[3 marks sum]

Question 13 Marks

See the following pattern carefully:

i. If $n$ denotes the number of figures and $S$ denotes the number of matches; find $S$ in terms of $n$.
ii. Find how many matches are required to make the :
(1) 15 th figure
(2) 40th figure
iii. Write a discretion of the pattern in words.

Answer

n 1 2 3 4
S 7 10 13 16

S = 3n + 4
(1) 15th figure has = 3 x 15 + 4 = 49 matches
(2) 40th figure has = 3 x 40 + 4 = 124 matches
It can easily be observed that each time the figure (n) is increased by 4, the number of matches (S) increased by 3.

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Question 23 Marks

Complete the following magic squares:

16	2	________
_______	10	________
_______	_______	4

Answer

Row-wise sum:
16 + 2 + 12 = 30,
6 + 10 + 14 = 30,
8 + 18 + 4 = 30
Column-wise sum:
16 + 6 + 8 = 30,
2 + 10 + 8 = 30,
12 + 14 + 4 = 30
Diagonal-wise sum:
16 + 10 + 4 = 30 and 12 + 10 + 8 = 30

16	2	12
6	10	14
6	18	4

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Question 33 Marks

Complete the following magic squares:

4	_______	8
_______	7	________
_______	_______	10

Answer

Row-wise sum:
4 + 9 + 8 = 21,
11 + 7 + 3 = 21,
6 + 5 + 10 = 21
Column-wise sum:
4 + 11 + 6 = 21,
9 + 7 + 5 = 21,
8 + 3 + 10 = 21
Diagonal-wise sum:
4 + 7 + 10 = 21 and 8 + 7 + 6 = 21

4	9	8
11	7	3
6	5	10

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Question 43 Marks

Complete the following magic squares:

6	7	_______
_______	5	9
8	_______	4

Answer

Row-wise sum:
6 + 7 + 2 = 15,
1 + 5 + 9 = 15,
8 + 3 +4 = 15
Column-wise sum:
6 + 5 + 4 = 15,
7 + 5 + 3 = 15,
2 + 9 + 4 = 15
Diagonal-wise sum:
6 + 5 + 4 = 15,
2 + 5 + 8 = 15

6	7	2
1	5	9
8	3	4

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Question 53 Marks

Divide $5936$ by $43$ to find the quotient and remainder. Also, check your division by using the formula, dividend $=$ divisor $\times$ quotient $+$ remainder.

Answer

On dividing $5936$ by Divisor $43$ gives quotient $138$ and remainder $2.$

Now, to verify,
$\text { Divided }=\text { divisor } \times \text { quotient }+ \text { remainder } $
$5936=43 \times 138+2 $
$=43 \times(100+38)+2 $
$=4300+1634+2$
$=5936$
Hence verified.

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MATHS [3 marks sum]

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