The correct orders among the following are:
Atomic radius: $$B \lt Al \lt Ga \lt In \lt Tl$$
Electronegativity: $$Al \lt Ga \lt In \lt Tl \lt B$$
Density: $$Tl \lt In \lt Ga \lt Al \lt B$$
1st Ionisation Energy: $$In \lt Al \lt Ga \lt Tl \lt B$$
Choose the correct answer from the options given below :

The five Group 13 elements in order of increasing atomic number are B, Al, Ga, In and Tl. To decide which of the four suggested sequences are correct we must compare them with the accepted experimental data for each property.

Case 1: Atomic radius
Standard covalent radii (pm) are B = 85, Al = 125, Ga = 122, In = 142, Tl = 145. Hence the correct ascending order is $$B \lt Ga \lt Al \lt In \lt Tl$$ The given order is $$B \lt Al \lt Ga \lt In \lt Tl,$$ which puts Al ahead of Ga and is therefore wrong.

Case 2: Electronegativity
Pauling electronegativities (averaged over common sources) are Al ≈ 1.5, Ga ≈ 1.6, In ≈ 1.7, Tl ≈ 1.8, B ≈ 2.0. Thus the correct ascending order is $$Al \lt Ga \lt In \lt Tl \lt B.$$ This is exactly the order supplied in the question, so the electronegativity sequence is correct.

Case 3: Density
Densities at 298 K (g cm$$^{-3}$$) are B = 2.34, Al = 2.70, Ga = 5.91, In = 7.31, Tl = 11.85. The correct ascending order is therefore $$B \lt Al \lt Ga \lt In \lt Tl.$$ The proposed order, $$Tl \lt In \lt Ga \lt Al \lt B,$$ is the exact reverse and is incorrect.

Case 4: First ionisation energy
First-ionisation energies (kJ mol$$^{-1}$$) are In = 558, Al = 577, Ga = 579, Tl = 589, B = 801. Hence the proper ascending order is $$In \lt Al \lt Ga \lt Tl \lt B,$$ which is identical to the order stated in the question, so it is correct.

Summarising: the correct sequences are Electronegativity (B) and First-ionisation energy (D) only.

Therefore the correct option is Option A (B and D only).