Mathematics
Assertion (A): 1003 x 997 = 999991
Reason (R): (a - b)(a + b) = a2 - b2
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).
Answer
Given,
⇒ (a - b)(a + b)
⇒ a(a + b) - b(a + b)
⇒ a2 + ab - ab - b2
⇒ a2 - b2
∴ Reason (R) is true.
Solving,
⇒ 1003 x 997
⇒ (1000 + 3)(1000 - 3)
⇒ 10002 - 32
⇒ 1000000 - 9
⇒ 999991.
∴ Assertion (A) is true.
∴ Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Hence, option 3 is the correct option.
Related Questions
Consider the following two statements :
Statement 1: If a + b = 0, then a2 + b2 = 0
Statement 2: a2 + b2 = (a + b)2.
Which of the following is valid?
Both the statements are true.
Both the statements are false.
Statement 1 is true, and Statement 2 is false.
Statement 1 is false, and Statement 2 is true.
Find the expansions of the following :
(i) (2x + 3y + 5)(2x + 3y - 5)
(ii) (6 - 4a - 7b)2
(iii) (7 - 3xy)3
(iv) (x + y + 2)3
Simplify (x - 2)(x + 2)(x2 + 4)(x4 + 16).