The no. of solutions of the equation `a^(f(x)) + g(x)=0` where a>0 , and g(x) has minimum value of 1/2 is :-

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If int (cosec ^(2)x-2010)/(cos ^(2010)x)dx = =(f (x))/((g (x ))^(2010))+C, where f ((pi)/(4))=1, then the number of solution of the equation (f(x))/(g (x))={x} in [0,2pi] is/are: (where {.} represents fractional part function)

If f(x) is an even function and satisfies the relation x^(2)f(x)-2f(1/x)=g(x),xne0 , where g(x) is an odd function, then find the value of f(2).

f(x) is a cubic polynomial x^(3)+ax^(2)+bx+c such that f(x)=0 has three distinct integral roots and f(g(x))=0 does not have real roots,where g(x)=x^(2)+2x-5, the minimum value of a+b+c is

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is 1/4 and when x= 7/2 then value of g(x) will be minimum. Value of b_2 is-

If f(x)=g(x)(x-a)^(2) , where g(a)ne0 , and g is continuous at x=a , then

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is -1/4 and when x= 7/2 then value of g(x) will be minimum. Minimum value of g(x) is-

Let f (x)=x^2+b_1x+c_1 and g(x)=x^2+b_2x+c_2 . When f(x)=0 then the real roots of f(x) are alpha,beta and when g(x)=0 then the real roots of g(x) are alpha+h,beta+h . Minimum value of f(x) is -1/4 and when x= 7/2 then value of g(x) will be minimum. Roots of g(x)=0 are-