Mathematics Q&A for Class 10
22 free answers in Mathematics for Class 10 students, across CBSE, ICSE and State boards.
Question & Answer
Questions
What is a composite number? Give examples.
A composite number is a natural number greater than 1 with more than two factors divisible by numbers other than just 1 and itself.Smallest composite number: 4All even numbers greater than 2 are composite.1 is neither prime nor composite.Number</
What is an irrational number? Give examples.
An irrational number is a real number with a non-terminating, non-repeating decimal expansion cannot be expressed as p/q.NumberValue (approx.)√21.41421356...√31.73205080...π3.14159265...e2.71828182...Note: √4 = 2 is rational. Only square roots of non-perfect squ
What are even numbers?
Even numbers are integers exactly divisible by 2 they leave no remainder when divided by 2.General form: 2n (where n is any integer)Zero is even. Negative even numbers exist (−2, −4, ...).Always end in: 0, 2, 4, 6, or 8Even + Even = Even; Even × Odd = Even; Even + Odd = Odd.<
What are natural numbers?
Natural numbers are the basic counting numbers: 1, 2, 3, 4, 5, ...Symbol: NAlways positive, never include zero (in standard school definition), no fractions or decimals.Infinite no largest natural number.Hierarchy: N ⊂ Whole (W) ⊂ Integers (Z) ⊂ Rational (Q) ⊂ Real (R)<
What is the greatest 7-digit number?
The greatest 7-digit number is 9,999,999 (Nine million, nine hundred and ninety-nine thousand, nine hundred and ninety-nine).Reasoning: Place the largest digit (9) in all seven positions.PositionDigitValueTen Lakhs990,00,000Lakhs99,00,000Ten Thousands990,000Thousand
What is the angle formed by one-fourth of a revolution?
One-fourth of a revolution = 90° (a right angle).Full revolution = 360°360° ÷ 4 = 90°FractionAngle1 revolution360°1/2180° (straight angle)1/490° (right angle)1/845°<tr
What is the value of 3³?
3³ = 273³ = 3 × 3 × 3 = 9 × 3 = 27"Cubed" because 3³ = volume of a cube with side 3.3¹ = 3; 3² = 9; 3³ = 273⁴ = 81
Why is the number zero so different and mysterious from other numbers?
Zero is the only number that breaks standard mathematical rules in multiple ways:Division by zero is undefined: 5/0 has no valid answer. If 5/0 = x, then 0 × x = 5 — but 0 times anything is always 0, never 5. The operation is a logical impossibility.Zero is neither positive nor negative: Every other number belongs to one category. Z
Why does 0 exist if it is nothing?
Zero exists precisely because "nothing" needs to be represented and that representation is not nothing at all.Historical context:Ancient Egypt, Rome, and Greece had no symbol for zero creating enormous problems in calculationThe concept of zero as a number was formally developed in India by Brahmagupta in the 7th century CE, then transmi
What is the most uncommon number between 1 and 100?
This has both a psychological and a mathematical answer.Psychologically: When asked to pick a "random" number between 1 and 100, people avoid obvious choices like 1, 10, 50, and 100. Research shows 37 and 73 are the most commonly chosen "random" numbers. This means the truly uncommon choices are the ones people overlook as "too obvious": 1, 2, 99, 100.Mathematically (most distinctive numbers near 100):<li data-list-item-id="e8f9ecf406c4e
How do you define a number in mathematics?
A number is a mathematical object used to count, measure, and label. It is an abstract concept representing quantity or position.The major types of numbers (hierarchy from simple to complex):TypeDescriptionExamplesNatural numbers (N)Counting numbers starting from 11, 2, 3, 4, 5...Whole numbers (W)Natural numbers including 0</td
7 & 8 Digit Numbers
QuestionAnswerGreatest 7-digit number9,99,99,999 — wait, 99,99,999 (Seven 9s)Greatest 7-digit number with 3 in hundreds place99,99,399Greatest 8-digit number9,99,99,999 (Nine crore ninety-nine lakh…)
Is tan 30 equal to 1?
No. tan 45° = 1 (not tan 30°). Quick reference:Angletan value0°030°1/√3 ≈ 0.57745°160°√3 ≈ 1.73290°undefinedPoint: tan 30° = 1/√3 ≈ 0.577. It is less than 1. Only tan 45° equals exactly 1.
Is tan 30 = 1/√3 or √3/3?
Both are exactly equal √3/3 is simply the rationalized form of 1/√3 (multiply top and bottom by √3). Both are fully correct; √3/3 is preferred in exams because it has no square root in the denominator.
What is the exact value of tan 30°?
tan 30° = 1/√3 = √3/3 ≈ 0.5774 Derived from a 30-60-90 triangle: opposite side = 1, adjacent side = √3, so tan = 1/√3.
"I love you" in Roman numerals
Most commonly expressed as I-IV-III (1-4-3), representing the letter count of each word (I=1 letter, love=4 letters, you=3 letters). As a full number: 143 = CXLIII.
What is XXVI VI?
XXVI = 26, VI = 6Most likely represents the date 26th June (26/6).
XXV, XXVI, XXVII, XXVIII, XXIX in numbers
RomanValueXXV25XXVI26XXVII27XXVIII28XXIX29
Numbers 1–9 in Roman numerals
NumberRomanNumberRoman1I6VI2II7VII3III8VIII4IV9IX5V Note: 4 = IV (subtractive: 5−1) and 9 = IX (10−1).
Does XVIII mean 18?
Yes.X(10) + V(5) + I + I + I(3) = 18