Re: Sample Questions of ISI ME I (Mathematics) 2010 Discussion

Posted by Amit Goyal on Apr 30, 2010; 4:15am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4983853.html

Last two now:
If f is a real valued function and af(x) + cf(−x) = b − dx for all x with a ≠ c and d ≠ 0. Then f(b/d) equals
(a) 0
(b) - (2bc/(sq(a) - sq(c)))
(c) (2bc/(sq(a) - sq(c)))
(d) More information is required to find the exact value of f(b/d).

For all x, y ∈ (0, ∞), a function f: (0, ∞) --> R satisfies the inequality
|f(x) - f(y)| ≤ cube(|x - y|). Then f is
(a) an increasing function
(b) a decreasing function
(c) a constant function
(d) None of these.