CTET 2 Math and Science 07 Jul 2024 Paper

To solve this problem, we need to use Euler's formula for polyhedra, which relates the number of faces $\left(\mathit{F}\right)$, edges $\left(\mathit{E}\right)$, and vertices $\left(\mathit{V}\right)$ of a polyhedron. Euler's formula states:
$\mathit{V}-\mathit{E}+\mathit{F}=2$
Calculation:
1. Given values: Faces $\left(\mathit{F}\right)=7$, Edges $\left(\mathit{E}\right)=15$, and Vertices $\left(\mathit{V}\right)=\mathit{x}$.
2. Substitute the given values into Euler's formula:
$\mathit{x}-15+7=2$
$\mathit{x}-8=2$
$\mathit{x}=10$
3. Now that we know the value of $\mathit{x}$ (vertices) is 10 , we can calculate the value of the expression ( $2\mathit{F}+3\mathit{E}-4\mathit{x}$ ):
$2\mathit{F}+3\mathit{E}-4\mathit{x}=2\left(7\right)+3\left(15\right)-4\left(10\right)$
$=14+45-40$
$=19$