A) 235 | B) 253 |

C) 325 | D) None of these |

Explanation:

Required number of signals =

= 5 + 20 + 60 + 120 + 120 = 325

A) 5 | B) 6 |

C) 7 | D) 8 |

Explanation:

The following arrangements satisfy all 3 conditions.

Arrangement 1: 3 books in a row; 12 rows.

Arrangement 2: 4 books in a row; 9 rows.

Arrangement 3: 6 books in a row; 6 rows.

Arrangement 4: 9 books in a row; 4 rows.

Arrangement 5: 12 books in a row; 3 rows.

Therefore, the possible arrangements are 5.

A) 11!/2 | B) 1024 |

C) 11! | D) 2048 |

Explanation:

Given 11 questions of type True or False

Then, Each of these questions can be answered in 2 ways (True or false)

Therefore, no. of ways of answering 11 questions = = 2048 ways.

A) 210 | B) 168 |

C) 1260 | D) 10!/6! |

Explanation:

we can select the 5 member team out of the 8 in 8C5 ways = 56 ways.

The captain can be selected from amongst the remaining 3 players in 3 ways.

Therefore, total ways the selection of 5 players and a captain can be made = 56x3 = 168 ways.

**(or)**

Alternatively, A team of 6 members has to be selected from the 8 players. This can be done in 8C6 or 28 ways.

Now, the captain can be selected from these 6 players in 6 ways.

Therefore, total ways the selection can be made is 28x6 = 168 ways.

A) 59 | B) 60 |

C) 61 | D) 64 |

Explanation:

The given digits are 1, 2, 3, 5, 7, 9

A) 3/17 | B) 4/21 |

C) 2/21 | D) 5/17 |

Explanation:

Given that there are three blue marbles, four red marbles, six green marbles and two yellow marbles.

Probability that both marbles are blue = ³C₂/¹⁵C₂ = (3 x 2)/(15 x 14) = 1/35

Probability that both are yellow = ²C₂/¹⁵C₂ = (2 x 1)/(15 x 14) = 1/105

Probability that one blue and other is yellow = (³C₁ x ²C₁)/¹⁵C₂ = (2 x 3 x 2)/(15 x 14) = 2/35

Required probability = 1/35 + 1/105 + 2/35

= 3/35 + 1/105 = 1/35(3 + 1/3)

= 10/(3 x 35) = 2/21