The equation $x \log x = 3 - x$:

If the function $f$ is given by $f(x)=x^3-3(a-2)x^2+3ax+7$,for some $a \in R$,is increasing in $(0,1]$ and decreasing in $[1,5)$,then a root of the equation $\frac{f(x)-14}{(x-1)^2}=0$ $(x \neq 1)$ is

Consider the function $f(x) = x(x - 1)(x - 2) \dots (x - 100)$. Which one of the following is correct?

If the function $f(x)=2 x^{3}-9 a x^{2}+12 a^{2} x+1$ attains its maximum and minimum at $p$ and $q$ respectively such that $p^{2}=q$,then $a$ equals

$x$ and $y$ are two variables such that $x > 0$ and $xy = 1$. Then the minimum value of $x + y$ is

On the interval $[0,1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point