Let `f(x)=x^3-6x^2+3(1+pi)x+7, pgtqgtr, then ({x-f(p)}(x-f(r)}}/(x-f(q))` has no value in (A) (p,q) (B) (q,r) (C) `(r,oo)` (D) none of these

Let f: R->R be a function such that f(x)=a x+3sinx+4cosxdot Then f(x) is invertible if (a) a in (-5,5) (b) a in (-oo,5) (c) a in (-5,+oo) (d) none of these

Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by sqrt(x+3) (b) sqrt(x)+3 (c) x+sqrt(3) (d) none of these

Let f: R->R be given by f(x)=x^2-3 . Then, f^(-1) is given by (a)sqrt(x+3) (b) sqrt(x)+3 (c) x+sqrt(3) (d) none of these

Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>f(x+1) for all x in R (c) f(x) is invertible (d) f(x)<0 for all x in R

Let f(x)=1/(1-x) . Then, {f\ o\ (f\ o\ f)}(x)=(a) x for all x in R (b) x for all x in R-{1} (c) x for all x in R-{0,\ 1} (d) none of these

If range of the function f(x)=(2sin^2x+2sinx+3)/(sin^2x+sinx+1) is [p ,q], then the value of 3 p+6q+1 is (a) (10)/3 (b) 7/3 (c) 28 (d) None of these

The function f(x)=x^9+3x^7+64 is increasing on (a) R (b) (-oo,\ 0) (c) (0,\ oo) (d) R_0

Let f(x)=|x^3sinxcosx6-1 0p p^2p^3|,w h e r ep is a constant. Then (d^3)/(dx^3)(f(x)) at x=0 is p (b) p-p^3 p+p^3 (d) independent of p

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these

The roots of the equation (q-r)x^2+(r-p)x+p-q=0 are (A) (r-p)/(q-r),1 (B) (p-q)/(q-r),1 (C) (q-r)/(p-q),1 (D) (r-p)/(p-q),1