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Each of the four inequalties given below defines  a region in the xy plane. One of these four regions does not have the following property. For any two points (x1, y1) and (x2, y2) in th e region , the point    is also in the region. The inequality defining this region is (1981 - 2 Marks)
  • a)
    x2 + 2y≤ 1
  • b)
  • c)
    x2 –y2 ≤ 1
  • d)
    y2 –x ≤ 0
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Each of the four inequalties given below defines a region in the xy pl...
(a) x2 + 2y2 ≤ 1 represents interior region of an ellipse where on taking any two pts the mid pt of that segment will also lie inside that ellipse
(b) Max { | x |, | y | } ≤  1 ⇒ | x | ≤ 1, | y | ≤ 1 ⇒ – 1 ≤ x ≤ 1 and – 1 ≤ y ≤ 1
which represents the interior region of a square with its sides x = ± 1 and y = ± 1 in which for any two pts, their mid pt also lies inside the region.
(c) x2 – y2 ≥ 1 repr esents the exterior r egion of hyperbola in which if we take two points (2, 0) and (– 2, 0) then their mid pt (0, 0) does not lie in the same region (as shown in the figure.)
(d) y2 ≤ x represents interior region of parabola in which for any two pts, their mid point also lie inside the region.
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Each of the four inequalties given below defines a region in the xy plane. One of these four regions does not have the following property. For any two points (x1, y1) and (x2, y2) in th e region , the point is also in the region. The inequality defining this region is (1981 - 2 Marks)a)x2 + 2y2≤ 1b)c)x2 –y2 ≤ 1d)y2 –x ≤ 0Correct answer is option 'C'. Can you explain this answer?
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Each of the four inequalties given below defines a region in the xy plane. One of these four regions does not have the following property. For any two points (x1, y1) and (x2, y2) in th e region , the point is also in the region. The inequality defining this region is (1981 - 2 Marks)a)x2 + 2y2≤ 1b)c)x2 –y2 ≤ 1d)y2 –x ≤ 0Correct answer is option 'C'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Each of the four inequalties given below defines a region in the xy plane. One of these four regions does not have the following property. For any two points (x1, y1) and (x2, y2) in th e region , the point is also in the region. The inequality defining this region is (1981 - 2 Marks)a)x2 + 2y2≤ 1b)c)x2 –y2 ≤ 1d)y2 –x ≤ 0Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each of the four inequalties given below defines a region in the xy plane. One of these four regions does not have the following property. For any two points (x1, y1) and (x2, y2) in th e region , the point is also in the region. The inequality defining this region is (1981 - 2 Marks)a)x2 + 2y2≤ 1b)c)x2 –y2 ≤ 1d)y2 –x ≤ 0Correct answer is option 'C'. Can you explain this answer?.
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