CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1)

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Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Question 12 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by

if e x + e y =e (x+y) , then dy/dx is :

(a) e (y-x)      (b) e (x+y)
(c) -e (y-x)     (d) 2 e (x-y)

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Transcript

Question 12 if ๐‘’^๐‘ฅ+ ๐‘’^๐‘ฆ=๐‘’^(๐‘ฅ+๐‘ฆ), ๐‘กโ„Ž๐‘’๐‘› ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ is : (a) ๐‘’^(๐‘ฆโˆ’๐‘ฅ) (b) ๐‘’^(๐‘ฅ+๐‘ฆ) (c) ใ€–โˆ’๐‘’ใ€—^(๐‘ฆโˆ’๐‘ฅ) (d) 2 ๐‘’^(๐‘ฅโˆ’๐‘ฆ) Given ๐‘’^๐‘ฅ+๐‘’^๐‘ฆ=๐‘’^(๐‘ฅ + ๐‘ฆ) ๐‘’^๐‘ฅ+๐‘’^๐‘ฆ=๐‘’^๐‘ฅ.๐‘’^๐‘ฆ Dividing by ๐’†^๐’™.๐’†^๐’š both sides ๐’†^๐’™/(๐’†^๐’™ ๐’†^๐’š )+๐’†^๐’š/(๐’†^๐’™ ๐’†^๐’š )=(๐’†^๐’™ ๐’†^๐’š)/(๐’†^๐’™ ๐’†^๐’š ) 1/๐‘’^๐‘ฆ +1/๐‘’^๐‘ฅ =1 ๐’†^(โˆ’๐’š)+๐’†^(โˆ’๐’™)=๐Ÿ Differentiating both sides w.r.t x ๐’…(๐’†^(โˆ’๐’š) )/๐’…๐’™+๐’…(๐’†^(โˆ’๐’™) )/๐’…๐’™=๐’…(๐Ÿ)/๐’…๐’™ ๐’†^(โˆ’๐’š).(๐’…(โˆ’๐’š))/๐’…๐’™โˆ’๐’†^(โˆ’๐’™)=๐ŸŽ โˆ’๐‘’^(โˆ’๐‘ฆ).๐‘‘๐‘ฆ/๐‘‘๐‘ฅโˆ’๐‘’^(โˆ’๐‘ฅ)=0 โˆ’๐‘’^(โˆ’๐‘ฆ).๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=๐‘’^(โˆ’๐‘ฅ) ๐’…๐’š/๐’…๐’™=๐’†^(โˆ’๐’™)/(โˆ’๐’†^(โˆ’๐’š) ) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆ’๐‘’^(โˆ’๐‘ฅโˆ’(โˆ’๐‘ฆ)) ๐‘‘๐‘ฆ/๐‘‘๐‘ฅ=โˆ’๐‘’^(โˆ’๐‘ฅ + ๐‘ฆ) ๐’…๐’š/๐’…๐’™=โˆ’๐’†^(๐’š โˆ’ ๐’™) 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.