## 10 May Few Problems - 3

- Let be an acute angled triangle such that . Let be a point on such that . Let be an internal point of the segment . Prove that if and only if .
- Show that there are infinitely many positive integers such that

- Show that is always composite for all natural numbers 1" />. (Hint : Factorise )
- Show that the number of natural numbers divisible by less than or equal to is .
- For real numbers 0" /> prove that

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## R gogoi

Posted at 08:16h, 17 MayPlease update Higher Secondary final year Science Question paper 2017