Page 8 - NCERT Books

96 MATHEMATICS

EXERCISE 6.1

1. What will be the unit digit of the squares of the following numbers?
(i) 81 (ii) 272 (iii) 799 (iv) 3853
(v) 1234 (vi) 26387 (vii) 52698 (viii) 99880
(ix) 12796 (x) 55555
2. The following numbers are obviously not perfect squares. Give reason.
(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222
(v) 64000 (vi) 89722 (vii) 222000 (viii) 505050
3. The squares of which of the following would be odd numbers?

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004
4. Observe the following pattern and find the missing digits.
2
11 = 121
2
101 = 10201
2
1001 = 1002001
2
100001 = 1 ......... 2 ......... 1
2
10000001 = ...........................
5. Observe the following pattern and supply the missing numbers.

11 = 1 2 1
2
2
101 = 1 0 2 0 1
10101 = 102030201
2
2
1010101 = ...........................
2
............ = 10203040504030201
6. Using the given pattern, find the missing numbers.
2
2
2
1 + 2 + 2 = 3 2
2
2
2
2 + 3 + 6 = 7 2 To find pattern
2
2
2
3 + 4 + 12 = 13 2 Third number is related to first and second
4 + 5 + _ = 21 2 number. How?
2
2
2
2
2
5 + _ + 30 = 31 2 Fourth number is related to third number.
2
How?
2
6 + 7 + _ = __ 2
2
2
7. Without adding, find the sum.
(i) 1 + 3 + 5 + 7 + 9
(ii) 1 + 3 + 5 + 7 + 9 + I1 + 13 + 15 + 17 +19
(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23
8. (i) Express 49 as the sum of 7 odd numbers.
(ii) Express 121 as the sum of 11 odd numbers.
9. How many numbers lie between squares of the following numbers?
(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100