Question

Assertion :The area of the ellipse $2x^2+3y^2=6$ will be more than the area bounded by $2\left|x\right|+3\left|y\right|\le 6.$ Reason: The length of the major axis of the ellipse $2x^2+3y^2=6$ is less than the distance between the points of $2\left|x\right|+3\left|y\right|\le 6$ on $x-$axis.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is D Assertion is incorrect but Reason is correct

Area of ellipse $2x^2+3y^2=6$
Divide the above equation by $6$ we get
$\Rightarrow$Area of the ellipse$=\frac{x^2}{3}+\frac{x^2}{2}=1$
is $\pi \sqrt{3}\sqrt{2}=3.14\times \sqrt{6}=7.8$(approx.)sq.unit,
The area bounded by $2\left|x\right|+3\left|y\right|\le 6$ is
$4\times \frac{1}{2}\times 3\times 2=12$.sq.unit.
and length of major axis $=2\sqrt{6}<2\sqrt{9}=\sqrt{9+9}$

Hence, the assertion is incorrect but reason is correct.