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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  1. Chapter 5 Class 12 Continuity and Differentiability (Term 1)
  2. Serial order wise

Transcript

Question 24 If x = t2, y = t3, then (๐‘‘^2 ๐‘ฆ)/(๐‘‘๐‘ฅ^2 ) is (A) 3/2 (B) 3/4๐‘ก (C) 3/2๐‘ก (D) 3/4 ๐‘ฅ=๐‘ก^2 & ๐‘ฆ=๐‘ก^3 Finding ๐’…๐’š/๐’…๐’™ ๐’…๐’š/๐’…๐’™=(๐’…๐’š/๐’…๐’•)/(๐’…๐’™/๐’…๐’•) Finding ๐’…๐’š/๐’…๐’• ๐‘ฆ=๐‘ก^3 ๐‘‘๐‘ฆ/๐‘‘๐‘ก=(๐‘‘(๐‘ก^3))/๐‘‘๐‘ก ๐’…๐’š/๐’…๐’•=๐Ÿ‘๐’•^๐Ÿ Finding ๐’…๐’™/๐’…๐’• ๐‘ฅ =๐‘ก^2 ๐‘‘๐‘ฅ/๐‘‘๐‘ก=(๐‘‘(๐‘ก^2))/๐‘‘๐‘ก ๐’…๐’™/๐’…๐’•=๐Ÿ๐’• Now, ๐’…๐’š/๐’…๐’™=(๐’…๐’š/๐’…๐’•)/(๐’…๐’™/๐’…๐’•) =(3๐‘ก^2)/2๐‘ก =๐Ÿ‘๐’•/๐Ÿ Finding (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ ) (๐’…^๐Ÿ ๐’š)/(๐’…๐’™^๐Ÿ )=๐‘‘(3๐‘ก/2)/๐‘‘๐‘ฅ =๐‘‘(3๐‘ก/2)/๐‘‘๐‘กร—๐’…๐’•/๐’…๐’™ =3/2ร—๐‘‘๐‘ก/๐‘‘๐‘ฅ =3/2ร—๐Ÿ/(๐’…๐’™/๐’…๐’•) Putting ๐‘‘๐‘ฅ/๐‘‘๐‘ก=2๐‘ก =3/2ร—๐Ÿ/๐Ÿ๐’• =๐Ÿ‘/๐Ÿ’๐’• So, the correct answer is (B)

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.