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

Posted by Amit Goyal on Apr 21, 2010; 5:58am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4935274.html

Next two now:
Let f be a real valued continuous function on [0, 3]. Suppose that f(x) takes only rational values and f(1) = 1. Then f(2) equals
(a) 2,
(b) 4,
(c) 8.
(d) None of these.

Consider the function f(x, y) = ∫[0, √(sq(x)+sq(y))] exp(-sq(w)/(sq(x)+sq(y)))dw with the property that f(0, 0) = 0. Then the function f(x, y) is
(a) homogeneous of degree −1,
(b) homogeneous of degree 0.5,
(c) homogeneous of degree 1.
(d) None of these.

∫[a, b] g(w)dw can be read as definite integral of g(w) from a to b, sq(t) stands for square of t.