If `f(x)=x^2+2b c+2c^2a n dg(x)=-x^2-2c x+b^2` are such that min `f(x)> m a xf(x)` , ten he relation between `ba n dc` is a. no relation b. `0

If a ,b , a n dc are in G.P. and x ,y , respectively, are the arithmetic means between a ,b ,a n db ,c , then the value of a/x+c/y is 1 b. 2 c. 1//2 d. none of these

Let f(x)=a x+ba n dg(x)=c x+d , a!=0. Assume a=1,b=2. If (fog)(x)=(gof)(x) for all x , what can you say about ca n dd ?

Let f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot Show that g(x)geq0AAx in Rdot

If f(x)=cos^2x+s e c^2x ,t h e n f(x)<1 (b) f(x)=1 (c) 2ltf(x)<1 (d) """"f(x)ge2

Statement 1: If 27 a+9b+3c+d=0, then the equation f(x)=4a x^3+3b x^2+2c x+d=0 has at least one real root lying between (0,3)dot Statement 2: If f(x) is continuous in [a,b], derivable in (a , b) such that f(a)=f(b), then there exists at least one point c in (a , b) such that f^(prime)(c)=0.

If f(x)=x^3+b x^2+c x+d and 0 le b^2 le c , then a) f(x) is a strictly increasing function b)f(x) has local maxima c) f(x) is a strictly decreasing function d) f(x) is bounded

If a ,b ,c in R^+a n d2b=a+c , then check the nature of roots of equation a x^2+2b x+c=0.

If f(x)=|x-2|a n dg(x)=f[f(x)],t h e ng^(prime)(x)= ______ for x>2

If f(x)=(x^(2)+3x+2)(x^(2)-7x+a) and g(x)=(x^(2)-x-12)(x^(2)+5x+b) , then the value of a and b , if (x+1)(x-4) is H.C.F. of f(x) and g(x) is

If f(x)=|x+a^2 a b ac a b x+b^2 bc a c b c x+c^2|, t h e n prove that f^(prime)(x)=3x^2+2x(a^2+b^2+c^2)dot