Let `f(x)=sinx+a x+bdot` Then which of the following is/are true? `f(x)=0` has only one real root which is positive if `a >1, b<0.` `f(x)=0` has only one real root which is negative if `a >1, b<0.` `f(x)=0` has only one real root which is negative if `a >1, b > 0.` `non eoft h e s e`

Let f(x)=sinx+ax+b.Then which of the following is/are true?

Let f(x)=x sin(e^((1)/(x))) for x!=0 and for x=0 which of the following is true?

Let F(x)={(x-1)(sin1)/(x-1),x!=1,{0,x=1 then which one of the following is true.

Let f(x) =cos^-1 x^2+ cos^-1x, then which one of the following is true? (A) f (x) is strictly decreasing (B) f (x) is decreasing in [0, 1] and increasing in [-1,0] (C) f(x) has only one local maxima. D) f(x) has only one local minima.

Let f(x)=ax^3+bx^2+x+d has local extrema at x=alpha and beta such that alphabetalt0 and f(alpha).f(beta)gt0 . Then the equation f(x)=0 (A) has 3 distinct real roots (B) has only one real which is positive o a.f(alpha)lt0 (C) has only one real root, which is negative a.f(beta)gt0 (D) has 3 equal roots

Let a in R and f : R rarr R be given by f(x)=x^(5)-5x+a , then (a) f(x)=0 has three real roots if a gt 4 (b) f(x)=0 has only one real root if a gt 4 (c) f(x)=0 has three real roots if a lt -4 (d) f(x)=0 has three real roots if -4 lt a lt 4

For the function f(x) = (e^(1/x) -1)/(e^(1//x) + 1) , x=0 , which of the following is correct .

[ 9.Let f(x)=ax+sin2x+b ,then f(x)=0 has (A) exactly one positive real root,if agt2 and blt0 (B) exactly one positive real root,if agt2 and bgt0 (C) Both(A)&(B) (D) None of these ]