Home
Class 12
MATHS
There are n locks and n matching keys. I...

There are `n` locks and `n` matching keys. If all the locks and keys are to be perfectly matched, find the maximum number of trails required to open a lock.

A

`n_(c_(2))`

B

`underset(k=2)overset(n)sum (k-1)`

C

`n!`

D

`""^(n+1)C_(2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION-I)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise PARAGRAPH BASED (MULTIPLE CHOICE) (COMPREHENSION-II)|3 Videos

  • MATHEMATICS TIPS

    FIITJEE|Exercise ASSERTION - REASONING|8 Videos

  • MATHEMATICS

    FIITJEE|Exercise NUMERICAL DECIMAL BASED QUESTIONS|15 Videos

  • MATRICES

    FIITJEE|Exercise NUMERICAL BASED|3 Videos

Similar Questions

Explore conceptually related problems

A number lock can be unlocked by a 3 digit code, each digit of the code could be any one of 0, 1 ....,9. What is the maximum number of trials required to unlock, if the following are known (a) the last digit (b) the sum of the first two digits is always less than or equal to the third?

The lock of a safe has a dial with holes, sasy ten, in which the numbers 0,1,2,……..9 are inscribed in each hole. The lock can be opened only when a specific code numbersay of six digits is dialled. Suppose the code number is 249916, it means that the can be opened when we first dial 2, then 4 nd so on. Find the maximum number of trials which do not result in opening the lock.

If each match box contains 50 matchsticks , the number of matchsticks required to fill n such boxes is

Who proposed the lock and key hypothesis ?

The chest is locked by a number of padlocks. All padlocks must be unlocked in order to open the chest. 12 Copies of the keys to the padlocks are distributed lie next to it, such that any group of 7 or more keys can open the chest should they choose to do so, but any group of less than 7 cannot. What is the minimal number of padlocks required to achieve this?

If N={a,b,c,..z} then find the number of all possible subsets of N.

FIITJEE-MATHEMATICS TIPS-MCQ (MULTIPLE CORRECT)
  1. Let vec(a)=2hati-hatj+hatk,vec(b)=hati+2hatj-hatk and vec( c )=hati+ha...

    Text Solution

    |

  2. If P(z(1)),Q(z(2)),R(z(3)) " and " S(z(4)) are four complex numbers re...

    Text Solution

    |

  3. The largest coefficient in the expansion of (4+3x)^(25) is

    Text Solution

    |

  4. Given that the 4th term in the expansion of [2+(3//8x)]^(10) has the m...

    Text Solution

    |

  5. If Deltar=|[2^(r-1),1/(r(r+1)),sin rtheta],[x, y, z],[2^n-1, n/(n+1),(...

    Text Solution

    |

  6. If a, b, c are even natural numbers, then Delta=|{:(a-1,a,a+1),(b-1,b,...

    Text Solution

    |

  7. There are n locks and n matching keys. If all the locks and keys are t...

    Text Solution

    |

  8. The number of ways in which we can choose 2 distinct integers from 1 t...

    Text Solution

    |

  9. Let n be a positive integer with f(n) = 1! + 2! + 3!+.........+n! and ...

    Text Solution

    |

  10. If m and n are positive integers more than or equal to 2, mgtn, then (...

    Text Solution

    |

  11. A drawer contains red and black balls. When two balls are drawn at ran...

    Text Solution

    |

  12. If A, B, C and D are four points with position vectors 3hati, 3hatj, 3...

    Text Solution

    |

  13. If |(a,b,aalpha+b),(b,c,balpha+c),(a alpha+b,b alpha+c,0)|=0 then

    Text Solution

    |

  14. The equation x^3/4((log)2x)^(2+(log)2x-5/4)=sqrt(2) has (1989, 2M) at ...

    Text Solution

    |

  15. If first and (2n-1)^th terms of an AP, GP. and HP. are equal and the...

    Text Solution

    |

  16. The nature of the intersection of the set of planes: 2x-4y+2z=5,5x-y...

    Text Solution

    |

  17. Let PM be the perpendicualr from the point P(1, 2, 3) to x-y plane. If...

    Text Solution

    |

  18. The det Delta=|{:(d^2+r,de,df),(de,e^2+r,ef),(df,ef,f^2+r):}| is divis...

    Text Solution

    |

  19. The inverse of a skew symmetric matrix is

    Text Solution

    |

  20. The number of ways of choosing triplet (x , y ,z) such that zgeqmax{x,...

    Text Solution

    |