List of top Algebra Questions on Ring Homomorphisms and Polynomial Rings asked in GATE MA

Let \( \mathbb{Q}[x] \) be the ring of all polynomials with coefficients in \( \mathbb{Q} \) under the usual polynomial addition and multiplication. Let \( T: \mathbb{Q}[x] \to \mathbb{Q}[x] \) be defined by \[ T(p(x)) = p(x^2), \quad \text{for all } p(x) \in \mathbb{Q}[x]. \] Which of the following statements is/are TRUE?