A) 129780 | B) 1587600 |

C) 35600 | D) None of these |

Explanation:

H L C N T A U I O

L N A I

There are total 131 letters out of which 7 are consonants and 6 are vowels. Also ther are 2L's , 2N's, 2A's and 2I's.

If all the consonants are together then the numberof arrangements = . But the 7 consonants can be arranged themselves in ways.

Hence the required number of ways = = = 1587600

A) 2580 | B) 3687 |

C) 4320 | D) 5460 |

Explanation:

Let 'Y' be the youngest player.

The last song can be sung by any of the remaining 3 players. The first 3 players can sing the song in (3!) ways.

The required number of ways = 3(3!) = 4320.

A) 215 | B) 268 |

C) 254 | D) 216 |

Explanation:

Since each ring consists of six different letters, the total number of attempts possible with the three rings is = 6 x 6 x 6 = 216. Of these attempts, one of them is a successful attempt.

Maximum number of unsuccessful attempts = 216 - 1 = 215.

A) 2(6!) | B) 6! x 7 |

C) 6! x ⁷P₆ | D) None |

Explanation:

We can initially arrange the six boys in 6! ways.

Having done this, now three are seven places and six girls to be arranged. This can be done in ⁷P₆ ways.

Hence required number of ways = 6! x ⁷P₆

A) 9!/(2!)^{2}x3! | B) 9! x 2! x 3! |

C) 0 | D) None |

Explanation:

n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.

The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.

Number of arrangements =

A) ²²C₁₀ + 1 | B) ²²C₉ + ¹⁰C₁ |

C) ²²C₁₀ | D) ²²C₁₀ - 1 |

Explanation:

The total number of ways of forming the group of ten representatives is ²²C₁₀.

The total number of ways of forming the group that consists of no seniors is ¹⁰C₁₀ = 1 way

The required number of ways = ²²C₁₀ - 1