If `f(x) = |[x+p,x+a,x+a],[x+b,x+q,x+a],[x+b,x+b,x+r]|` and `g(x)=(p-x)(q-x)(r-x)`, then the value of `f(0)` is

x^(p-q).x^(q-r).x^(r-p)

f(x)=x,x in Q and f(x)=1-x,x in R-Q Then find the value of [f(1)]+|(f(e))]|

If f(x) = {:{(px^(2)-q, x in [0,1)), ( x+1 , x in (1,2]):} and f(1) =2 , then the value of the pair ( p,q) for which f(x) cannot be contiinuous at x =1 is

Let a,b,c be the roots of the equation x^(4)+x^(3)+x^(2)+x-1=0. Let f(x)=x^(6)-6x^(2)+6x+7 and g(x)=px^(2)+qx+r , (p,q,r in R,p!=0). If f(a)=g(a); f(b)=g(b) and f(c)=g(c); then the value of (2)/(g(1)) is

If a function f(x) satisfies f'(x)=g(x) . Then, the value of int_(a)^(b)f(x)g(x)dx is

If f''(x)>0 and Q(x)=2f((x^2)/2)+f(6-x^2),AAx in R , then function Q(x) is

f(x)=x^(2)-2x,x in R, and g(x)=f(f(x)-1)+f(5-f(x)) Show that g(x)>=0AA x in R

Let F:R to R be such that F for all x in R (2^(1+x)+2^(1-x)), F(x) and (3^(x)+3^(-x)) are in A.P., then the minimum value of F(x) is:

The HCF of the polynomials 9(x +a)^(p) (x -b)^(q) (x + c)^(r) and 12(x + a)^(p +3) (x -b)^(q-3) (x +c)^(r +2) " is " 3(x +a)^(6) (x -b)^(6) (x + c)^(6) , then the value of p +q -r is