Assertion :The area of the ellipse 2x2+3y2=6 will be more than the area bounded by 2|x|+3|y|≤6. Reason: The length of the major axis of the ellipse 2x2+3y2=6 is less than the distance between the points of 2|x|+3|y|≤6 on x−axis.
A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Assertion is incorrect but Reason is correct
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Solution
The correct option is D Assertion is incorrect but Reason is correct Area of ellipse 2x2+3y2=6 Divide the above equation by 6 we get ⇒Area of the ellipse=x23+x22=1 is π√3√2=3.14×√6=7.8(approx.)sq.unit, The area bounded by 2|x|+3|y|≤6 is 4×12×3×2=12.sq.unit. and length of major axis =2√6<2√9=√9+9
Hence, the assertion is incorrect but reason is correct.