-by-step Calculation:

$${}^{\circ }\text{C}=\frac{5}{9}(83-32)=\frac{5}{9}\times 51=\frac{255}{9}={28.3}^{\circ }\text{C}$$

✅ Correct Answer: D. 28.3° C

To convert Celsius to Fahrenheit, we use the formula:

$$\mathrm{°}F=(\frac{9}{5}\times \mathrm{°}C)+32$$

Given:

$$\mathrm{°}C=72$$

Now apply the formula:

$$\mathrm{°}F=(\frac{9}{5}\times 72)+32=(129.6)+32=161.6\mathrm{°}F$$

✅ Correct Answer: B. 161.6° F

Step 1: Know the conversion factor

1 meter = 100 centimeters

Step 2: Convert

$$781\text{ cm/s}=\frac{781}{100}\text{ m/s}=7.81\text{m/s}$$

Answer: (C) 7.81 m/s

Step-by-step conversion:

We know the metric conversions:

• 1 gram (g) = 1000 mg

• 1 decigram (dg) = 100 mg

• 1 centigram (cg) = 10 mg

Now convert each unit to mg:

1. 3 grams = 3 × 1000 = 3000 mg

2. 2 decigrams = 2 × 100 = 200 mg

3. 5 centigrams = 5 × 10 = 50 mg

Add all together:

3000 mg + 200 mg + 50 mg = 3250 mg

✅ Final Answer: C. 3250 mg

✅ Step-by-step Calculation:

$$4\text{ L}=4\times 100=400\text{cl}$$

✅ Correct Answer: A. 400 cl

107 cm

Conversion:

$$107÷100=1.07\text{m}$$

✅ Correct Answer:  1.07 m$$$$

• 1 km = 1000 meters

• 1 meter = 1000 millimeters (mm)

So:

$$1\text{ km}=1000\text{ m}\times 1000\text{ mm/m}=1,000,000\text{mm}$$

Therefore:

• 1 kilometer = 1,000,000 millimeters

• ✅ Correct answer: D. 1000000 mm

• 1 kilometer = 1000 meters

• 1 hour = 3600 seconds
  So,

$$1\text{m/s}=\frac{1000}{3600}\text{km/hr}=\frac{5}{18}\text{km/hr}$$

Then,

$$10^{-1}$$