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MathematicsClass 10CBSE

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…)

MathematicsClass 10CBSE

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.

MathematicsClass 10CBSE

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.

MathematicsClass 10CBSE

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.

MathematicsClass 10CBSE

"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.

MathematicsClass 10CBSE

What is XXVI VI?

XXVI = 26, VI = 6Most likely represents the date 26th June (26/6).

MathematicsClass 10CBSE

XXV, XXVI, XXVII, XXVIII, XXIX in numbers

RomanValueXXV25XXVI26XXVII27XXVIII28XXIX29

MathematicsClass 10CBSE

Numbers 1–9 in Roman numerals

NumberRomanNumberRoman1I6VI2II7VII3III8VIII4IV9IX5V Note: 4 = IV (subtractive: 5−1) and 9 = IX (10−1).

MathematicsClass 10CBSE

Does XVIII mean 18? 

Yes.X(10) + V(5) + I + I + I(3) = 18

MathematicsClass 10CBSE

Is 0 a factor of 12? 

NO. Division by zero is undefined. 0 is a multiple of every number, never a factor.

MathematicsClass 10CBSE

Spellings 11–20

NumberSpellingNumberSpelling11Eleven16Sixteen12Twelve17Seventeen13Thirteen18Eighteen14Fourteen19Nineteen15Fifteen20Twenty19 = Nineteen, 90 = Ninety (both retain the 'e' from "nine" common error: "Ninty" is wrong)XIX = 19 (not 21 IX means 9 via subtractive rule; XXI = 21)11th = Eleventh | 12th = TwelfthFactors:NumberFactors121, 2, 3, 4, 6, 12151, 3, 5, 15181, 2, 3, 6, 9, 18201, 2, 4, 5, 10, 20211, 3, 7, 21231, 23 (prime)241, 2, 3, 4, 6, 8, 12, 24271, 3, 9, 27361, 2, 3, 4, 6, 9, 12, 18, 36

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