# Monthly Archives: June 2012

## Bumper Problems

These are the set of 5 problems each of 5 marks

The person who get more than 20 points will get a mathematics book on any topic he want…

So try these beautiful problems to test your mathematics abilities and getting new things…

Ways by which you can answer :

I am adding a form in the end of this post , you can answer there ….

Note : You have give solution of your answer too..

**Problem 1)**

The bisectors of the angles and of the meet the sides

and at the points and , respectively.

Assuming that , determine the angle

**Problem 2)**

Given a and be point on side such that ,

, and

Find the value of

**Problem 3)**

If p and q are natural numbers so that

Prove that p is divisible by 1979 .

Problem 4)

Find highest degree n of 1991 for which 1991ⁿ divides the number :

**Problem 5)**

Let ƒ(n) denote the sum of the digits of n. Let N = 4444⁴⁴⁴⁴

Find ƒ(ƒ(ƒ(n))))

You can use these symbols to write solutions more conveniently

Mathematical Operators |
||||||||||||||||

∀ | ∁ | ∂ | ∃ | ∄ | ∅ | ∆ | ∇ | ∈ | ∉ | ∊ | ∋ | ∌ | ∍ | ∎ | ∏ | |

∐ | ∑ | − | ∓ | ∔ | ∕ | ∖ | ∗ | ∘ | ∙ | √ | ∛ | ∜ | ∝ | ∞ | ∟ | |

∠ | ∡ | ∢ | ∣ | ∤ | ∥ | ∦ | ∧ | ∨ | ∩ | ∪ | ∫ | ∬ | ∭ | ∮ | ∯ | |

∰ | ∱ | ∲ | ∳ | ∴ | ∵ | ∶ | ∷ | ∸ | ∹ | ∺ | ∻ | ∼ | ∽ | ∾ | ∿ | |

≀ | ≁ | ≂ | ≃ | ≄ | ≅ | ≆ | ≇ | ≈ | ≉ | ≊ | ≋ | ≌ | ≍ | ≎ | ≏ | |

≐ | ≑ | ≒ | ≓ | ≔ | ≕ | ≖ | ≗ | ≘ | ≙ | ≚ | ≛ | ≜ | ≝ | ≞ | ≟ | |

≠ | ≡ | ≢ | ≣ | ≤ | ≥ | ≦ | ≧ | ≨ | ≩ | ≪ | ≫ | ≬ | ≭ | ≮ | ≯ | |

≰ | ≱ | ≲ | ≳ | ≴ | ≵ | ≶ | ≷ | ≸ | ≹ | ≺ | ≻ | ≼ | ≽ | ≾ | ≿ | |

⊀ | ⊁ | ⊂ | ⊃ | ⊄ | ⊅ | ⊆ | ⊇ | ⊈ | ⊉ | ⊊ | ⊋ | ⊌ | ⊍ | ⊎ | ⊏ | |

⊐ | ⊑ | ⊒ | ⊓ | ⊔ | ⊕ | ⊖ | ⊗ | ⊘ | ⊙ | ⊚ | ⊛ | ⊜ | ⊝ | ⊞ | ⊟ | |

⊠ | ⊡ | ⊢ | ⊣ | ⊤ | ⊥ | ⊦ | ⊧ | ⊨ | ⊩ | ⊪ | ⊫ | ⊬ | ⊭ | ⊮ | ⊯ | |

⊰ | ⊱ | ⊲ | ⊳ | ⊴ | ⊵ | ⊶ | ⊷ | ⊸ | ⊹ | ⊺ | ⊻ | ⊼ | ⊽ | ⊾ | ⊿ | |

⋀ | ⋁ | ⋂ | ⋃ | ⋄ | ⋅ | ⋆ | ⋇ | ⋈ | ⋉ | ⋊ | ⋋ | ⋌ | ⋍ | ⋎ | ⋏ | |

⋐ | ⋑ | ⋒ | ⋓ | ⋔ | ⋕ | ⋖ | ⋗ | ⋘ | ⋙ | ⋚ | ⋛ | ⋜ | ⋝ | ⋞ | ⋟ | |

⋠ | ⋡ | ⋢ | ⋣ | ⋤ | ⋥ | ⋦ | ⋧ | ⋨ | ⋩ | ⋪ | ⋫ | ⋬ | ⋭ | ⋮ | ⋯ | |

⋰ | ⋱ | ⋲ | ⋳ | ⋴ | ⋵ | ⋶ | ⋷ | ⋸ | ⋹ | ⋺ | ⋻ | ⋼ | ⋽ | ⋾ | ⋿ | |

Exponents : ⁰ ¹ ² ³ ⁴ ⁵ ⁶ ⁷ ⁸ ⁹ ⁺ ⁻ ⁼ ⁽ ⁾ ₀ ₁ ₂ ₃ ₄ ₅ ₆ ₇ ₈ ₉ ₊ ₋ ₌ ₍ ₎ |

## Problem of the day 3

Nice problem !

**Functional Equations !
**

Q)

Determine all functions ƒ satisfying the functional relations

ƒ(x) + ƒ(1/(1-x)) =( 2(1-2x)/(x(1-x))

where x is a real number x ≠ 0 , x ≠ 1

Post your answer in comments with whole solution 🙂

person who give best answer of problem of the day more than 4 times will be awarded a book