`S_(1)` : Even at different temperature and pressure, equal volume of all the gases contains equal number of moles.
`S_(2) : 11.2 L CO_(2)(g)` at `STP` contains the same number of free entity as `22.4 L O_(2)(g)` at `STP`.
`S_(3) :` If reacting species in a reaction are not taken in their stoichiometric coefficient ratio then one of the reactant will be limiting reagent.
`S_(4) :` If two different solutions having different solute are mixed in certain volume proportion then resulting concentration of the components will decrease.

Options

A. a. `F F T T `
B. b. `T T F F `
C. c. `T F T F`
D. d. `F T F T `

Answer

To analyze the given statements, we will evaluate each one step by step.

### Statement S1:
**Statement**: Even at different temperature and pressure, equal volume of all the gases contains equal number of moles.

**Analysis**: According to the Ideal Gas Law, \( PV = nRT \). If we have equal volumes of gas at different temperatures and pressures, we can express the number of moles as:
\[ n = \frac{PV}{RT} \]
If we take two conditions (1 and 2) with equal volumes but different pressures and temperatures:
- For condition 1: \( n_1 = \frac{P_1V}{RT_1} \)
- For condition 2: \( n_2 = \frac{P_2V}{RT_2} \)

Taking the ratio:
\[ \frac{n_1}{n_2} = \frac{P_1T_2}{P_2T_1} \]
Since \( P_1 \) and \( P_2 \) can be different and \( T_1 \) and \( T_2 \) can also be different, \( n_1 \) does not equal \( n_2 \). Therefore, this statement is **False**.

### Statement S2:
**Statement**: 11.2 L of CO₂(g) at STP contains the same number of free entities as 22.4 L of O₂(g) at STP.

**Analysis**: At STP (Standard Temperature and Pressure), 1 mole of any gas occupies 22.4 L.
- For CO₂:
\[ \text{Moles of CO₂} = \frac{11.2 \text{ L}}{22.4 \text{ L/mol}} = 0.5 \text{ moles} \]
- For O₂:
\[ \text{Moles of O₂} = \frac{22.4 \text{ L}}{22.4 \text{ L/mol}} = 1 \text{ mole} \]

Since 0.5 moles of CO₂ is not equal to 1 mole of O₂, this statement is **False**.

### Statement S3:
**Statement**: If reacting species in a reaction are not taken in their stoichiometric coefficient ratio, then one of the reactants will be a limiting reagent.

**Analysis**: The limiting reagent is the reactant that is completely consumed first in a chemical reaction, limiting the amount of product formed. If the reactants are not in the stoichiometric ratio, one reactant will be used up before the other, confirming that there will be a limiting reagent. Thus, this statement is **True**.

### Statement S4:
**Statement**: If two different solutions having different solutes are mixed in a certain volume proportion, then the resulting concentration of the components will decrease.

**Analysis**: When two solutions are mixed, the total volume increases while the amount of solute remains constant. This dilution effect results in a lower concentration of each solute in the mixture. Therefore, this statement is **True**.

### Conclusion:
- **S1**: False
- **S2**: False
- **S3**: True
- **S4**: True

The correct option based on the analysis is that statements S3 and S4 are true.