Question 40 - 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 number of solutions of 3 ^{x + y} = 243 and 243 ^{x − y} = 3 is

(a) 0 (b) 1 (c) 2 (d) infinite

Ques 40 (MCQ) - The number of solutions of 3^(x+y) = 243 and 243^(x-y) - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ]

part 2 - Question 40 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards - Class 10

part 3 - Question 40 - CBSE Class 10 Sample Paper for 2022 Boards - Maths Standard [MCQ] - Solutions of Sample Papers for Class 10 Boards - Class 10

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Transcript

Question 40 The number of solutions of 3x + y = 243 and 243x − y = 3 is (a) 0 (b) 1 (c) 2 (d) infinite 3x + y = 243 3x + y = 35 Comparing powers x + y = 5 243x − y = 3 (35)x − y = 3 35(x − y) = 31 Comparing powers 5(x − y) = 1 x − y = 𝟏/𝟓 Adding (1) and (2) (x + y) + (x − y) = 5 + 1/5 2x = (5(5) + 1)/5 2x = (25 + 1)/5 2x = 26/5 x = 𝟏𝟑/𝟓 Putting value of x in (1) x + y = 5 13/5 + y = 5 y = 5 − 𝟏𝟑/𝟓 y = (𝟓(𝟓) − 𝟏𝟑)/𝟓 y = (𝟐𝟓 − 𝟏𝟑)/𝟓 y = 𝟏𝟐/𝟓 Thus, x = 𝟏𝟑/𝟓 , y = 𝟏𝟐/𝟓 Since only one pair of solutions are there ∴ Number of solutions = 1 So, the correct answer is (b)

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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

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