Mathematics
Assertion (A) : 687 x 687 - 313 x 313 = 37400
Reason (R) : The product of the sum and difference of the same two terms = The square of their difference.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Answer
We know that,
The product of the sum and difference of the same two terms = Difference of their squares.
(a + b)(a - b) = a2 - b2
So, reason (R) is true.
Given,
⇒ 687 x 687 - 313 x 313 = 34700
Solving, L.H.S.
⇒ 687 x 687 - 313 x 313
⇒ 6872 - 3132
⇒ (687 - 313)(687 + 313)
⇒ 374 x 1000
⇒ 374000.
Since, L.H.S. ≠ R.H.S.
So, assertion (A) is false.
Hence, option 4 is the correct option.
Related Questions
Assertion (A) : If we add 9 with 49x2 - 42x, the resultant expression will be a perfect square expression.
Reason (R) : The product of the sum and difference of the same two terms = Difference of their squares.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Assertion (A) : If the volume of a cube is a3 + b3 + 3ab(a + b), then the edge of the cube is (a + b)
Reason (R) : (1st term + 2nd term)3 = (1st term)3 + 3(1st term)2 .(2nd term) + 3(2nd term)2 .(1st term) + (2nd term)3.
Both A and R are correct, and R is the correct explanation for A.
Both A and R are correct, and R is not the correct explanation for A.
A is true, but R is false.
A is false, but R is true.
Evaluate :
(2a + 0.5)(7a - 0.3)