A cube is painted blue on two adjacent surfaces and black on the surfaces opposi

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Question
A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces .Now the cube is cut into 216 smaller cubes of equal size.
Options
A. 56
B. 48
C. 32
D. 64

Correct Answer

64

Explanation

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

$? {(6 - 2)}^{3} = 64$

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1. A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 3 and 5, then which of the following statements is necessarily true?
Options
A. 4 is adjacent to 6
B. 2 is adjacent to 5
C. 1 is adjacent to 6
D. 1 is adjacent to 4

2. Four usual dice are thrown on the ground. The total of numbers on the top faces of these four dice is 13 as the top faces showed 4, 3, 1 and 5 respectively. What is the total of the faces touching the ground?
Options
A. 12
B. 13
C. 15
D. Cannot be determined

3. A dice is numbered from 1 to 6 in different ways. If 1 is adjacent to 2, 4 and 6, then which of the following statements is necessarily true?
Options
A. 2 is opposite to 6
B. 1 is adjacent to 3
C. 3 is adjacent to 5
D. 3 is opposite to 5

4. One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn find the probability the card drawn is red.
Options
A. 2/3
B. 1/2
C. 1/52
D. 13/51

5. A fair coin is tossed 11 times. What is the probability that only the first two tosses will yield heads ?
Options
A. (1/2)^11
B. (9)(1/2)
C. (11C2)(1/2)^9
D. (1/2)

6. A dice is numbered from 1 to 6 in different ways. If 1 is opposite to 5 and 2 is opposite to 3, then
Options
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

7. A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1.5 inch margin is left all around. What area in square inches does the picture cover?
Options
A. 76
B. 35
C. 49
D. 38.5

8. Tea worth of Rs. 135/kg & Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?
Options
A. Rs. 169.50
B. Rs.1700
C. Rs. 175.50
D. Rs. 180

9. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16 : 65. How much wine the cask hold originally?
Options
A. 18 litres
B. 24 litres
C. 32 litres
D. 42 litres

10. A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Options
A. 10
B. 20
C. 21
D. 25

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