TANCET 2025 Solved Papers

Concept:The inequality $x^{2} > x$ is true only when $x < 0$ or $x > 1$.Explanation:Rewrite the inequality as $x^{2} - x > 0$.Factorize it as $x(x - 1) > 0$.So, $x^{2} > x$ holds for $x < 0$ or $x > 1$.Statement (1): $x > 0$.For $0 < x < 1$, say $x = 0.5$, we get $0.25 > 0.5$, which is false.For $x > 1$, say $x = 2$, we get $4 > 2$, which is true.Thus, Statement (1) alone is not sufficient.Statement (2): $x \neq 1$.This allows values like $0.5$ and $2$, giving both false and true outcomes.Thus, Statement (2) alone is not sufficient.Combining both statements: $x > 0$ and $x \neq 1$.This still includes $0 < x < 1$ and $x > 1$.For $x = 0.5$, the inequality is false; for $x = 2$, it is true.Therefore, both statements together are not sufficient.Answer:D. Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.