Q1: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 and 4 only
(b) 3 and 4 only
(c) 1 and 2 only
(d) 2 and 3 only
Ans: (a)
Explanation: The fig. (X) is similar to the Form I. So, when the sheet shown in fig. (X) is folded to form a cube then one of the two half-shaded faces lies opposite to one of the blank faces and the other half-shaded face lies opposite to another blank face. The two remaining blank faces lie opposite to each other. Thus, both the cubes shown in figures (1).and (4) can be formed when the sheet shown in fig. (X) is folded. Also, though the cubes shown in figures (2) and (3) have faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form either of the two. Hence, the cubes in figures (2) and (3) cannot be formed.
Q2: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 and 3 only
(b) 1 and 4 only
(c) 2 and 4 only
(d) 3 and 4 only
Ans: (a)
Explanation: The fig. (X) is similar to Form II. So, when the sheet shown in fig. (X) is folded to form a cube then the two half-shaded faces lie opposite to each other, the face bearing a circle lies opposite to one of the two blank faces and the two remaining blank faces lie opposite to each other. Therefore, the cubes shown in fig. (4) which has the two half-shaded faces adjacent to each other, cannot be formed by folding the sheet shown in fig. (X). Also, the cube shown in fig. (2) has the face bearing a circle adjacent to two blank faces. This is not possible since there is one blank face opposite to the circle and one blank face opposite to the third blank face. Hence, only the cubes in figures (1) and (3) can be formed.
Q3: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 only
(b) 1 and 3 only
(c) 1, 3 and 4 only
(d) 1, 2, 3 and 4
Ans: (c)
Explanation: When the sheet in fig. (X) 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.
Q4: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 only
(b) 2 only
(c) 3 only
(d) 4 only
Ans: (b)
Explanation: The fig. (X) is similar to the Form III. So, when the sheet in fig. (X) is folded to form a cube, then the half-shaded face appears opposite to the face bearing a rhombus, the face with a black circle appears opposite to one of the two blank faces and the face with a '+' sign appears opposite to the other blank face. Clearly, the cubes shown in figures (1) and (4) cannot be formed since they have the half-shaded face adjacent to the face bearing the rhombus. Also, though the cube shown in fig. (3) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form fig. (3). Hence, the cube in fig. (3) cannot be formed. Thus, only the cube shown in fig. (2) can be formed.
Q5: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 2 and 3 only
(b) 1, 3 and 4 only
(c) 2 and 4 only
(d) 1 and 4 only
Ans: (b)
Explanation: The fig. (X) is similar to the Form V. So, when the sheet in fig. (X) is folded to form a cube, then the face bearing a dot lies opposite to one of the shaded faces. Therefore, the cube shown in fig. (2) which has both the shaded faces adjacent to the face bearing the dot, cannot be formed. Hence, the cubes shown in figures (1), (2) and (4) can be formed.
Q6: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 and 2 only
(b) 1, 2 and 3 only
(c) 1 and 3 only
(d) 1, 2, 3 and 4
Ans: (a)
Explanation: The fig. (X) is similar to the Form VI. So, when a cube is formed by folding the sheet shown in fig. (X), then is one of the faces of the cube and this face lies opposite to a blank face. Also, a face bearing a circle lies opposite to one bearing a dot. Clearly, this cube does not have faces as shown in the cubes in figures (3) and (4). Hence, only the cubes shown in figures (1) and (2) can be formed.
Q7: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 and 2 only
(b) 1, 2 and 4 only
(c) 1 and 4 only
(d) 1, 2 and 3 only
Ans: (b)
Explanation: The fig. (X) is similar to the Form V. So, when the sheet shown in fig. (X) is folded to form a cube then the shaded face lies opposite to one of the blank faces, the face bearing a circle lies opposite to another blank face and the face bearing a shaded square lies opposite to the third blank face. Thus, each one of the cubes shown in figures (1), (2) and (4) can be formed. Also, though the cube shown in fig. (3) has faces that can appear adjacent to each other but the cube formed by folding the sheet in fig. (X) cannot be rotated to form fig. (3). Hence, the cube in fig.(3) cannot be formed.
Q8: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 4 only
Ans: (c)
Explanation: The fig. (X) is similar to Form V. So, when the sheet shown in fig. (X) is folded to form a cube, then the face with shading lies opposite to the free bearing a square, the face bearing a dot lies opposite to a blank face and the face bearing a circle (with a '+' sign inside it) lies opposite to another blank face. The cubes in figures (2) and (4) have the shaded face adjacent to the face bearing a square. Therefore, the cubes in these two figures cannot be formed. Hence, only cubes in figures (1) and (3) can be formed.
Q9: Choose the box that is similar to the box formed from the given sheet of paper (X).
(a) 1 and 3 only
(b) 2 and 4 only
(c) 3 and 4 only
(d) 1 and 4 only
Ans: (a)
Explanation: The fig. (X) is similar to Form I. So, when the sheet shown in fig. (X) is folded to form a box (cuboid), then the two rectangular-shaded faces lie opposite to each other, two rectangular white faces lie opposite to each other and the two square shaped faces (one shaded and one white) lie opposite to each other. Clearly, the cuboids shown in figures (2) and (4) cannot be formed as in each of the two cuboids the two shaded rectangular faces appear adjacent to each other. So, only the cuboids in figures (1) and (3) can be formed.
Q10: When the following figure is folded to form a cube, how many dots lie opposite the face bearing five dots?
(a) 1
(b) 2
(c) 3
(d) 4
Ans: (c)
Explanation: The given figure is similar to Form III. Therefore, when this figure is folded to form a cube then the face bearing three dots will lie opposite the face bearing five dots.