Select the correct option.

Options

A. The `15^(th)` term from the end in the A.P. 13, 16, 19, ..., 160 is 108.
B. If the first, second and last terms of an A.P. are 6, 9 and 33 respectively, then the number of terms of the A.P. is 10.
C. The sum of an A.P. 2, 5, 8, ...., 152 is 3925.
D. All of these

Answer

To solve the problem step by step, we need to analyze the given arithmetic progression (AP) and find the correct option based on the information provided.

### Step-by-Step Solution:

1. **Identify the AP**: The given arithmetic progression is:
\[ 13, 16, 19, \ldots, 160 \]
Here, the first term \( a = 13 \) and the common difference \( d = 16 - 13 = 3 \).

2. **Find the number of terms**: To find the number of terms in the AP, we can use the formula for the nth term of an AP:
\[ a_n = a + (n-1)d \]
We need to find \( n \) such that \( a_n = 160 \):
\[ 160 = 13 + (n-1) \cdot 3 \]
Rearranging gives:
\[ 160 - 13 = (n-1) \cdot 3 \implies 147 = (n-1) \cdot 3 \]
Dividing both sides by 3:
\[ n - 1 = 49 \implies n = 50 \]

3. **Find the 15th term from the end**: The 15th term from the end can be found using:
\[ a_{n-14} = a + (n-14-1)d \]
Substituting \( n = 50 \):
\[ a_{50-14} = a + (50-14-1)d = a + 35d \]
Now substituting the values of \( a \) and \( d \):
\[ a_{36} = 13 + 35 \cdot 3 = 13 + 105 = 118 \]

4. **Check the options**: We have calculated the 15th term from the end to be 118. Now we need to check the options provided in the question to see if this matches any of them.

5. **Conclusion**: After checking the options, we find that the second option is correct as it states that the number of terms in the AP is 50, which we have calculated.

### Final Answer:
The correct option is **Option 2**.