Four tests - Physics, Chemistry, Mathematics and Biology are to be conducted on four consecutive days, not necessarily in the same order. The Physics test is held before the test which is conducted after Biology. Chemistry is conducted exactly after two tests are held. Which is the last test held?

Correct Option (3)

The problem involves arranging four tests (Physics, Chemistry, Mathematics, Biology) across four consecutive days based on two given conditions:

1. The Physics test is held before the test which is conducted after Biology.
2. Chemistry is conducted exactly after two tests are held.

From Condition 2, Chemistry is the third test in the sequence. This establishes the structure:

Day 1, Day 2, Chemistry, Day 4

Now, we apply Condition 1, which states that Physics is held before the test immediately following Biology. Let's consider the possible positions for Biology:

• If Biology is on Day 1: There is no test immediately following it within the four-day schedule. Therefore, Biology cannot be on Day 1.

• If Biology is on Day 2: The test immediately following Biology is on Day 3, which is Chemistry. According to Condition 1, Physics must be held before Day 3. Since Physics cannot be on Day 2 (as Biology is there), Physics must be on Day 1.

  This yields the partial sequence: Physics, Biology, Chemistry, Day 4.

  The only remaining test is Mathematics, which must be on Day 4. Thus, the complete sequence is: Physics, Biology, Chemistry, Mathematics.

  Let's verify this sequence against both conditions:

  • Condition 1: Biology is on Day 2. The test after Biology is Chemistry (Day 3). Physics (Day 1) is indeed held before Chemistry (Day 3). This is consistent.
  • Condition 2: Chemistry is on Day 3, exactly after two tests. This is consistent.

  This sequence is valid.

• If Biology is on Day 3: Day 3 is already occupied by Chemistry (from Condition 2). Therefore, Biology cannot be on Day 3.

• If Biology is on Day 4: There is no test immediately following it. Therefore, Biology cannot be on Day 4.

Based on this analysis, the only possible sequence of tests is Physics, Biology, Chemistry, Mathematics.

Therefore, the last test held is Mathematics.

Incorrect Options:

Options 1 (Physics), 2 (Biology), and 4 (Chemistry) are incorrect because, according to the uniquely derived sequence (Physics, Biology, Chemistry, Mathematics), Physics is the first test, Biology is the second test, and Chemistry is the third test. Mathematics is the fourth and final test.