Question

Assertion: 98 × 102 = 9996

Reason: (a + b)(a – b) = a² – b²

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:

Assertion: 98 × 102 = 9996 is true.

This can be evaluated using the algebraic identity:

(a + b)(a – b) = a² – b²

Here, 98 × 102 can be seen as (100 – 2)(100 + 2).

Applying the identity:

(100 – 2)(100 + 2)

= 100² – 2²

= 10000 – 4 

= 9996

Reason states the identity used, which is true and crucial for the explanation of the assertion.

Thus, both Assertion and Reason are true and Reason correctly explains the Assertion.