Hots Questions - Real Numbers Class 10 Notes | EduRev

Class 10 Mathematics by VP Classes

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:
∵ All composite numbers ending with 0 have 10 as a factor.
∴10 is a factor of 6n
∴ We have: 6n =  10 × p, where p is a natural number
⇒ (2 × 3)=  2 × 5 × p
⇒ 2n × 3n = 2 × 5 × p
i.e. 5 is a prime factor of 2n × 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 whichHots Questions - Real Numbers Class 10 Notes | EduRev is rational.
Hint:
If possible, let ‘n’ be a positive integer such thatHots Questions - Real Numbers Class 10 Notes | EduRev is rational.

Let Hots Questions - Real Numbers Class 10 Notes | EduRev
Hots Questions - Real Numbers Class 10 Notes | EduRev
(using componendo and dividendo)

Hots Questions - Real Numbers Class 10 Notes | EduRev

Since Hots Questions - Real Numbers Class 10 Notes | EduRev are rational numbers.
Hots Questions - Real Numbers Class 10 Notes | EduRev are also rational.

i.e. Hots Questions - Real Numbers Class 10 Notes | EduRev are perfect squares of +ve integers. It is not possible. 

[∵ two perfect squares differ by 3] ⇒  Our assumption is not possible.

Ques 3: If Hots Questions - Real Numbers Class 10 Notes | EduRev is an irrational number, then show thatHots Questions - Real Numbers Class 10 Notes | EduRev is also irrational. 
Hint:
If possible, letHots Questions - Real Numbers Class 10 Notes | EduRev be a rational number.

Hots Questions - Real Numbers Class 10 Notes | EduRev

But it contradicts our assumption thatHots Questions - Real Numbers Class 10 Notes | EduRevis irrational.Thus,Hots Questions - Real Numbers Class 10 Notes | EduRev 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:
Hots Questions - Real Numbers Class 10 Notes | EduRev

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

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