Step 1: Mendel's Cross of Pea Plants
Mendel crossed a homozygous long pea plant (dominant, TT) with a homozygous dwarf pea plant (recessive, tt). The F\(_1\) generation consisted of offspring with genotype Tt, where the dominant trait (long plant) expresses itself.
Step 2: Result of the Cross
In Mendel's experiment, all the plants in the F\(_1\) generation were heterozygous (Tt) and exhibited the dominant trait (long plants). The percentage of long plants was 100%. However, in the F\(_2\) generation (produced by self-crossing F\(_1\) plants), the expected ratio of long to dwarf plants was 3:1.
Step 3: Conclusion
Since the F\(_1\) generation consists of 100% long plants (heterozygous Tt), the correct answer is 50% long and 50% dwarf plants in the next generation.
\[
\boxed{\text{50% long and 50% dwarf plants}}
\]
Find the unknown frequency if 24 is the median of the following frequency distribution:
\[\begin{array}{|c|c|c|c|c|c|} \hline \text{Class-interval} & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 \\ \hline \text{Frequency} & 5 & 25 & 25 & \text{$p$} & 7 \\ \hline \end{array}\]
Two concentric circles are of radii $8\ \text{cm}$ and $5\ \text{cm}$. Find the length of the chord of the larger circle which touches (is tangent to) the smaller circle.