Question

6. Outside a temple, there is a shoe-keeping shelf with 9 blocks. The blocks are
numbered 1 to 9 in a random order. A man wishes to place his shoes in two different
blocks of the shelf, such that the product of the two numbers on the blocks should not
be a perfect square. In how many ways can he place his shoes?
(b) 31
(c) 32
(d) 33
(a) 30
IZE

Answer 1

Answer:

(C) 32

Explanation:

Perfect Squares from numbers 1 to 9  are 1,4,9,16,25,36,49,64,81.

Now We need pairs of non-repititive ∴ (9*8)/2 = 36 pairs possible.

⇒ we can't get 1,25,49,81 (prime numbers square)  from different numbers ∴ (2,8), (9,4), (1,4),(1,9). We can't achieve 64 from given set of numbers without using 8 two times.

⇒ So, 36-4 = 32