iit-jee math

1..Find the nature of roots of f(x)=e*x-x-1 =0.
2..the value of the parameter a for which the fuction f(x)=1+ax,where (a is nonzero), is inverse of itself is...
3..find the number of spherical balls in a complete pyramidal pile, whose base is an equilateral triangle each side of which contains n balls.

iit-jee math

QUESTION.THE equation of a circle with origin as centre and passing through the vertics of an equilateral triangle ,whose median of length 3a.
answer...we have to find equation of circum circle.we are given
1..origin is the centre.
2..tringle is equilateral.
method
1..quation of circle have three unknowns,if we find three vertices of triangle,we can find circle.
2.centre of circle is given ,if we find its radius,we can find circle.
we leave first method????,in case of equilateral triangle
circum radius =3/2(median) =3/2(3a)=2a
so equation of circle is x*2 +y*2 = ( 2a)*2.