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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 March 16, 2023 by

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

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

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Question 12 if 𝑒^π‘₯+ 𝑒^𝑦=𝑒^(π‘₯+𝑦), π‘‘β„Žπ‘’π‘› 𝑑𝑦/𝑑π‘₯ is : (a) 𝑒^(π‘¦βˆ’π‘₯) (b) 𝑒^(π‘₯+𝑦) (c) γ€–βˆ’π‘’γ€—^(π‘¦βˆ’π‘₯) (d) 2 𝑒^(π‘₯βˆ’π‘¦) Given 𝑒^π‘₯+𝑒^𝑦=𝑒^(π‘₯ + 𝑦) 𝑒^π‘₯+𝑒^𝑦=𝑒^π‘₯.𝑒^𝑦 Dividing by 𝒆^𝒙.𝒆^π’š both sides 𝒆^𝒙/(𝒆^𝒙 𝒆^π’š )+𝒆^π’š/(𝒆^𝒙 𝒆^π’š )=(𝒆^𝒙 𝒆^π’š)/(𝒆^𝒙 𝒆^π’š ) 1/𝑒^𝑦 +1/𝑒^π‘₯ =1 𝒆^(βˆ’π’š)+𝒆^(βˆ’π’™)=𝟏 Differentiating both sides w.r.t x 𝒅(𝒆^(βˆ’π’š) )/𝒅𝒙+𝒅(𝒆^(βˆ’π’™) )/𝒅𝒙=𝒅(𝟏)/𝒅𝒙 𝒆^(βˆ’π’š).(𝒅(βˆ’π’š))/π’…π’™βˆ’π’†^(βˆ’π’™)=𝟎 βˆ’π‘’^(βˆ’π‘¦).𝑑𝑦/𝑑π‘₯βˆ’π‘’^(βˆ’π‘₯)=0 βˆ’π‘’^(βˆ’π‘¦).𝑑𝑦/𝑑π‘₯=𝑒^(βˆ’π‘₯) π’…π’š/𝒅𝒙=𝒆^(βˆ’π’™)/(βˆ’π’†^(βˆ’π’š) ) 𝑑𝑦/𝑑π‘₯=βˆ’π‘’^(βˆ’π‘₯βˆ’(βˆ’π‘¦)) 𝑑𝑦/𝑑π‘₯=βˆ’π‘’^(βˆ’π‘₯ + 𝑦) π’…π’š/𝒅𝒙=βˆ’π’†^(π’š βˆ’ 𝒙) 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.