2 Marks

Question 12 Marks

Find the number of dots in the tenth figure of the following pattern.

Answer

The number of dots given are 1, 4, 9, 11, 16, 25, ...
The no. of dots are in the pattern 1 × 1, 2 × 2, 3 × 3, 4 × 4, 5 × 5, ...... 10 × 10
The number of dots in the $10^{th}$ figure = 100.

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Question 22 Marks

How many Triangles are there in the following figure?

Answer

The single portions A, B, C, D, E, F, G and H are 8 triangles.
Taking the combination of two E and F, F and G and H and E and H are 4 triangles.
There are 8 + 4 = 12 triangles.

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Question 32 Marks

Put the numbers 1, 2, 3, 4, 5, 6 and 7 in the circles so that each straight line of three numbers add up to the same total.

Answer

Here there is even number of terms.
Also we know that $1+6=7,2+5=7,3+4=7$,
So placing 7 at the centre, and the pairs $(1,6)(2,5)$ and $(3,4)$ at the opposite ends we get,

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Question 42 Marks

You 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

Answer

Listing all possible towers
$ R-B-R-B$
$R-R-B-B$
$B-R-R-B$
$B-R-R-B$
$B-B-R-R$
$R-B-B-R $
So we have 6 possibilities.

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Question 52 Marks

Find the minimum number of straight lines used in forming the following figure.