Home
Class 12
MATHS
Let Tn be the number of all possible ...

Let `T_n` be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If `T_(n+1)-T_n=""10` , then the value of n is (1) 5 (2) 10 (3) 8 (4) 7

A

5

B

10

C

8

D

7

Text Solution

Verified by Experts

The correct Answer is:
A
`because T_(n+1)-T_(n)=10 implies.^(n+1)C_(3)-.^(n)C_(3)=10implies.^(n)C_(2)=.^(n)C_(3)-.^(n)C_(3)=10`
`implies.^(n)C_(2)=10=(20)/(2)=(5*4)/(1*2)=.^(5)C_(2)impliesn=5`
Promotional Banner

Topper's Solved these Questions

  • PERMUTATIONS AND COMBINATIONS

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|17 Videos

  • PARABOLA

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|35 Videos

  • PROBABILITY

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|55 Videos

Similar Questions

Explore conceptually related problems

Let n(P) = 4 and n(Q) = 5. The number of all possible injections from P to Q is :

The number of diagonals of a regular polygon of n sides are:

If ""^(2n+1)P_(n-1): ""^(2n-1)P_n =3:5 then the value of n equals :

Let A_(1), A_(2), A_(3),…,A_(n) be the vertices of an n-sided regular polygon such that (1)/(A_(1)A_(2))=(1)/(A_(1)A_(3))+(1)/(A_(1)A_(4)). Find the value of n.

The number of triangles that can be formed with 10 points as vertices n of them being collinear, is 10. Then n is a. 3 b. 4 c. 5 d. 6

Let n denote the number of all n-digit positive integers formed by the digits 0, 1 or both such that no consecutive digits in them are 0. Let b_n = the number of such n-digit integers ending with digit 1 and c_n = the number of such n-digit integers ending with digit 0. The value of b_6 , is

A regular polygon of n sides has ......... Number of lines of symmetry.

Let T_r be the rth term of an A.P. whose first term is a and common difference is d. If for some positive integers, m,n, m ne n, T_m =1/n and T_n=1/m , then a-d equals :

The numbers 1,3,6,10,15,21,28"..." are called triangular numbers. Let t_(n) denote the n^(th) triangular number such that t_(n)=t_(n-1)+n,AA n ge 2 . The value of t_(50) is:

ARIHANT MATHS-PERMUTATIONS AND COMBINATIONS -Exercise (Questions Asked In Previous 13 Years Exam)
  1. In a shop, there are five types of ice-creams available. A child buys ...

    Text Solution

    |

  2. The number of seven digit integers, with sum of the digits equal to 10...

    Text Solution

    |

  3. Three boys and two girls stand in a queue. The probability that the nu...

    Text Solution

    |

  4. There are two urns. Urn A has 3 distinct red balls and urn B has 9 ...

    Text Solution

    |

  5. In how many ways 5 different balls can be distributed into 3 boxes so ...

    Text Solution

    |

  6. There are 10 points in a plane, out of these 6 are collinear. The numb...

    Text Solution

    |

  7. The total number of ways in which 5 balls of differert colours can be ...

    Text Solution

    |

  8. Let n denote the number of all n-digit positive integers formed by the...

    Text Solution

    |

  9. Let a(n) denote the number of all n-digit numbers formed by the digits...

    Text Solution

    |

  10. Assuming the balls to be identical except for difference in colours, t...

    Text Solution

    |

  11. Let Tn be the number of all possible triangles formed by joining ve...

    Text Solution

    |

  12. Consider the set of eight vector V={a hat i+b hat j+c hat k ; a ,bc in...

    Text Solution

    |

  13. A coin is tossed 4 times and the outcomes are recorded . how many poss...

    Text Solution

    |

  14. Let ngeq2 be integer. Take n distinct points on a circle and join each...

    Text Solution

    |

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

    Text Solution

    |

  16. The number of integers greater than 6,000 that can be formed, using...

    Text Solution

    |

  17. find the area of the rectangle whose sides are 3cm and 5cm

    Text Solution

    |

  18. If all the words (with or without meaning) having five letters, formed...

    Text Solution

    |

  19. A debate club consists of 6 girls and 4 boys. A team of 4 members is t...

    Text Solution

    |

  20. A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y ...

    Text Solution

    |