Question 14 - CBSE Class 12 Sample Paper for 2022 Boards (MCQ Based - for Term 1) - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at Dec. 16, 2024 by Teachoo

If y = 5 cos x – 3 sin x, then (d ² y)/(dx ² ) is equal to:

(a) −y (b) y
(c) 25y (d) 9y

This question is inspired from Ex 5.7, 11 - Chapter 5 Class 12 - Continuity and Differentiability

Next: Question 15 → Go Ad-free

Transcript

Question 14 If y = 5 cos x – 3 sin x, then (𝑑^2 𝑦)/(𝑑𝑥^2 ) is equal to: (a) −y (b) y (c) 25y (d) 9y y = 5 cos⁡〖𝑥−3 sin⁡𝑥 〗 Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(5 cos⁡〖𝑥−3 sin⁡𝑥 〗))/𝑑𝑥 𝑑𝑦/𝑑𝑥 = (𝑑(5 cos⁡𝑥))/𝑑𝑥 − (𝑑(3 sin⁡𝑥))/𝑑𝑥 𝒅𝒚/𝒅𝒙 = − 5 𝒔𝒊𝒏⁡𝒙 − 3 𝒄𝒐𝒔⁡𝒙 Again Differentiating 𝑤.𝑟.𝑡.𝑥 𝑑/𝑑𝑥 (𝑑𝑦/𝑑𝑥) = (𝑑 〖(− 5 sin〗⁡𝑥 〖− 3cos〗⁡〖𝑥)〗)/𝑑𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = −(𝑑(5 sin⁡𝑥))/𝑑𝑥 − (𝑑(3 cos⁡𝑥))/𝑑𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = − 5 cos⁡𝑥 − 3 〖(−sin〗⁡〖𝑥)〗 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = − 5 cos⁡𝑥 + 3 sin⁡𝑥 (𝑑^2 𝑦)/(𝑑𝑥^2 ) = − (5 𝒄𝒐𝒔⁡𝒙 − 3 𝒔𝒊𝒏⁡𝒙) (𝒅^𝟐 𝒚)/(𝒅𝒙^𝟐 ) = −y So, the correct answer is (A)

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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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