Question

Assertion: If $a\ne b$, then $(a,b)\ne (b,a)$.
Reason: $(4,-3)$ lies in Quadrant $IV$
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.

Answer 1

Assertion (A):

If $a\ne b$ then $(a,b)\ne (b,a)$

A point represent a location in cartesian plane.

If the coordinates of a point are not equal them after interchanging them their location on cartesian plane also changes.

Observe the following figure, here the location of the points $A(1,2)$ and $B(2,1)$ are different.

i.e., the statement $a\ne b$ then $(a,b)\ne (b,a)$ is true.

Reason ( R ):

$(4,-3)$ lies in Quadrant $IV$.

Here, $x$-coordinate $=4$ is positive

$y$-coordinate $=-3$ is negative.

So, $(4,-3)$ is in the form of $(+,-)$.

Since, in Quadrant $IV$, any point is in the form of $(+,-)$.

Hence, the statement $(4,-3)$ lies in Quadrant $IV$ is true.

But, the reason does not justify the assertion.
i.e., Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.

​Hence, the correct answer is (b).