• ( 1 ) Two positions of a dice are shown below: When 2 is at the bottom, what number will be at the top?

    • 1) 6
    • 2) 4
    • 3) 1
    • 4) 5
    • Discussion in forum
      Answer : 3) 1
      Solution : Number 3 is common to both the figures (i) and (ii). The dice in fig. (ii) is assumed to be rotated so that 3 remains on the FR-RH face (i.e. face I as per activity 1) and the numbers 5 and 2 move to the faces hidden behind the numbers 6 and 1 respectively [in fig. (i)]. Thus, the combined figure will have 3 on FR-RH face (i.e. face I), 5 on RR-RH face (i.e. face II), 2 on Bottom face (i.e. face VI), 1 on the Top face (i.e. face V) and 6 on FR-LH face (i.e. face IV). Clearly, 2 lies opposite 1. Hence, when 2 is at the bottom, then 1 will be at the top.








      discussion


      Answer : 3) 1

    • ( 2 ) The four positions of a cube are shown, which symbol will be on the opposite face of ÷

    • 1) %
    • 2) +
    • 3) o
    • 4) ÷
    • Discussion in forum
      Answer : 3) o
      Solution : From both the position of a dice + is the common face at different position then
      + -Δ - ÷
      + - % - o
      concluded
      opposite of ÷ is o
      opposite of Δ is %








      discussion


      Answer : 3) o

    • ( 3 ) On the basis of the given two positions of single dice, find the letter at the face opposite to the face having letter A.

    • 1) B
    • 2) C
    • 3) D
    • 4) E
    • Discussion in forum
      Answer : 4) E
      Solution : From both the position of a dice C is the common face at different position then
      C - B - A
      C - D - E
      concluded
      opposite of B is D
      opposite of A is E








      discussion


      Answer : 4) E

    • ( 4 ) From the given two positions of a single dice, find the letter at the face opposite to the face having letter V.

    • 1) S
    • 2) U
    • 3) J
    • 4) I
    • Discussion in forum
      Answer : 1) S
      Solution : From both the position of a dice J is the common face then uncommon faces will be opposite to each other. Then opposite of V will be S








      discussion


      Answer : 1) S

    • ( 5 ) A cube has six different symbols drawn over its six faces. The symbols are dot, circle, triangle, square, cross and arrow. Three different positions of the cube are shown in figures X, Y, and Z.
      Which symbol occurs at the bottom of fig.(Y)?

    • 1) Arrow
    • 2) Triangle
    • 3) Circle
    • 4) Dot
    • Discussion in forum
      Answer : 3) Circle
      Solution : From figures X and Y, we conclude that dot, circle, square and cross lie adjacent to the triangle. Therefore, the arrow must lie opposite the triangle. From figures X and Z, we conclude that dot, triangle, arrow and cross lie adjacent to the circle. Therefore, the square must lie opposite the circle. Thus, the arrow lies opposite the triangle, the square lies opposite the circle and consequently, the cross lies opposite the dot.
      Since the square lies at the top of fig. (Y) and the circle lies opposite the square (as analysed above), so the circle occurs at the bottom of fig. (Y).








      discussion


      Answer : 3) Circle

    • ( 6 ) Given below are three different positions of a dice. Find the number of dots on the face opposite the face bearing 3 dots.

    • 1) 4
    • 2) 5
    • 3) 6
    • 4) Cannot be determined
    • Discussion in forum
      Answer : 3) 6
      Solution : From figures (i), (ii) and (iii), we conclude that 3, 4, 6 and 1 dots appear adjacent to 2 dots. Therefore, 5 dots appear opposite 2 dots. Now, from figures (i) and (iii), we conclude that 2, 4 and 1 dots appear adjacent to 3 dots. Therefore, either 5 or 6 dots appear opposite 3 dots. Since, 5 dots appear opposite 2 dots, it follows that 6 dots appear opposite 3 dots








      discussion


      Answer : 3) 6

    • ( 7 ) Choose the box that is similar to the box formed from the given sheet of paper (X).

    • 1) 1 and 3 only
    • 2) 2 and 4 only
    • 3) 3 and 4 only
    • 4) 1 and 4 only
    • Discussion in forum
      Answer : 1) 1 and 3 only
      Solution : 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.








      discussion


      Answer : 1) 1 and 3 only

    • ( 8 ) Choose the box that is similar to the box formed from the given sheet of paper (X).

    • 1) 1 and 3 only
    • 2) 1 and 4 only
    • 3) 2 and 4 only
    • 4) 3 and 4 only
    • Discussion in forum
      Answer : 1) 1 and 3 only
      Solution : 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.








      discussion


      Answer : 1) 1 and 3 only

    • ( 9 ) Choose the box that is similar to the box formed from the given sheet of paper (X).

    • 1) 1 and 2 only
    • 2) 1, 2 and 3 only
    • 3) 1 and 3 only
    • 4) 1, 2, 3 and 4
    • Discussion in forum
      Answer : 1) 1 and 2 only
      Solution : 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.








      discussion


      Answer : 1) 1 and 2 only

    • ( 10 ) Choose the box that is similar to the box formed from the given sheet of paper (X).

    • 1) 1 only
    • 2) 2 only
    • 3) 3 only
    • 4) 4 only
    • Discussion in forum
      Answer : 2) 2 only
      Solution : 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.








      discussion


      Answer : 2) 2 only





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