A) 2 x (17!) | B) 2 x (18!) |

C) (3!) x (18!) | D) (17!) |

Explanation:

A person can be choosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf , Manmohan and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.

Required number of permutations = 18 x (17!) x 2 = 2 x 18!

A) 14 × 13 × 13! | B) 15 × 14 × 14! |

C) 14 × 12 × 12! | D) 15 × 13 × 13! |

Explanation:

15! - 14! - 13!

= (15 × 14 × 13!) - (14 × 13!) - (13!)

= 13! (15 × 14 - 14 - 1)

= 13! (15 × 14 - 15)

= 13! x 15 (14 - 1)

= **15 × 13 × 13!**

A) 7920 | B) 74841 |

C) 14874 | D) 10213 |

Explanation:

ST candidates vacancies can be filled by 5**C**3 ways = 10

Remaining vacancies are 5 that are to be filled by 12

=> 12**C**5 = (12x11x10x9x8)**/**(5x4x3x2x1) = 792

Total number of filling the vacancies = 10 x 792 = 7920

A) F is third to the left of B | B) F is second to the right of B |

C) B is an immediate neighbour of D | D) All of the above |

Explanation:

From the given information, the circular arrangement is

Here F is second to the right of B and the remaning all are wrong.

A) 43929 | B) 59049 |

C) 15120 | D) 0 |

Explanation:

Number of words with 5 letters from given 9 alphabets formed =

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is =

Number of words can be formed which have at least one letter repeated = -

= 59049 - 15120

= 43929

A) 5040 | B) 3650 |

C) 4150 | D) 2520 |

Explanation:

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

=> Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.