If p is a positive fraction less than 1, then
K
1
1.
(a) - is less than 1 (b) - is a positive integer
P
р
(c) p2 is less than p
2
-p is a positive number
P
Answers
Given : p is a positive fraction less than 1
To Find : Which of the option/s are correct ?
(a) 1/p is less than 1
(b) 1/p is a positive integer
(c) p² is less than p
(d) (2/p)-p is a positive number
Solution:
p is a positive fraction less than 1
=> 0 < p < 1
=> 1/0 > 1/p > 1
1/p is less than 1 - INCORRECT
1/p is a positive integer not always true
p = 2/3
=> 1/p = 3/2 not an integer
p² is less than p CORRECT
p - p²
= p ( 1 - p)
p is +VE also p < 1
Hence 1 - p is + ve
=> p ( 1- p) > 0
=> p - p² > 0
=> p > p²
=> p² < p
Hence p² is less than p is CORRECT
(2/p) - p is a positive number
(2 - p²) / p 2 - p² = + ve as p² < p < 1
also p is +ve
=> (2 - p²) / p is a positive number
Hence this is also CORRECT
Two options are correct
p² is less than p is CORRECT
(2/p) - p is a positive number is CORRECT
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