In a test paper first section contain 5 questions each with 4 choices and second sections contains 4 questions each with 3 choices . In how many different ways can the paper be answered if all the questions are attempted ?

Answer

To solve the problem step by step, we will break it down into manageable parts.

### Step 1: Understand the Problem
The test paper has two sections:
- **Section 1**: Contains 5 questions, each with 4 choices.
- **Section 2**: Contains 4 questions, each with 3 choices.

We need to find the total number of ways to answer all the questions if every question is attempted.

### Step 2: Calculate the Ways to Answer Section 1
For Section 1, there are 5 questions, and each question has 4 choices. The total number of ways to answer all questions in this section can be calculated using the formula for permutations, which in this case is:
\[ \text{Ways for Section 1} = 4^5 \]
Calculating \(4^5\):
\[ 4^5 = 4 \times 4 \times 4 \times 4 \times 4 = 1024 \]

### Step 3: Calculate the Ways to Answer Section 2
For Section 2, there are 4 questions, and each question has 3 choices. The total number of ways to answer all questions in this section is:
\[ \text{Ways for Section 2} = 3^4 \]
Calculating \(3^4\):
\[ 3^4 = 3 \times 3 \times 3 \times 3 = 81 \]

### Step 4: Combine the Results
To find the total number of ways to answer the entire test paper, we multiply the number of ways to answer Section 1 by the number of ways to answer Section 2:
\[ \text{Total Ways} = \text{Ways for Section 1} \times \text{Ways for Section 2} \]
Substituting the values we calculated:
\[ \text{Total Ways} = 1024 \times 81 \]

### Step 5: Perform the Multiplication
Now, we calculate \(1024 \times 81\):
\[ 1024 \times 81 = 82944 \]

### Final Answer
Thus, the total number of different ways the paper can be answered is:
\[ \boxed{82944} \]