How many of given statements are true for lanthanums?
1. The common oxidation state of all lanthanides is +3.
2. All lantanides belongs to group III of modern periodic table.
3. All lanthanides belongs to seventh period of periodic table
4. The radius for all lanthanides cations `(M^(+3))` decrease from `Ce^(+3)` to `Lu^(+3)`.
5. The basic character of hydroxide increases on moving from `Ce(OH)_(3)` to `Lu(OH)_(3)`
6. All lanthanides are metals.
7. The reducing power of lanthanides decreases from Ce to Lu.
8. Lanthanides reacts with cold water to liberate `H_(2)`.

Explanation

To determine how many of the given statements about lanthanides are true, let's analyze each statement one by one.

1. **The common oxidation state of all lanthanides is +3.**
- This statement is **True**. While the common oxidation state for lanthanides is indeed +3, some can exhibit +2 and +4 oxidation states as well.

2. **All lanthanides belong to group III of the modern periodic table.**
- This statement is **True**. Lanthanides are often placed in the f-block, but they are considered part of the group III elements in the periodic table.

3. **All lanthanides belong to the seventh period of the periodic table.**
- This statement is **False**. Lanthanides actually belong to the sixth period of the periodic table.

4. **The radius for all lanthanide cations (M^(+3)) decreases from Ce^(+3) to Lu^(+3).**
- This statement is **True**. The ionic radius of lanthanide cations decreases from cerium (Ce) to lutetium (Lu) due to the phenomenon known as lanthanide contraction.

5. **The basic character of hydroxides increases on moving from Ce(OH)₃ to Lu(OH)₃.**
- This statement is **False**. The basic character of hydroxides actually decreases from Ce(OH)₃ to Lu(OH)₃.

6. **All lanthanides are metals.**
- This statement is **True**. All lanthanides are indeed classified as metals.

7. **The reducing power of lanthanides decreases from Ce to Lu.**
- This statement is **True**. The reducing power of lanthanides does decrease from cerium to lutetium.

8. **Lanthanides react with cold water to liberate H₂.**
- This statement is **True**. Lanthanides react with cold water to produce hydrogen gas (H₂).

Now, let's summarize the truth values of each statement:
1. True
2. True
3. False
4. True
5. False
6. True
7. True
8. True

Counting the true statements:
- True statements: 1, 2, 4, 6, 7, 8 (Total: 6)
- False statements: 3, 5 (Total: 2)

Thus, **6 statements are true** for lanthanides.