Question

Assertion : The inequality $ax+by<0$ is strict inequality.
Reason : The inequality $ax+b\ge 0$ is slack inequality.

• A. Assertion is correct, reason is correct; reason is a correct explanation for assertion.
• B. Assertion is correct, reason is correct; reason is not a correct explanation for assertion
• C. Assertion is correct, reason is incorrect
• D. Assertion is incorrect, reason is correct.

Answer 1

Answer: (B)

Let us consider some inequalities:
$ax+b<0\dots$ (i)
$ax+b>0\dots$(ii)
$ax+b\le 0\dots$ (iii)
$ax+b\ge 0\dots$ (iv)
$ax+by>c\dots$ (v)
$ax+by\le c\dots$(vi)
$a{x}^2+bx+c>0\dots$(vii)
$a{x}^2+bx+c\le 0\dots$ (viii)
Inequalities (i), (ii), (v) and (vii) are strict inequalities, while inequalities (iii), (iv), (vi) and (viii) are slack inequalities.
$\therefore$ Both Assertion and Reason are correct but Reason cannot explain Assertion.