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

Posted by Benhur on May 02, 2010; 11:32am
URL: http://discussion-forum.276.s1.nabble.com/Sample-Questions-of-ISI-ME-I-Mathematics-2010-Discussion-tp4850019p4992718.html

i am having prob in understanding dese ques..can ny1 plz help??

Let f and g be two differentiable functions on (0, 1) such that f(0) = 2, f(1) = 6, g(0) = 0 and g(1) = 2. Then there exists θ ∈ (0, 1) such that f'(θ) equals
(b) 2g'(θ)


The sum C(n+0, 0) + C(n+1, 1) +............C(n+m, m) equals
(d) C(n+m+1, n+1).


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
(c) homogeneous of degree 1.
(Hint: Its not necessary to compute integral to check for homogeneity)


If f(1) = 0, f'(x) > f(x) for all x > 1, then f(x) is
(a) positive valued for all x > 1


Let f: R → R and g: R → R be defined as
f(x) = −1, x < −0.5
      = −0.5, −0.5 ≤ x < 0
      = 0, x = 0
      = 1, x > 0
and g(x) = 1 + x − [x], where [x] is the largest integer not exceeding x.
Then f(g(x)) equals
(d) 1.


For all x, y ∈ (0, ∞), a function f: (0, ∞) --> R satisfies the inequality
|f(x) - f(y)| ≤ cube(|x - y|). Then f is
(c) a constant function