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Your Progress - Chapter 60% complete
1Exercise 6.12 questions
Q.1Suppose, you have two pairs of shorts, one is black and the other one is blue; three shirts which are white, blue and red. You again wish to make different combinations, but you always want to make sure that the shorts and shirt that you wear are of different colours. List and check how many combinations are possible now.v
Answer:
5 combinations are possible
Black-White
Black-Blue
Black-Red
Blue-White
Blue-Red
Q.2You have two red and two blue blocks. How many different towers can you build that are four blocks high using these blocks? List all the possibilities.v
Answer:
6 Possibilities,
R – B – R – B
R – R – B – B
B – R – R – B
B – R – B – R
B – B – R – R
R – B – B – R
2Exercise 6.25 questions
Q.1In the following magic triangle, arrange the numbers from 1 to 6, so that you get the same sum on all its sides.v
Answer:
One of the answers is:
Top: 1
Middle row (left to right): 5, 6
Bottom row (left to right): 3, 4, 2
Q.2Using the numbers from 1 to 9
(i) Can you form a magic triangle?
(ii) How many magic triangles can be formed?
(iii) What are the sums of the sides of the magic triangle?v
Answer:
(i) Yes
(ii) 5
(iii) 17, 19, 20, 21, 23
Q.3Arrange the odd numbers from 1 to 17 without repetition to get a sum of 30 on each side of the magic triangle.v
Answer:
One arrangement is:
Top: 1
Left side (top to bottom): 17, 7
Right side (top to bottom): 11, 15
Bottom row (left to right): 5, 13, 9, 3
Q.4Put the numbers 1, 2, 3, 4, 5, 6 & 7 in the circles so that each straight line of three numbers add up to the same total.v
Answer:
One arrangement is:
Centre: 7
One diagonal: 1, 7, 6
Horizontal: 2, 7, 5
Other diagonal: 3, 7, 4
Q.5Place the number 1 to 12 in the 12 circles so that the sum of the numbers in each of the six lines of the star is 26. Use each number from 1 to 12 exactly once. Find more possible ways?v
Answer:
One arrangement is:
Top: 4
Upper row (left to right): 3, 12, 10, 1
Middle row (left to right): 8, 5
Lower row (left to right): 2, 6, 11, 7
Bottom: 9
3Exercise 6.36 questions
Q.1How many Triangles are there in each of the following figures?v
Answer:
(i) 12 triangles
(ii) 16 triangles
(iii) 32 triangles
(iv) 35 triangles
Q.2Find the number of dots in the tenth figure of the following patterns.v
Answer:
(i) 55
(ii) 100
Q.3(i) Draw the next pattern.
(ii) Prepare a table for the number of dots used for each pattern.
(iii) Explain the pattern.
(iv) Find the number of dots in the 25th pattern.v