Institution: Bangladesh Bank Exam: Officer (General) |-Sonali | Janata | Bangladesh Krishi_Bangladesh Development bank ২৪.০৫.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine the number of ways a student can choose 10 out of 13 questions with the constraint of selecting at least 4 from the first 5 questions, we can break the problem down into cases based on how many questions the student selects from the first 5.

### Case 1: Choose 4 from the first 5 questions
- Choose 4 questions from the first 5: \( \binom{5}{4} = 5 \)
- Choose the remaining 6 from the remaining 8 questions (questions 6 to 13): \( \binom{8}{6} = 28 \)
- Total for this case: \( 5 \times 28 = 140 \)

### Case 2: Choose 5 from the first 5 questions
- Choose all 5 from the first 5: \( \binom{5}{5} = 1 \)
- Choose the remaining 5 from the remaining 8 questions: \( \binom{8}{5} = 56 \)
- Total for this case: \( 1 \times 56 = 56 \)

### Combining Cases
Now we sum the total choices from both cases:
- Total = Case 1 (140) + Case 2 (56) = \( 140 + 56 = 196 \)

Thus, the total number of ways the student can select the questions, ensuring at least 4 from the first 5, is **196**. This is why the correct answer is option B.