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 Sept. 4, 2021 by Teachoo

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

Question 14 If y = 5 cos x β 3 sin x, then (π^2 π¦)/(ππ₯^2 ) is equal to: (a) βy (b) y (c) 25y (d) 9y
y = 5 cosβ‘γπ₯β3 sinβ‘π₯ γ
Differentiating π€.π.π‘.π₯
ππ¦/ππ₯ = (π(5 cosβ‘γπ₯β3 sinβ‘π₯ γ))/ππ₯
ππ¦/ππ₯ = (π(5 cosβ‘π₯))/ππ₯ β (π(3 sinβ‘π₯))/ππ₯
π π/π π = β 5 πππβ‘π β 3 πππβ‘π
Again Differentiating π€.π.π‘.π₯
π/ππ₯ (ππ¦/ππ₯) = (π γ(β 5 sinγβ‘π₯ γβ 3cosγβ‘γπ₯)γ)/ππ₯
(π^2 π¦)/(ππ₯^2 ) = β(π(5 sinβ‘π₯))/ππ₯ β (π(3 cosβ‘π₯))/ππ₯
(π^2 π¦)/(ππ₯^2 ) = β 5 cosβ‘π₯ β 3 γ(βsinγβ‘γπ₯)γ
(π^2 π¦)/(ππ₯^2 ) = β 5 cosβ‘π₯ + 3 sinβ‘π₯
(π^2 π¦)/(ππ₯^2 ) = β (5 πππβ‘π β 3 πππβ‘π)
(π ^π π)/(π π^π ) = βy
So, the correct answer is (A)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.