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

Last updated at March 29, 2023 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 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.