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Write (T) for true and (F) for false for each of the statements given below:
The number of digits in a perfect square is even.

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The correct Answer is:
To determine whether the statement "The number of digits in a perfect square is even" is true or false, we can analyze the number of digits in various perfect squares. ### Step-by-Step Solution: 1. **Understand what a perfect square is**: A perfect square is a number that can be expressed as the square of an integer. For example, \(1^2 = 1\), \(2^2 = 4\), \(3^2 = 9\), \(4^2 = 16\), \(5^2 = 25\), and so on. 2. **Calculate the squares of some integers**: - \(1^2 = 1\) (1 digit) - \(2^2 = 4\) (1 digit) - \(3^2 = 9\) (1 digit) - \(4^2 = 16\) (2 digits) - \(5^2 = 25\) (2 digits) - \(6^2 = 36\) (2 digits) - \(7^2 = 49\) (2 digits) - \(8^2 = 64\) (2 digits) - \(9^2 = 81\) (2 digits) - \(10^2 = 100\) (3 digits) - \(11^2 = 121\) (3 digits) 3. **Count the number of digits**: - From the calculations, we observe: - Perfect squares of \(1\), \(2\), and \(3\) have 1 digit (odd). - Perfect squares of \(4\), \(5\), \(6\), \(7\), \(8\), and \(9\) have 2 digits (even). - Perfect squares of \(10\) and \(11\) have 3 digits (odd). 4. **Conclusion**: The number of digits in a perfect square can be either odd or even. Therefore, the statement "The number of digits in a perfect square is even" is **False**. ### Final Answer: (F)
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RS AGGARWAL-SQUARES-EXERCISE 3B
  1. Which of the are square of even number ? 196 441 900 625 32...

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  2. Without adding, find the sum: (1+3+5+7+9+11+13) (1+3+5+7+9+11+13+1...

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  3. Express 81 as the sum of 9 odd numbers.

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  4. Express 100 as the sum of 10 odd numbers.

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  5. Write the Pythagorena triplet whose smallest number is 6 14 16 ...

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  6. Evalute: (38)^(2) - (37)^(2) (75)^(2)-(74)^(2) (92)^(2) -(91)^(2...

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  7. Using the formula (a+b)^(2) = (a^(2) + 2ab+b ^(2)), evaluate: (310)^...

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  8. Evaluate: 69xx71

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  9. Evaluate: 94xx106

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  10. Evaluate: 88xx92

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  11. Evaluate: 78xx82

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  12. Fill in the blanks: The square of an even number is ………

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  13. Fill in the blanks: The square of an odd number is ……….

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  14. Fill in the blanks: The square of a proper fraction is ……. than the ...

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  15. Fill in the blanks: n^(2)= the sum of first n……….natural numbers.

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  16. Write (T) for true and (F) for false for each of the statements given ...

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  17. Write (T) for true and (F) for false for each of the statements given ...

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  18. Write (T) for true and (F) for false for each of the statements given ...

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  19. Write (T) for true and (F) for false for each of the statements given ...

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  20. Write (T) for true and (F) for false for each of the statements given ...

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