Correct statement(s) about the compounds P, Q and R is(are)
Xe(g) + F₂(g) →^{873 K, 7 bar} P (1 : 5 ratio)
P + O₂F₂ →^{143 K} Q + O₂
Q + H₂O →^{complete hydrolysis} R + HF

The correct statements are: P has two lone pairs of electrons on the central atom., Q can act as a fluorinating agent., and The molecular structure of R is trigonal pyramidal.

Let us identify the chemical compounds P, Q, and R step-by-step based on the given chemical reactions:

Step 1: Identification of Compound P
When xenon (Xe) and fluorine (F₂) are mixed in a 1 : 5 molar ratio at 873 K and 7 bar pressure, xenon tetrafluoride (XeF₄) is formed.
$\mathrm{Xe}+2F_2\stackrel{873\text{K},7\text{bar}}{\to }{\mathrm{XeF}}_4\text{(P)}$
Thus, compound P is XeF₄.

Step 2: Identification of Compound Q
Xenon tetrafluoride (P) reacts with dioxygen difluoride (O₂F₂) at 143 K to yield xenon hexafluoride (XeF₆) and oxygen gas.
${\mathrm{XeF}}_4+O_2{F}_2\stackrel{143\text{K}}{\to }{\mathrm{XeF}}_6\text{(Q)}+O_2$
Thus, compound Q is XeF₆.

Step 3: Identification of Compound R
Complete hydrolysis of xenon hexafluoride (Q) with water yields xenon trioxide (XeO₃) and hydrogen fluoride (HF).
${\mathrm{XeF}}_6+3H_{2}O\to {\mathrm{XeO}}_3\text{(R)}+6\mathrm{HF}$
Thus, compound R is XeO₃.

Step 4: Evaluating the given statements

1. "P has two lone pairs of electrons on the central atom."
In XeF₄ (P), the central xenon atom has 8 valence electrons. Four of these form single bonds with four fluorine atoms, leaving 4 non-bonding electrons, which equal 2 lone pairs. (Geometry: square planar with sp³d² hybridization).
Hence, this statement is correct.

2. "Q has a perfect octahedral geometry."
In XeF₆ (Q), xenon has 6 bond pairs and 1 lone pair of electrons (total 7 electron pairs). Its structure is a distorted octahedral, not a perfect octahedral structure.
Hence, this statement is incorrect.

3. "Q can act as a fluorinating agent."
XeF₆ readily donates fluoride ions or acts as a strong fluorinating agent in various chemical reactions.
Hence, this statement is correct.

4. "The molecular structure of R is trigonal pyramidal."
In XeO₃ (R), xenon forms 3 double bonds with oxygen atoms and retains 1 lone pair. The geometry around the xenon atom is tetrahedral, giving it a trigonal pyramidal molecular shape.
Hence, this statement is correct.