[" snole conect "],[" melessivalue of "alpha in R" for which "4 alpha x^(2)+(1)/(x)>=1," for all "x>0," is "],[qquad [" (B) "(1)/(32)]]

The least value of alpha in R for which 4alphax^(2)+(1)/(x)ge1, for all xgt0, is

The least value of alpha in R for which 4ax^2+(1)/(x)ge1 , for all xgt 0 , is

If x in R and alpha = (x^(2))/((1+x^(4))) , thens

If x in R " and "alpha=(x^(2))/(1+x^(4)) , then alpha lies in the interval

If x in R " and "alpha=(x^(2))/(1+x^(4)) , then alpha lies in the interval

Let f:R rarr R be defined by f(x)=2+alpha x,alpha!=0 , If f(x)=f^(-1)(x) , for all x in R , then alpha equals

If one root of the equation (alpha-4)x^2+2x+1=0 is 1, then alpha =

If alpha is a root of x^(4) + x^(2) - 1 = 0 , the value of (alpha^(6) + 2 alpha^(4))^(2012) is

IF alpha is a root of the equation 4x ^2 +2x-1=0 then 4 alpha ^3 - 3 alpha is

The set of values of alpha for which the point (alpha,1) lies inside the curves c_1: x^2+y^2-4=0 and c_2: y^2=4x is (a) |alpha| < sqrt(3) (b) |alpha|<2 (c) 1/4 < alpha < sqrt(3) (d) none of these