A) 109 | B) 190 |

C) 901 | D) 910 |

Explanation:

Number of positive integral solutions =

=

= 190

A) 851250 | B) 751210 |

C) 362880 | D) 907200 |

Explanation:

The number of letters in the given word CREATIVITY = **10**

Here T & I letters are repeated

=> Number of Words that can be formed from CREATIVITY = **10!/2!x2! **

= 3628800/4

= **907200**

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