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

Last updated at Dec. 16, 2024 by Teachoo

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

Class 12 Maths [MCQ] - If x = t2, y = t3, then (𝑑^2 𝑦)/(𝑑𝑥^2 ) is - NCERT Exemplar - MCQs

part 2 - Question 22 - NCERT Exemplar - MCQs - Serial order wise - Chapter 5 Class 12 Continuity and Differentiability

part 3 - Question 22 - NCERT Exemplar - MCQs - Serial order wise - Chapter 5 Class 12 Continuity and Differentiability

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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

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 and Computer Science at Teachoo

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