Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Differentiation

NDA 2019 · Mathematics · Differentiation

If y=a 2 x+b 2 x , then

If y=acos⁡2x+bsin⁡2xy=a \cos 2 x+b \sin 2 x, then

Options

  1. Ad2ydx2+y=0\frac{d^2 y}{d x^2}+y=0
  2. Bd2ydx2+2y=0\frac{d^2 y}{d x^2}+2 y=0
  3. Cd2ydx2−4y=0\frac{d^2 y}{d x^2}-4 y=0
  4. Dd2ydx2+4y=0\frac{d^2 y}{d x^2}+4 y=0

Correct answer

D. d2ydx2+4y=0\frac{d^2 y}{d x^2}+4 y=0

Step-by-step solution

y=acos⁡2x+bsin⁡2xy=a \cos 2 x+b \sin 2 x⇒dydx=−2asin⁡2x+2bcos⁡2x⇒d2ydx2=−4acos⁡2x−4bsin⁡2x⇒d2ydx2=−4(acos⁡2x+bsin⁡2x)\begin{aligned} & \Rightarrow \frac{d y}{d x}=-2 a \sin 2 x+2 b \cos 2 x \\ & \Rightarrow \frac{d^2 y}{d x^2}=-4 a \cos 2 x-4 b \sin 2 x \\ & \Rightarrow \frac{d^2 y}{d x^2}=-4(a \cos 2 x+b \sin 2 x)\end{aligned}$\begin{aligned} & \Rightarrow \frac{d^2 y}{d x^2}=-4 y \\ & \Rightarrow \frac{d^2 y}{d x^2}+4 y=0\end{aligned}
Practice Differentiation on Quantrex Academy →

More from Differentiation

Passage: Let (e^y)^x-y=0 , where y is a function of x whose domain is (0,10] . Question… NDA 2026If [4] y =x+ x^2+4 , then what is x^2+4 \,(dy)/(dx) equal to ? NDA 2026Passage: Let (e^y)^x-y=0 , where y is a function of x whose domain is (0,10] . Question… NDA 2026For the following two (02) items: Consider the function f(x) = cases 4(5^x), & x What is… NDA 2025Consider the following for the two (02) items that follow: Let x = θ - θ and y = ^4θ… NDA 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q… NDA 2025Consider the following for the two (02) items that follow: Let y = ^ -1 (x… NDA 2025For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . If x = θ… NDA 2025Consider the following for the two (02) items that follow: Let (x+y)^ p+q = x^p y^q… NDA 2025For the following three (03) items: Let y = f(x) = x ^ -1 x 1 - x^2 + 1 - x^2 . What is… NDA 2025Consider the following for the two (02) items that follow: Let x = θ - θ and y = ^4θ… NDA 2025Paragraph: Let f:(-1,1) arrow R be a differentiable function with f(0)=-1 and f^ (0)=1 .… NDA 2024Let f(x) and g(x) be two functions such that g(x)=x-(1)/(x) and f o g(x)=x^3-(1)/(x^3) .… NDA 2024Paragraph: Let f:(-1,1) arrow R be a differentiable function with f(0)=-1 and f^ (0)=1 .… NDA 2024Let a function f be defined on ℝ-\ 0\ and 2 f(x)+f((1)/(x))=x+3 If f is differentiable… NDA 2023If f(x)=| | x| | where 0 < x < 1 , then what is f^ (0.5) equal to? NDA 2023 Full Differentiation list Differentiation JEE Maths PYQsJEE Mathematics PYQs All NDA PYQs