If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is

(A) (-5)/4   (B) 2/5   (C) 15/4    (D) 3/2

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Question 9 If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is (A) (−5)/4 (B) 2/5 (C) 15/4 (D) 3/2 3x + 2ky − 2 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 3 , b1 = 2k , c1 = −2 2x + 5y + 1 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = 5, c2 = 1 Therefore, a1 = 3 , b1 = 2k , c1 = −2 & a2 = 2 , b2 = 5, c2 = 1 𝑎1/𝑎2 = 3/2 𝑏1/𝑏2 = 2𝑘/5 𝑐1/𝑐2 = (−2)/1 𝑐1/𝑐2 = −2 Since the lines are coincident 𝒂𝟏/𝒂𝟐 = 𝒃𝟏/𝒃𝟐 ≠ 𝒄𝟏/𝒄𝟐 3/2=2𝑘/5≠1/2 Thus, 3/2=2𝑘/5 3/2 × 5/2 = k k = 𝟏𝟓/𝟒 So, the correct answer is (C)

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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.