# Practice Test

Q1) What is the maximum number of identical pieces a cube can be cut into by 3 cuts? Show Answer

Q2) What is the maximum number of identical pieces a cube can be cut into 4 cuts? Show Answer

Q3) A cube is cut parallel to one face by making 10 cuts [such that all the resulting pieces are identical].
What is the maximum number of identical pieces that can be obtained by now making two more cuts (in any direction)? Show Answer

Q4) What is the maximum number of identical pieces a cube can cut into by 13 cute? Show Answer

Q5) What is the least number of cuts required to cut a cube into 24 identical pieces? Show Answer

Q6) How many small cubes are there without any face painted? Show Answer

Q7) How many small cubes are there with at least two different colours on their faces? Show Answer

Q8) How many small cubes are there with exactly one face painted red? Show Answer

Q9) How many small pieces have black colour on their faces? Show Answer

Q10) How many small pieces have at least two different colours on their faces? Show Answer

Q11) How many small pieces have only one face painted? Show Answer

Q12) How many small pieces have no colour on their faces? Show Answer

Q13) How many of the small cubes have exactly two faces painted ? Show Answer

Q14) How many of the small cubes have no face painted? Show Answer

Q15) How many of the small cubes have exactly one face painted? Show Answer

Q16) What is the maximum number of identical pieces a cube can be cut into by 7 cuts? Show Answer

Q17) What is the least number of cuts required to divide a cube into 120 identical pieces? Show Answer

Q18) What is the maximum number of identical pieces into which a cube can be divide by 12 cuts? Show Answer

Q19) What is the maximum number of identical pieces a cube can cut into by 6 cuts? Show Answer

Q20) What is the maximum number of identical pieces a cube can be cut into by 5 cuts? Show Answer

Q21) What is the least number of identical cuboids, each of dimensions 2 cm x 4 cm x 5 cm, that are required to form a cube? Show Answer

Q22) 125 small but identical cubes have been put together to form a large cube. How many more such small cubes will be required to cover this large cube completely? Show Answer

Q23) 64 smaller but identical cubes are placed on a table to form a large cube. How many more such smaller cubes are now required to enclose this large cube placed on the table completely? Show Answer

Q24) A cube of side 6 cm has been cut into 64 smaller but identical cubes. If it was estimated that it would take 4 litres to paint to paint all the faces of the original cube, then how much paint is required to paint all the faces of all the smaller cubes? Show Answer

Q25) 125 small but identical cubes are put together on a table to form one large cube. A knife is passed through this cube starting along one edge of the top face to the diagonally opposite edge on the bottom face. How many of the small cubes are cut by this knife? Show Answer

Q26) Each of a cube is painted either white or black. In how many different ways can be the cube be painted? Show Answer

Q27) A cube is cut into smaller but identical cubes such that the edges small cube are integers. It was found that a particular cube X could be cut into 27 identical cubes or 64 identical cubes. What is the largest number of small, but identical cubes, that can be cut from X, if X has the least possible dimension? Show Answer

Q28) How many of the smaller cubes have no face painted at all? Show Answer

Q29) How many of the smaller cubes have exactly one face painted? Show Answer

Q30) How many of the smaller cubes have exactly two faces painted? Show Answer

Q31) How many of the smaller cubes have exactly three faces painted? Show Answer

Q32) How many smaller cubes are painted in exactly one colour? Show Answer

Q33) How many smaller cubes are painted in green ? Show Answer

Q34) How many smaller cubes are painted in exactly three colours? Show Answer

Q35) How many smaller cubes are painted in only red and blue? Show Answer

Q36) How many small cubes are there with no red paint at all? Show Answer

Q37) How many small cubes are there with at least two different colours on their faces? Show Answer

Q38) How many small cubes are there without any face painted? Show Answer

Q39) How many small cubes are there with only red and green on their faces? Show Answer

Q40) How many small cubes are there showing only green or only blue on their faces? Show Answer

Q41) How many small cubes are there with no red paint at all? Show Answer

Q42) How many small cubes are there with at least two different colours on their face ? Show Answer

Q43) How many small cubes are there with one face painted red? Show Answer

Q44) How many small cubes are with both red and green on their faces? Show Answer

Q45) How many small cubes are there showing only green or only blue on their faces? Show Answer

