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Answer 1

Madhava Mathematics Competition
(A Mathematics Competition for Undergraduate Students)
Organized by Department of Mathematics, S.P. College, Pune and Homi Bhabha Centre for Science Education, T.I.F.R, Mumbai
Date:13/12/2015
Time:12-3pm
Part I 20 marks, Part II 30 marks, Part III 50 marks

Part I each question carries 2 marks in Part I
Q1) Let A(t) denote the area bounded by the curve
\[y=e^{-|x|}\], the X-axis and the straight lines x=-t and x=t, then
\[\lim_{t \rightarrow \infty} A(t)\]
is
a) 2
b) 1
c) 0.5
d) e

Q2) How many triples of real numbers(x,y,z) are common solutions of the equations \[x+y=2\]\[xy-z^2=1\]
a)0
b)1
c)2
d)infinitely many

Q3)For non negative integers x,y the function f(x,y) satisfies the relations
\[f(x,0)=x\]
and
\[f(x,y+1)=f(f(x,y),y)\].
Then which if the following is the largest?
a)f(10,15)
b)f(12,13)
c)f(13,12)
d)f(14,11)

q4) Suppose p,q,r,s are 1,2,3,4 in some order
Let
\[x=\frac{1}{p+\frac{1}{q+\frac{1}{r+\frac{1}{s}}}}\]
We choose p,q,r,s so that x is as large as possible, then s is
a)1
b)2
c)3
d)4

q5)Let

then
f''(0) is
a)0
b)2
c)3
d)none of these

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