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Question 24 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)

Last updated at Nov. 18, 2021 by

If x = t 2 , y = t 3 , then (d 2 y)/(dx 2 ) is

(A) 3/2Β 

(B) 3/4t

(C) 3/2tΒ 

(D) 3/4

This question is similar to Question 16 (Or 2nd) - CBSE Class 12 - Sample Paper for 2019 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

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Transcript

Question 24 If x = t2, y = t3, then (𝑑^2 𝑦)/(𝑑π‘₯^2 ) is (A) 3/2 (B) 3/4𝑑 (C) 3/2𝑑 (D) 3/4 π‘₯=𝑑^2 & 𝑦=𝑑^3 Finding π’…π’š/𝒅𝒙 π’…π’š/𝒅𝒙=(π’…π’š/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) Finding π’…π’š/𝒅𝒕 𝑦=𝑑^3 𝑑𝑦/𝑑𝑑=(𝑑(𝑑^3))/𝑑𝑑 π’…π’š/𝒅𝒕=πŸ‘π’•^𝟐 Finding 𝒅𝒙/𝒅𝒕 π‘₯ =𝑑^2 𝑑π‘₯/𝑑𝑑=(𝑑(𝑑^2))/𝑑𝑑 𝒅𝒙/𝒅𝒕=πŸπ’• Now, π’…π’š/𝒅𝒙=(π’…π’š/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) =(3𝑑^2)/2𝑑 =πŸ‘π’•/𝟐 Finding (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 ) (𝒅^𝟐 π’š)/(𝒅𝒙^𝟐 )=𝑑(3𝑑/2)/𝑑π‘₯ =𝑑(3𝑑/2)/𝑑𝑑×𝒅𝒕/𝒅𝒙 =3/2×𝑑𝑑/𝑑π‘₯ =3/2Γ—πŸ/(𝒅𝒙/𝒅𝒕) Putting 𝑑π‘₯/𝑑𝑑=2𝑑 =3/2Γ—πŸ/πŸπ’• =πŸ‘/πŸ’π’• So, the correct answer is (B)

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.