Q46) How many of the smaller cubes have no faces painted at all? Show Answer

Q47) How many of the smaller cubes have exactly one face painted? Show Answer

Q48) How many of the smaller cubes have exactly two faces painted ? Show Answer

Q49) What is the least number of the smaller cubes that will have exactly three faces painted? Show Answer

Q50) How many of the smaller cubes have exactly two faces painted? Show Answer

Q51) What are the least and the largest numbers of small cubes that have exactly one face painted? Show Answer

Q52) What is the least number of small cubes that have exactly one face painted red and no other face painted? Show Answer

Q53) What is the maximum numbers of small cubes that have one face painted green and one face blue and no other face painted? Show Answer

Q54) What are the least and the maximum numbers of cubes that have no face painted at all? Show Answer

Q55) How many smaller cubes was the original large cube cut into? Show Answer

Q56) How many small cubes have exactly one face painted? Show Answer

Q57) How many small cubes have exactly two faces painted? Show Answer

Q58) How many small cubes have three faces painted? Show Answer

Q59) It was found that a cube can be cut into certain number of identical cuboids each measuring 1 cm x 2 cm x 5 cm. What is the side of the smallest such cube? How many such cuboids can be formed from such a cube? Show Answer

Q60) If a cube is cut by three planes parallel to the faces to yield the maximum number of identical pieces, then what is the percentage increase in the total surface area? Show Answer

Q61) 343 smaller but identical cubes are put together to form a large cube. A knife is passed through one side AB of top face ABCD to the diagonally opposite edge of the bottom face. The knife is then again passed through the side CD of top face to the diagonally opposite edge of the bottom face ? How many of the smaller cubes are not by the Knife at all? Show Answer

Q62) What is the total number of distinct corners from where red and blue colours are visible? Show Answer

Q63) What is the total number of ways in which all three colours can be seen? Show Answer

Q64) What is the total number of distinct posible combinations of three colous that can be seen? Show Answer

Q65) What is the total number of distinguishably different ways in which the sum of the numbers on the visible faces of both the cubes together is 20? Show Answer

Q66) What is the total number of distinguishably different ways in which the sum of numbers on visible faces is exactly 10 on at least one die? Show Answer

Q67) What is the total number of ways in which a specified number is visible on both the dice? Show Answer

Q68) What is the maximum possible sum of the values on the faces that can be seen? Show Answer

Q69) For a specified number to appear on the front face of both the cubes (Designate the three faces that can be seen as top, front and side) what is the number of ways in which the cubes can be placed? Show Answer

Q70) What is the total number of ways in which the blue colour is not seen at all when the cube is kept on a table? Show Answer

Q71) What is the total number of ways in which two faces painted blue are seen? Show Answer

Q72) What is the total number of ways in which exactly one face painted blue is seen? Show Answer

Q73) How many small pieces have White colour on their faces? Show Answer

Q74) How many small pieces have at least two different colours on their faces? Show Answer

Q75) How many small pieces have no colour on their faces? Show Answer

Q76) How many small pieces have only one face painted? Show Answer

Q77) Totally in how many different ways can the cube be painted? Show Answer

Q78) In how many different ways can the cube be painted with at least two faces blue ? Show Answer

Q79) In how many different ways can the cube be painted such that all three colours are there on the cube? Show Answer

Q80) In how many different ways can the cube be painted such that no two adjacent faces have the same colour? Show Answer

Q81) The two cubes are placed next to each other on the table touching each other such that , whether the positions of P and Q are interchanged or left as they are, the two faces of P and Q touching each other are of the same colour. If the top faces of both P and Q have to be of the same colour, then which of the following must be true? Show Answer

Q82) Q is placed on the top of P such that no Blue face of either cube is horizontal. If Brown and Blue are the front faces of P and Q respectively, then which of the following statements must be false? Show Answer

Q83) If cube Q is kept behind cube P in such a way, that the Yellow face of P faces the Brown face of cube Q and the faces touching the table are of Red and Black colours, then which faces of both the cubes have same colour? Show Answer

Q84) 64 small but identical cubes have been put together to form a large cube. How many more such small cubes will be required to cover this large cube completely? Show Answer

Q85) What is the number of the smaller cubes that have exactly two colours on them? Show Answer

Q86) What is the number of the smaller cubes that have no face painted at all? Show Answer

Q87) What is the number of the smaller cubes whose at least one face is painted Red? Show Answer

Q88) What is the least number of identical cuboids, each of dimensions 3cm x 5cm x 7cm, that are required to form a cube? Show Answer