Question

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): Ancient Indians discovered the concept of zero about the second century BCE. Reason (R): The Arabs learnt and adopted it from India and spread it in Europe. In the light of the above statements, choose the most appropriate answer from the options given below:

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Ancient Indian contributions:
• Zero
• Decimal system
• Algebra and astronomy Indian numerals spread to Europe through Arab scholars.

Answer 1

The Correct Option is B

Concept: Ancient India made remarkable contributions to mathematics and science. One of the greatest discoveries in world mathematical history was the concept of zero. Indian mathematicians developed:
• decimal notation,
• place value system,
• and the use of zero as a number. This contribution later spread to different parts of the world.

Step 1: Understanding Assertion (A). Assertion (A) states: \[ \text{Ancient Indians discovered the concept of zero about the second century BCE.} \] This statement is generally accepted as correct in the context of ancient Indian mathematical development. Indian mathematical traditions gradually evolved the use of:
• zero,
• positional notation,
• and decimal calculations. These developments became foundational for modern mathematics.

Step 2: Understanding Reason (R). Reason (R) states: \[ \text{The Arabs learnt and adopted it from India and spread it in Europe.} \] This statement is also correct. Arab scholars:
• studied Indian mathematical systems,
• adopted Indian numerals,
• and transmitted mathematical knowledge to Europe. As a result, the Hindu-Arabic numeral system became globally influential.

Step 3: Evaluating the relationship between Assertion and Reason. Although both statements are correct, the Reason does not directly explain why ancient Indians discovered zero. The Reason only explains:
• how the knowledge spread,
• not the actual cause or basis of the discovery. Therefore:
• Assertion (A) is correct,
• Reason (R) is correct,
• but Reason (R) is not the correct explanation of Assertion (A).

Step 4: Historical importance of zero. The invention of zero transformed mathematics because it:
• simplified calculations,
• enabled algebraic development,
• and strengthened scientific progress. Without zero, modern mathematics and computer science would not have developed in the same way.

Step 5: Final conclusion. Since both statements are correct but the Reason does not explain the Assertion, the correct answer is: \[ \boxed{\text{Both (A) and (R) are correct but (R) is not the correct explanation of (A)}} \]