Please post a brief soln to the problem
1) The no. of right triangles with integer sides and inradius r=2013
2)Let a,b,c,d be non zero digits. If n is the no. of 4 digit no.s abcd such that ab+cd is even, then last digit of n is :
3)If the eqn of ax^{2}+y^{2}+bz^{2}+ 2yz+zx+3xy=0 represents a pair of perpendicular planes, then a=?
4)Let f(x) be aoneone polynomial function func such that f(x)f(y)=f(x)+f(y)+f(xy), for all x,y belonging to R{0}, f(1)â‰ 1, f'(1)=3.
Let g(x) =Ï€4(f(x)+3)  âˆ«_{0}^{x}f(x)dx, then
a) g(x)=0 has exactly 1 root for x belongs to (0,1)
b) g(x)=0 has exactly 2 root for x belongs to (0,1)
c)g(x)â‰ 0 for x belongs to R{0}
d)g(x)=0 for x belongs to R{0}
5)Letf_{1}(x) and f_{2}(x) be continuous and differentianble
If f_{1}(0)=f_{1}(2)=f_{1}(4)
and f_{1}(1)+f_{1}(3)=0=f_{2}(2)=f_{2}(4)=.
If f_{1}(x) and f_{2}'(x) have no common root, then the min no. of common roots of
f_{1}'(x)f_{2}'(x)+f_{1}(x)f_{2}''(x) in [0,4] is

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2 Answers
can anyone please solve the question number 3 bcoz here x,y,z maens what?axes? i am just unable to understand.