
Among the given species. \( \text{S}_2\text{O}_3^{2-} \) (thiosulfate ion) has a pyramidal geometry around the central sulfur atom due to the presence of a lone pair on sulfur, resulting in a trigonal pyramidal shape.\( \text{SO}_4^{2-} \) (sulfate ion) has a tetrahedral geometry due to its symmetrical distribution of oxygen atoms around the central sulfur atom.\( \text{SO}_3^{2-} \) (sulfite ion) also adopts a trigonal pyramidal structure around sulfur, but in this context, \( \text{S}_2\text{O}_3^{2-} \) is more relevant to pyramidal geometry.\( \text{S}_2\text{O}_7^{2-} \) (disulfate ion) has a tetrahedral arrangement with respect to its central atoms, making it non-pyramidal.
Therefore, only one species, \( \text{S}_2\text{O}_3^{2-} \), exhibits pyramidal geometry.
The equivalent resistance between the points \(A\) and \(B\) in the given circuit is \[ \frac{x}{5}\,\Omega. \] Find the value of \(x\). 
Method used for separation of mixture of products (B and C) obtained in the following reaction is: 
In the following \(p\text{–}V\) diagram, the equation of state along the curved path is given by \[ (V-2)^2 = 4ap, \] where \(a\) is a constant. The total work done in the closed path is: 
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.