Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Let f:[2,4] 
R be a differentiable function such that (x log e z)f'(z)+(log e x)f(x)+f(x) 
1, x 
[2,4] with f(b)= 
and f(d)= 
. Consider the following two statements:
A
f(x) 
1, for all x 
[2,4] Neither statement nor statement and is true
1, for all x [2,4] Neither statement nor statement and is true
B
f(x) 
1/8, for all x 
[2,4] Then, is true Only statement is true are true
1/8, for all x [2,4] Then, is true Only statement is true are true
C
Both the statements
D
Only statement
Text Solution
Verified by ExpertsThe correct answer is:
C
Given,
Domain and range of function,
Hence, h(x) = x(lnx)f(x)-x is a increasing function,
Similarly, h(x)<h(d)
Hence both A & B are correct.
Note this question was bonus in Jee Main 2023 April session, as LMVT on f(x). x ln x can't be satisfied.
Hence, no such f(x) exist.
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