Question 22 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 by

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

(A) 3/2 

(B) 3/4t

(C) 3/2t 

(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 22 If x = t2, y = t3, then (𝑑^2 𝑦)/(𝑑𝑥^2 ) is (A) 3/2 (B) 3/4𝑡 (C) 3/2𝑡 (D) 3/4 𝑥=𝑡^2 & 𝑦=𝑡^3 Finding 𝒅𝒚/𝒅𝒙 𝒅𝒚/𝒅𝒙=(𝒅𝒚/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) Finding 𝒅𝒚/𝒅𝒕 𝑦=𝑡^3 𝑑𝑦/𝑑𝑡=(𝑑(𝑡^3))/𝑑𝑡 𝒅𝒚/𝒅𝒕=𝟑𝒕^𝟐 Finding 𝒅𝒙/𝒅𝒕 𝑥 =𝑡^2 𝑑𝑥/𝑑𝑡=(𝑑(𝑡^2))/𝑑𝑡 𝒅𝒙/𝒅𝒕=𝟐𝒕 Now, 𝒅𝒚/𝒅𝒙=(𝒅𝒚/𝒅𝒕)/(𝒅𝒙/𝒅𝒕) =(3𝑡^2)/2𝑡 =𝟑𝒕/𝟐 Finding (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 ) (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 )=𝑑(3𝑡/2)/𝑑𝑥 =𝑑(3𝑡/2)/𝑑𝑡×𝒅𝒕/𝒅𝒙 =3/2×𝑑𝑡/𝑑𝑥 =3/2×𝟏/(𝒅𝒙/𝒅𝒕) Putting 𝑑𝑥/𝑑𝑡=2𝑡 =3/2×𝟏/𝟐𝒕 =𝟑/𝟒𝒕 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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.