JEE Exam > JEE Questions > Direction : A cube is divided into 216 ident...
Start Learning for Free
Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.
Q. How many cubits ere there which are painted with at most one color?
- a)124
- b)108
- c)160
- d)96
Correct answer is option 'C'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
Direction : A cube is divided into 216 identical cubelets. Each cut i...
Because cube was painted with same color on opposite set of faces. We can still used formula.
View all questions of this test
[(n-2) + 2]3 = 3Co(n-2)3 + 3C1(n-2)2 x 2 + 3C2 (n-2) x 22 + 3C3 x 23
Basically in this question we are looking for no. of cubeit, which are colored on just one face.
= 3C0(n-2)3 + 3C1(n-2)2 x 2
= (n-2)3 + 3 x 2 x (n-2)2= 43 + 6 x 42
⇒ 64 + 96 = 160.
Alternatively : Total no. cubelets which are colored an at most are face - total no. of cube lets - total no. of cube let's which are colored on multiple faces. = 216 - 56 = 160.
Most Upvoted Answer
Direction : A cube is divided into 216 identical cubelets. Each cut i...
Solution:
Given, a cube is divided into 216 identical cubelets and is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set. We need to find the number of cubits that are painted with at most one color.
Let's consider each color separately.
Green colored cubelets:
The green color is painted on one set of opposite faces. So, the cubelets that are painted green can be obtained by cutting the cube parallel to one of the green faces. Each side of the green face is divided into 6 equal parts (due to the 6 x 6 division of the cube), and the green color is painted on 6 x 6 = 36 cubelets. So, there are a total of 36 x 6 = 216 green colored cubelets.
Similarly, we can find that there are 216 red colored cubelets and 216 blue colored cubelets.
Now, we need to find the number of cubelets that are painted with at most one color. This means that there should be either no color or only one color on a cubelet.
Number of cubelets with no color:
Each of the 6 faces of the cube has a region of 5 x 5 cubelets that do not have any color. So, the total number of cubelets with no color = 6 x 5 x 5 = 150.
Number of cubelets with only one color:
Each face of the cube has a region of 4 x 4 cubelets that are painted with only one color. So, the total number of cubelets with only one color = 6 x 4 x 4 x 3 = 288.
(Note: We multiplied by 3 as there are 3 colors.)
Therefore, the total number of cubelets that are painted with at most one color = 150 + 288 = 438.
Hence, the correct option is (c) 160.
Given, a cube is divided into 216 identical cubelets and is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set. We need to find the number of cubits that are painted with at most one color.
Let's consider each color separately.
Green colored cubelets:
The green color is painted on one set of opposite faces. So, the cubelets that are painted green can be obtained by cutting the cube parallel to one of the green faces. Each side of the green face is divided into 6 equal parts (due to the 6 x 6 division of the cube), and the green color is painted on 6 x 6 = 36 cubelets. So, there are a total of 36 x 6 = 216 green colored cubelets.
Similarly, we can find that there are 216 red colored cubelets and 216 blue colored cubelets.
Now, we need to find the number of cubelets that are painted with at most one color. This means that there should be either no color or only one color on a cubelet.
Number of cubelets with no color:
Each of the 6 faces of the cube has a region of 5 x 5 cubelets that do not have any color. So, the total number of cubelets with no color = 6 x 5 x 5 = 150.
Number of cubelets with only one color:
Each face of the cube has a region of 4 x 4 cubelets that are painted with only one color. So, the total number of cubelets with only one color = 6 x 4 x 4 x 3 = 288.
(Note: We multiplied by 3 as there are 3 colors.)
Therefore, the total number of cubelets that are painted with at most one color = 150 + 288 = 438.
Hence, the correct option is (c) 160.
Attention JEE Students!
To make sure you are not studying endlessly, EduRev has designed JEE study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in JEE.
|
Explore Courses for JEE exam
|
|
Top Courses for JEEView all
Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer?
Question Description
Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer?.
Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer?.
Solutions for Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for JEE.
Download more important topics, notes, lectures and mock test series for JEE Exam by signing up for free.
Here you can find the meaning of Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice Direction : A cube is divided into 216 identical cubelets. Each cut is made parallel to some surface of cube. But before cutting the cube is colored with green color on one set of opposite faces, red on the other set of opposite faces and blue on the third set.Q. How many cubits ere there which are painted with at most one color?a)124b)108c)160d)96Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice JEE tests.
|
|
Explore Courses for JEE exam
|
|
Suggested Free Tests
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup