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Write the cubes of 5 natural numbers of the form `3n+2(idote .5 ,8, 11 , )` and verify the following : The cube of a natural number of the form `3n+2\ ` is a natural number of the same form i.e. when it is dividend by 3 the remainder is 2

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To solve the problem, we need to find the cubes of 5 natural numbers of the form \(3n + 2\) and then verify that their cubes also fall into the same form \(3n + 2\). ### Step-by-Step Solution: **Step 1: Identify 5 natural numbers of the form \(3n + 2\)** The natural numbers that fit the form \(3n + 2\) can be generated by substituting different values of \(n\). - For \(n = 0\): \(3(0) + 2 = 2\) - For \(n = 1\): \(3(1) + 2 = 5\) ...
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RD SHARMA-CUBES AND CUBE ROOTS-All Questions
  1. Write the cubes of 5 natural number which are multiples of 3 and ver...

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  2. Write the cubes of 5 natural number which are of form 3n+1(eg. 4 ,7,...

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  3. Write the cubes of 5 natural numbers of the form 3n+2(idote .5 ,8, 1...

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  4. Write the cubes of 5 natural numbers of which are multiples of 7 and...

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  5. Which of the following are perfect cubes? (I)64            (ii) 216 ...

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  6. Which of the following are perfect cubes? (I)1000               (ii) 1...

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  7. Which of the following are perfect cubes ? (I)4608        (ii) 10648...

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  8. Which of the following are cubes of even natural numbers? 216, 512,...

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  9. Which of the following are cubes of odd natural numbers? 125, 343,17...

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  10. What is the smallest number by which the following numbers must be m...

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  11. What is the smallest number by which the following numbers must be m...

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  12. By which smallest number must the following numbers be divided so th...

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  13. By which smallest number must the following numbers be divided so th...

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  14. Prove that if a number is trebled then its cube is 27 times the cube...

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  15. What happens to the cube of a number if the number multiplied by (I...

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  16. Find the volume of a cube, one face of which has an area of 64 m^2do...

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  17. Find the volume of cube whose surface area is 384 m^2dot

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  18. Evaluate the following : (I){(5^2+12^2)^(1/2)}^3 (ii) {(6^2+8^2)^(1...

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  19. Write the unit digit of the cube of each of the following numbers: ...

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  20. Find the cubes of the following numbers by column method: 35      ...

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