TIFR ECE 2010 | Question: 18

Question

Under what conditions is the following inequality true for $a, b>0$
$$
\log _e(a+b) \geq \lambda \log _e(a / \lambda)+(1-\lambda) \log _e(b /(1-\lambda))
$$

• A. $\lambda=0.5$
• B. $0<a / \lambda \leq 1, b /(1-\lambda)>0$
• C. $a / \lambda>0,0<b /(1-\lambda) \leq 1$
• D. All of the above
• E. None of the above

Answer 1

Option D

by jensens inquality functions like log(x) , sq root of x, sin(0 to pi) are having  concave coordinates lines between 0 to 1 first 3 options satisfies this condition so option D