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Question 2 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards

Last updated at Dec. 16, 2024 by Teachoo

The value of k for which the lines 5x + 7y =3 and 15x + 21y = k coincide is

(a) 9   (b) 5   (c) 7   (d) 18

Transcript

Question 2 The value of k for which the lines 5x + 7y =3 and 15x + 21y = k coincide is (a) 9 (b) 5 (c) 7 (d) 18 Given equations 5x + 7y = 3 15x + 21y = k 5x + 7y – 3 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 5 , b1 = 7 , c1 = –3 15x + 21y − k = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 15 , b2 = 21 , c2 = –k Now, 𝑎1/𝑎2 = 5/15 𝑎1/𝑎2 = 1/3 𝑏1/𝑏2 = 7/21 𝑏1/𝑏2 = 1/3 𝑐1/𝑐2 = (−3)/(−𝑘) 𝑐1/𝑐2 = 3/𝑘 Since lines are coincident 𝑎1/𝑎2 = 𝑏1/𝑏2 = 𝑐1/𝑐2 𝟏/𝟑 = 𝟏/𝟑 = 𝟑/𝒌 Thus, 1/3 = 3/𝑘 k = 3 × 3 k = 9 So, the correct answer is (a)
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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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo