Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
BITSAT 2009
Exam
BITSAT
Year
2009
Subject
Mathematics
Chapter
Functions

BITSAT 2009 · Mathematics · Functions

If (y=e^ -x x) and y_4+k y=0 , where (y_4=(d^4 y)/(d x^4)), then k=

If (y=e^{-x} \cos x) and y4+ky=0y_4+k y=0, where (y_4=\frac{d^4 y}{d x^4}), then k=k=

Options

  1. A4
  2. B-4
  3. C2
  4. D-2

Correct answer

A. 4

Step-by-step solution

Let (y=e^{-x} \cos x) (y1=−e−xsin⁡x−e−xcos⁡x=−e−xsin⁡x−yy2=−e−xcos⁡x+e−xsin⁡x−y1⇒y2=−y−y1+e−xsin⁡x=−2(y+y1)⇒y3=−2(y1+y2)=−2(e−xsin⁡x−y)⇒y4=4y1+2y2=4y1−4y−4y1 or y4+4y=0⇒k=4\begin{aligned} & \mathrm{y}_1=-e^{-x} \sin x-e^{-x} \cos x=-e^{-x} \sin x-y \\ & y_2=-e^{-x} \cos x+e^{-x} \sin x-y_1 \\ & \Rightarrow y_2=-y-y_1+e^{-x} \sin x=-2\left(y+y_1\right) \\ & \Rightarrow y_3=-2\left(y_1+y_2\right)=-2\left(e^{-x} \sin x-y\right) \\ & \Rightarrow y_4=4 y_1+2 y_2=4 y_1-4 y-4 y_1 \text{ or } y_4+4 y=0 \\ & \Rightarrow k=4 \end{aligned})
Practice Functions on Quantrex Academy →

More from Functions

Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x| , then the value of f… BITSAT 2024Number of real solution of 5- _2|x| =3- _2|x| is equal to BITSAT 2024f(x)=( x)/([(2 x)/(π)]+(1)/(2)) , where x is not an integral multiple of π and [.]… BITSAT 2024The function f: R arrow R defined by f(x)= x 1+x^2 is BITSAT 2024If f: R arrow R, g: R arrow R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f^ -1 (3)… BITSAT 2024The domain of the real valued function f(x)= (2 x^2-7 x+5)/(3 x^2-5 x-2) is BITSAT 2024If a function f: R-\ l\ arrow R-\ m\ defined by f(x)=(x+3)/(x-2) is a bijection, then 3… BITSAT 2024f(x)= x+ x, g(x)=x^2-1 , then g(f(x)) is invertible if BITSAT 2024Let the function g:(-∞, ∞) arrow (-(π)/(2), (π)/(2)) be given by g(u)=2 ^ -1… BITSAT 2024The domain of the function f(x)= x- 1-x^2 is BITSAT 2023Consider the function f in A=R-\ (2)/(3)\ defined as f(x)=(4 x+3)/(6 x-4) , then f^ -1 is… BITSAT 2023If f(x)= x 1+x^2 , then (fof of) (x) is BITSAT 2023If g(x)=x^2+x-2 and (1)/(2) g o f(x)=2 x^2-5 x+2 then f(x) is equal to BITSAT 2022The domain of the function f(x)= 1 x^ 12 -x^ 9 +x^ 4 -x+1 is given by BITSAT 2021Let [x] denote the greatest integer ≤ x . If f(x)=[x] and g(x)=|x|, then the value of f… BITSAT 2020The domain of the function f(x)= x- 1-x^ 2 is BITSAT 2020 Full Functions list Functions JEE Maths PYQsJEE Mathematics PYQs All BITSAT PYQs