5. The least perfect square, which is divisible by each of 21, 36 and 66 is:
A. 213444
B. 214344
C. 214434
D. 231444
6. How many two-digit numbers satisfy this property : The last digit (units digit) of the square of the two-digit number is 8 ?
A. 1
B. 2
C. 3
D. None of these
7.A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 59.29, the number of the member is the group is:
A. 57
B. 67
C. 77
D. 87
8. A group of students decided to collect as many paise from each member of group as is the number of members. If the total collection amounts to Rs. 98.01, the number of the member is the group is:
A. 101
B. 98
C. 99
D. 88
9.A man plants 49284 apple trees in his garden and arranges them so that there are as many rows as there are apples trees in each row. The number of rows is
A. 182
B. 202
C. 222
D. 122
10.If 0.13÷p^2=13, then p equals :
A. 0.01
B. 0.1
C. 10
D 100
ANSWER AND SOLUTION :
6(D)Explanation :
A number ending with 8 can never become a perfect square
Let's examine this in detail
1 × 1 = 1
Hence, if the unit digit of a number is 1, unit digit of its square is 1
2 × 2 = 4
Hence, if the unit digit of a number is 2, unit digit of its square is 4
3 × 3 = 9
Hence, if the unit digit of a number is 3, unit digit of its square is 9
4 × 4 = 16
Hence, if the unit digit of a number is 4, unit digit of its square is 6
5 × 5 = 25
Hence, if the unit digit of a number is 5, unit digit of its square is 5
6 × 6 = 36
Hence, if the unit digit of a number is 6, unit digit of its square is 6
7 × 7 = 49
Hence, if the unit digit of a number is 7, unit digit of its square is 9
8 × 8 = 64
Hence, if the unit digit of a number is 8, unit digit of its square is 4
9 × 9 = 81
Hence, if the unit digit of a number is 9, unit digit of its square is 1
0 × 0 = 0
Hence, if the unit digit of a number is 0, unit digit of its square is 0
