Step 1: Understanding the Concept: A test cross is a fundamental genetic cross designed to determine the exact, unknown genotype of an organism exhibiting a dominant phenotype.
Step 2: Key Formula or Approach: Analyze the definition of a test cross and the logical implications of its resulting phenotypic ratios.
Step 3: Detailed Explanation: Statement I correctly defines a standard test cross: it involves crossing an organism with a dominant phenotype (which could be TT or Tt) with a homozygous recessive individual (tt). Thus, Statement I is completely true.
Statement II discusses interpreting the phenotypic results of this test cross.
If the test cross produces a ratio containing BOTH dominant and recessive traits (e.g., a 1:1 ratio), it logically implies that the unknown parent had to pass down a recessive allele, meaning it was heterozygous (Tt), NOT homozygous dominant.
Conversely, if the unknown organism is homozygous dominant (TT), all F\(_{1}\) offspring will be heterozygous (Tt) and show ONLY the dominant trait (100% dominant, 0% recessive), yielding no mixed ratio.
Therefore, observing a mixed ratio indicates a heterozygous genotype, making Statement II false.
Step 4: Final Answer: Statement I is true, and Statement II is false.