Which one of the following best represent the graph of $y = \frac{|x-x^2|}{x^2-x}$ ?
The domain of definition of the function $y(x)$ given by ${2^x} + {2^y} = 2$ is
The set of values of $'a'$ for which the inequality ${x^2} - (a + 2)x - (a + 3) < 0$ is satisfied by atleast one positive real $x$ , is
The function $f$ satisfies the functional equation $3f(x) + 2f\left( {\frac{{x + 59}}{{x - 1}}} \right) = 10x + 30$ for all real $x \ne 1$. The value of $f(7)$ is
Let $A= \{1, 2, 3, 4\}$ and $R : A \to A$ be the relation defined by $R = \{ (1, 1), (2, 3), (3, 4), ( 4, 2) \}$. The correct statement is
Minimum integral value of $\alpha$ for which graph of $f(x) = ||x -2| -\alpha|-5$ has exactly four $x-$intercepts-