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 ax2+y2+bz2+ 2yz+zx+3xy=0 represents a pair of perpendicular planes, then a=?

4)Let f(x) be aone-one 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)≠1, f'(1)=3.

Let g(x) =π4(f(x)+3) - ∫0xf(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)≠0 for x belongs to R-{0}
d)g(x)=0 for x belongs to R-{0}

5)Letf1(x) and f2(x) be continuous and differentianble
If f1(0)=f1(2)=f1(4)
and f1(1)+f1(3)=0=f2(2)=f2(4)=.
If f1(x) and f2'(x) have no common root, then the min no. of common roots of
f1'(x)f2'(x)+f1(x)f2''(x) in [0,4] is

2 Answers

Anik Chatterjee ·

5)2 roots?

Amartya Kumar Mistry ·

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

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