Home
Class 12
MATHS
Balls are arranged in rows to form an eq...

Balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row of two balls and so on. If 669 more balls are added,then all the balls can be arranged in the shape of a square and each of the sides, then contains 8 balls less than each side of the triangle. Determine the initial number of balls.

Text Solution

AI Generated Solution

To solve the problem, we will follow these steps systematically: ### Step 1: Define the variables Let \( n \) be the number of rows in the equilateral triangle. The total number of balls in the triangle can be expressed as the sum of the first \( n \) natural numbers: \[ S = \frac{n(n + 1)}{2} \] ...
Promotional Banner

Topper's Solved these Questions

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|38 Videos

  • SEQUENCES AND SERIES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • PROPERTIES AND SOLUTION OF TRIANGLES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|21 Videos

  • SETS, RELATIONS AND FUNCTIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|12 Videos

Similar Questions

Explore conceptually related problems

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of row balls and so on. If 99 more identical balls are added to the total number of balls used in forming the equilateral triangle, then all these balls can be arranged in a square whose each side contains exactly 2 balls less than the number of balls each side of the triangle contains. Then, the number of balls used to form the equilateral triangle is

In how many ways can 3 red and 4 black balls be arranged in a row?

The number of ways in which 4 different red balls and 8 similar green balls can be arranged in a row so that at most 3 red balls are together is equal to

Find the number of ways by which 4 green, 3 red and 2 white balls can be arranged in a row such that no two balls of the same colour are together. All balls of the same colour are identical.

In how many ways can 2t+1 identical balls be placed in three distinct boxes so that any two boxes together will contain more balls than the third?

In how many ways can 2t+1 identical balls be placed in three distinct boxes so that any two boxes together will contain more balls than the third?

In how many ways can 7 red and 6 black balls be arranged in a row, if no two black balls are together?

In how many ways 4 different white balls and 6 different black balls be arranged in a row that no two white balls are together ?

There are 2 identical white balls, 3 identical red balls, and 4 green balls of different shades. Find the number of ways in which they can be arranged in a row so that atleast one ball is separated from the balls of the same color.

Out of 10 white, 8 black and 6 red balls, the number of ways in which one or more balls can be selected is (assuming balls of the same colour are identical)

ARIHANT MATHS ENGLISH-SEQUENCES AND SERIES-Exercise (Subjective Type Questions)
  1. If the first four terms of an arithmetic sequence are a,2a,b and (a-6-...

    Text Solution

    |

  2. If 1/1^2+1/2^2+1/3^2+...oo=pi^2/6 then value of 1-1/2^2+1/3^2-1/4^2+.....

    Text Solution

    |

  3. If the arithmetic mean of a(1),a(2),a(3),"........"a(n) is a and b(1),...

    Text Solution

    |

  4. If a(1),a(2),a(3),"........" is an arithmetic progression with common ...

    Text Solution

    |

  5. If t(1)=1,t(r )-t( r-1)=2^(r-1),r ge 2, find sum(r=1)^(n)t(r ).

    Text Solution

    |

  6. Prove that I(1),I(2),I(3)"..." form an AP, if I(n)=int(0)^(pi)(sin...

    Text Solution

    |

  7. Consider the sequence S=7+13+21+31+".....+"T(n) , find the value of T(...

    Text Solution

    |

  8. Find value of (x+(1)/(x))^(3)+(x^(2)+(1)/(x^(2)))^(3)+"........"+(x^(n...

    Text Solution

    |

  9. If the sequence a1, a2, a3,....... an ,dot forms an A.P., then prove ...

    Text Solution

    |

  10. If three unequel numbers are in HP and their squares are in AP, show ...

    Text Solution

    |

  11. Ifa(1),a(2),a(3),"........",a(n) are in AP with a(1)=0, prove that (a(...

    Text Solution

    |

  12. Balls are arranged in rows to form an equilateral triangle. The first ...

    Text Solution

    |

  13. If theta(1),theta(2),theta(2), theta(3),"…………" Theta(n) are in AP w...

    Text Solution

    |

  14. Show that,(1+5^(-1))(1+5^(-2))(1+5^(-4))(1+5^(-8))"....."(1+5^(-2n))= ...

    Text Solution

    |

  15. Evaluate S=sum(n=0)^n(2^n)/((a^(2^n)+1) (where a>1).

    Text Solution

    |

  16. Find the sum of the series :tan^- 1(1/3)+tan^- 1(2/9)+....+tan^- 1((2^...

    Text Solution

    |

  17. Find the sum to n terms, whose nth term is tan[alpha+(n-1)beta]tan (al...

    Text Solution

    |

  18. If sum(r=1)^n tr=n/8(n+1)(n+2)(n+3), then find sum(r=1)^n1/(tr)dot

    Text Solution

    |

  19. If s1,s2,s3 denote the sum of n terms of 3 arithmetic series whose fir...

    Text Solution

    |

  20. Three friends whose ages form a G.P. divide a certain sum of money in ...

    Text Solution

    |