Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The greatest of the numbers 1, 2 1/2 , 3 1/3 , 4 1/4 , 5 1/5 , 6 1/6 and 7 1/7 is
Text Solution
Verified by ExpertsThe correct answer is:
B
Assuming the function
f(x) = x 1/x {x > 0}
f '(x) = x 1/x 
f '(x) = x 1/x 
f '(x) = – 
(1 + log x)
clearly when x > e, f '(x) will be negative f(x) is decreasing
when 0 < x < e, f '(x) will be positive f(x) is increasing
it means 3 1/3 > 4 1/4 > 5 1/5 > 6 1/6 > 7 1/7
Now compare (1) and (2) 1/2 and (3) 1/3
Apply same power on given three numbers
(1) 6 (2) 1/2 × 6 (3) 1/3 × 6 1 2
3 3 2 1 < 8 < 9
(1) <(2)
1/2 < (3) 1/3
So maximum number is (3) 1/3
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