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The point which does not lie in the half plane 2x + 3y −12 ≤ 0 is 

(a) (1, 2)                  (b) (2, 1)                 (c) (2, 3)             (d) (−3, 2)

The point which does not lie in the half plane 2x + 3y - 12 <= 0 is

Question 5 - CBSE Class 12 Sample Paper for 2020 Boards - Part 2
Question 5 - CBSE Class 12 Sample Paper for 2020 Boards - Part 3 Question 5 - CBSE Class 12 Sample Paper for 2020 Boards - Part 4

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Question 5 The point which does not lie in the half plane 2x + 3y −12 ≤ 0 is (a) (1, 2) (b) (2, 1) (c) (2, 3) (d) (−3, 2) We need to check if point satisfies the equation For (1, 2) Putting x = 1,y = 2 in the equation 2x + 3y – 12 ≤ 0 2(1) + 3(2) – 12 ≤ 0 2 + 6 – 12 ≤ 0 8 – 12≤ 0 –4 ≤ 0 which is true So, (1, 2) lies in the plane For (2, 1) Putting x = 2,y = 1 in the equation 2x + 3y – 12 ≤ 0 2(2) + 3(1) – 12 ≤ 0 4 + 3 – 12 ≤ 0 7 – 12≤ 0 –5 ≤ 0 which is true So, (2, 1) lies in the plane For (2, 3) Putting x = 2,y = 3 in the equation 2x + 3y – 12 ≤ 0 2(2) + 3(3) – 12 ≤ 0 4 + 9 – 12 ≤ 0 13 – 12≤ 0 1 ≤ 0 which is false So, (2, 3) does not lie in the plane Hence, our answer is (c) = (2, 3) Since we have got our answer, we can stop here. But, for practice, lets check the last point as well For (–3, 2) Putting x = –3,y = 2 in the equation 2x + 3y – 12 ≤ 0 2(–3) + 3(2) – 12 ≤ 0 –6 + 6 – 12 ≤ 0 0 – 12≤ 0 –12 ≤ 0 which is true So, (–3, 2) lies in the plane

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.