A) 4! | B) 5! |

C) 6! | D) Can't be determined |

Explanation:

NUMERICAL has 9 positions in which 2, 4, 6, 8 are even positions.

And it contains 5 consonents i.e, N, M, R, C & L. Hence this cannot be done as 5 letters cannot be placed in 4 positions.

Therefore, Can't be determined.

A) 1/8 | B) 0 |

C) 1/4 | D) 1 |

Explanation:

Non collision can happen only when all the cars move in same direction.

That is either all cars moving in clockwise direction or all cars moving in anti clockwise direction.

P(all cars not colliding)

= P(all cars moving in the same direction)

= P(all cars moving in clockwise direction) + P(all cars moving in anticlockwise direction)

= [p(A --> C) x p(C --> B) x p(B --> A)] + [p(A --> B) x p(B --> C) x p(C --> A)]

= [1/2 x 1/2 x 1/2] + [1/2 x 1/2 x 1/2]

= 1/8 + 1/8

= 1/4

A) 42 | B) 142 |

C) 119 | D) 21 |

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.

A) A to G : 2, 3, 7, 6, 5, 1, 4 | B) A to G : 1, 4, 5, 6, 2, 7, 3 |

C) A to G : 5, 4, 7, 6, 3, 1, 2 | D) None |

Explanation:

This can be done in two ways

1. A to G : 2, 3, 7, 6, 5, 1, 4

2. A to G : 4, 3, 7, 5, 6, 2, 1