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# Hots Questions - Real Numbers Class 10 Notes | EduRev

## Class 10 : Hots Questions - Real Numbers Class 10 Notes | EduRev

The document Hots Questions - Real Numbers Class 10 Notes | EduRev is a part of the Class 10 Course Class 10 Mathematics by VP Classes.
All you need of Class 10 at this link: Class 10

Ques 1: Show that 6n cannot end with the digit 0.
Sol: If possible, let the composite number 6n have a value which ends with the digit 0.
Hint:
âˆµ All composite numbers ending with 0 have 10 as a factor.
âˆ´10 is a factor of 6n
âˆ´ We have: 6n =  10 Ã— p, where p is a natural number
â‡’ (2 Ã— 3)=  2 Ã— 5 Ã— p
â‡’ 2n Ã— 3n = 2 Ã— 5 Ã— p
i.e. 5 is a prime factor of 2n Ã— 3n which is not possible.
Thus, our assumption was wrong and 6n cannot end with the digit 0.

Ques 2: Show that there is no integer for which is rational.
Hint:
If possible, let â€˜nâ€™ be a positive integer such that is rational.

Let

(using componendo and dividendo)

Since  are rational numbers.
âˆ´  are also rational.

i.e.  are perfect squares of +ve integers. It is not possible.

[âˆµ two perfect squares differ by 3] â‡’  Our assumption is not possible.

Ques 3: If  is an irrational number, then show that is also irrational.
Hint:
If possible, let be a rational number.

But it contradicts our assumption thatis irrational.Thus, is irrational.

Ques 4: How many prime numbers are there of the form 10n + 3, where n is a whole number 1 < n < 10?
Hint:
Substituting 1, 2, 3, .................... 10 in 10 n + 3, we have:

Thus, the required numbers are: 13, 23, 43, 53, 73 and 83.

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