# Cubes and Dice Questions

A) 130 | B) 132 |

C) 138 | D) 140 |

Explanation:

In the figure, there are

5 columns containing 4 cubes each;

33 columns containing 3 cubes each;

9 columns containing 2 cubes each and 3 columns containing 1 cube each.

$\therefore $ Total Number of cubes = ( 5 x 4) + (33 x 3) + (9 x 2) + (3 x 1) = 20 + 99 + 18 + 3 = 140

A) Option 1,2 and 3 | B) Option 1,3 and 4 |

C) Option 2 and 3 | D) Option 2,3 and 4 |

Explanation:

When the sheet in fig. (A) is folded, then one of the faces of the cube formed will be of the form and this face will lie opposite the face bearing a square. Also, one of the blank faces lies opposite another blank face and the third blank face lies opposite the face bearing an '=' sign. Clearly, all the three blank faces cannot appear adjacent to each other. So, the cube shown in fig. (2) which has all the three blank faces adjacent to each other cannot be formed. Hence, only the cubes shown in figures A, C and D can be formed.

A) 2 is opposite to 6 | B) 1 is adjacent to 3 |

C) 3 is adjacent to 5 | D) 3 is opposite to 5 |

Explanation:

If 1 is adjacent to 2, 4 and 6 then either 3 or 5 lies opposite to 1. So, the numbers 3 and 5 cannot lie opposite to each other. Hence, 3 is adjacent to 5 (necessarily).

A) 4 is adjacent to 6 | B) 2 is adjacent to 5 |

C) 1 is adjacent to 6 | D) 1 is adjacent to 4 |

Explanation:

If 1 is adjacent to 2, 3 and 5, then either 4 or 6 lies opposite to 1. So, the numbers 4 and 6 cannot lie opposite to each other. Hence, 4 necessarily lies adjacent to 6.

A) 56 | B) 48 |

C) 32 | D) 64 |

Explanation:

We know that Cubes with no surface painted can be find using ${\left(x-2\right)}^{3}$, where x is number of cuttings. Here x=6.

$\therefore {\left(6-2\right)}^{3}=64$

A) 2 | B) 4 |

C) 5 | D) 6 |

Explanation:

From figures (i), (ii) and (iv), we conclude that 6, 4,1 and 2 dots appear adjacent to 3 dots. Clearly, there will be 5 dots on the face opposite the face with 3 dots.

A) 4 is adjacent to 3 and 6 | B) 2 is adjacent to 4 and 6 |

C) 4 is adjacent to 5 and 6 | D) 6 is adjacent to 3 and 4 |

Explanation:

If 1 is opposite to 5 and 2 is opposite to 3, then 4 definitely lies opposite to 6. Therefore, 2 cannot lie opposite to any of the two numbers - 4 or 6. Hence, 2 necessarily lies adjacent to both 4 and 6.

A) Option 1,2 and 3 | B) Option 1,2 and 4 |

C) Option 2 and 3 | D) Option 2,3 and 4 |

Explanation:

when a cube is formed by folding the sheet shown in fig. (A), then is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a square lies opposite to another blank face. The remaining two blank faces lie opposite to each other. Clearly, in the cube shown in fig. (1), the face consisting of the four symbols is not the same as that formed (as shown above). Hence, the cube in fig. (1) cannot be formed