Home
Class 12
MATHS
m n squares of the equal size are arrang...

`m n` squares of the equal size are arranged to form a rectangle of dmensin `mb yn ,w h e r ema n dn` are natural number. Two square will be called neighbours if they have exactly one common side. A number is written in each square such that the number written in any square is the arithmetic men of the numbers written in its neighboring squares. Show that this is possible only if all the numbers used are equal.

Promotional Banner

Topper's Solved these Questions

  • PERMUTATION & COMBINATION

    VMC MODULES ENGLISH|Exercise LEVEL-2|88 Videos
  • MOCK TEST 9

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos
  • PROBABILITY

    VMC MODULES ENGLISH|Exercise JEE ADVANCED (ARCHIVE)|102 Videos

Similar Questions

Explore conceptually related problems

mn squares of equal size are arranged to form a rectangle of dimension m by n, where m and n are natural numbers. Two square will be called neighbors if they have exactly one common side. A number is written in each square such that the number written in any square is the arithmetic mean of the numbers written in its neighboring squares. Show that this is possible only if all the numbers used are equal.

The arithmetic mean of the squares of first n natural numbers is

Find the squares of the number127

The arithmetic mean of two numbers is 18(3)/(4) and the positive square root of their product is 15. The larger of the two numbers is

The sum of a number and its positive square root is 6/25.Find the number.

Find the number of ways of selecting pair of black squares in chessboard such that they have exactly one common corner

Find the smallest square number that is divisible by each of the numbers 4, 9 and 10.

Find the smallest square number that is divisible by each of the numbers 8, 15 and 20.

Find the square roots of the numbers by expressing each number as the product of primes : 64

Find the square roots of the numbers by expressing each number as the product of primes : 81

VMC MODULES ENGLISH-PERMUTATION & COMBINATION-JEE ARCHIVE
  1. Let ngeq2 be integer. Take n distinct points on a circle and join each...

    Text Solution

    |

  2. Let A be a set of n distinct elements. Then the total number of distin...

    Text Solution

    |

  3. In a certain test, a students gave wrong answers to at least i questio...

    Text Solution

    |

  4. A committee of 12 is to be formed from nine women and eight men. In...

    Text Solution

    |

  5. about to only mathematics

    Text Solution

    |

  6. A box contains 2 white balls, 3 black balls & 4 red balls. In how many...

    Text Solution

    |

  7. 7 relatives of a man comprises 4 ladies and 3 gentlemen, his wife has ...

    Text Solution

    |

  8. m men and n women are to be seated in a row so that no two women sit...

    Text Solution

    |

  9. m n squares of the equal size are arranged to form a rectangle of dmen...

    Text Solution

    |

  10. If ""^(n)C(r -1) = 36, ""^(n)C(r) = 84 " and " ""^(n)C(r +1) = 126, th...

    Text Solution

    |

  11. Let n1<n2<n3<n4<n5 be positive integers such that n1+n2+n3+n4+n5=20...

    Text Solution

    |

  12. The total number of ways in which 5 balls of different colours can be ...

    Text Solution

    |

  13. Let n and k be positive integers such that n gt (k(k+1))/2. The number...

    Text Solution

    |

  14. about to only mathematics

    Text Solution

    |

  15. (i) In how many ways can a pack of 52 cards be divided equally a...

    Text Solution

    |

  16. Six cards and six envelopes are numbered 1, 2, 3, 4, 5, 6 and cards...

    Text Solution

    |

  17. PARAGRAPH A There are five students S1,\ S2,\ S3,\ S4 and S5 in a musi...

    Text Solution

    |

  18. PARAGRAPH A There are five students S1,\ S2,\ S3,\ S4 and S5 in a musi...

    Text Solution

    |

  19. The number of 5 digit numbers which are divisible by 4, with digits ...

    Text Solution

    |

  20. In a high school, a committee has to be formed from a group of 6 bo...

    Text Solution

    |