Processing math: 68%

CBSE Questions for Class 12 Commerce Maths Differential Equations Quiz 7 - MCQExams.com

The general solution of the differential equation exdy+(yex+2x)dx=0 is
  • xex+x2=C
  • xexy2=C
  • yex+x2=C
  • yexx2=C
The solution of differential equation cosx.sinydx+sinx.cosydy=0 is 
  • sinxsiny=c
  • sinx.siny=c
  • sinx+siny=c
  • cosx.cosy=c
Solution of the differential equation: (2xcosy+y2cosx)dx+(2ysinxx2siny)dy=0 is :
  • x2sinx+y2cosx=c
  • x2siny+y2cosx=c
  • x2cosy+y2sinx=c
  • None of these
For the given differential equation find the general solution:
dydx+2y=sinx
  • 15[2sinxcosx]+Ce2x
  • 15[2sinxcosx]+C
  • 12[5sinxcosx]+Ce2x
  • None of these
The differential equation of the system of circles touching the x-axis at origin is  
  • (x2y2)dydx2xy=0
  • (x2+y2)dydx+2xy=0
  • (x2y2)dydx+2xy=0
  • (x2+y2)dydx2xy=0
The solution of xdx+ydy=xdyydxx2+y2 is ________________________.
  • x2+y2=2tan1yx+C
  • x2y2=2tan1yx+C
  • x2+y2=2tan1xy+C
  • x2y2=2tan1xy+C
Solution of differential equation dydx+xsin2y= sinycosyis
  • tany=(x1)+cex
  • coty=(x1)+cex
  • tany=(x1)ex+c
  • coty=(x1)ex+c
Let y=y(x) be the solution of the differential equation sinxdydx+ycosx=4x,x(0,π). If y=(π2)=0,theny(π6) is equal to :
  • 493π2
  • 893π2
  • 89π2
  • 49π2
Let f(x)=cos1(cosx) then 
  • f\left( x \right) is differentable for all xϵR
  • f\left( x \right) is not differentable atxϵ0
  • f\left( x \right) is not differentable ifx=nπ.nϵI
  • f\left( x \right) is not differentable ifx=nπ2nϵI
differential equation of all parabolas whose axis s y - axis.......
  • ydydx+xd2ydx2=1
  • xd2ydx2dydx=1
  • y2dydx+2xdydx=0
  • xdydxx2d2ydx2=0
Letyy(x) be the solution of the differential
equation sinxdydxycosx4x,xϵ(0,π).ify(π2) = 0,
then y (π6) is equal to 
  • 49π2
  • 493π2
  • 893π2
  • None of these
Integrating factors of the differential equation dydx+y=1+yx is 
  • x/ex
  • ex/x
  • xex
  • ex
Solution of differential equation dydx+yx=1(1+nx+ny) is (where C is an integration constant)
  • 2(1+n(xy))=x2+C
  • xyn(xy)=x2+C
  • (1+n(xy))=x2+C
  • 2xyn(xy)=x2+C
The solution of the differential equation (x2yx2)y3x=k+y2+xy2=0 is?
  • log(xy)=1x+1y+c
  • log(yx)=1x+1y+c
  • log(xy)=1x+1y+c
  • log(xy)+1x+1y=c
An integrating factor for the DE:(1+y2)dx(tan1yx)dy=0 is 
  • tan1y
  • etan1y
  • 11+y2
  • 1x(1+y2)
Solution of differential equation (2y+xy3)dx+(x+x2y2)dy=0
  • xy2+x3y33=c
  • xy2x3y33=c
  • x2y+x4y43=c
  • None of these
Solution of the differential equation (x2+1)y+2xy=4x2 is 
  • y(1+x2)=4x33+C
  • y(1x2)=x3+C
  • y(1x2)=x32+C
  • None of these
Consider the differential equation, ydx(x+y2)dy=0. If for y=1, x takes value 1, then value of x when y=4 is:

  • 16
  • 36
  • 64
  • 9
General solution of the differential equation dydx=1+xy is
  • y=cex2/2
  • y=cex2/2
  • y=(x+c)ex2/2
  • None
The solution of the differentiable equation x2dydx.cos1xysin1x=1, where y1 as x is
  • y=sin1xcos1x
  • y=x+1xsin1x
  • y=cos1xsin1x
  • y=x+1xcos1x
The population  p(t)  at time  t  of a certain mouse species satisfies the differential equation  dp(t)dt=0.5p(t)450.  If  p(0)=850,  then the time at which the population becomes zero is
  • 12ln18
  • ln18
  • 2ln18
  • ln9
The solution of differential equation  cos2xdydx(tan2x)y=cos4x,|x|<π4,  where y(π6)=338
  • y=tan2xcos2x
  • y=cot2xcos2x
  • 2y=tan2xcos2x
  • 2y=cot2xcos2x
The order of the differential equation
2x2d2ydx23dydx+y=0 is
  • 2
  • 1
  • 0
  • Not defined
The general solution of the differential equation ydxxdyy=0 is
  • xy=C
  • x=Cy2
  • y=Cx
  • y=Cx2
A differential equation associated with the primitive y=a+b e5x+c e7x is
  • y3+2y2y1=0
  • y3+2y235y1=0
  • 4y3+5y220y1=0
  • none of these
If υμ+μυ=6, then dυdμ=
  • 17μυμ17υ
  • μ17υ17μυ
  • 17μ+υμ17υ
  • μ+17υ17μυ
The number of arbitrary constant in the particular solution of a differential equation is
  • 3
  • 4
  • infinite
  • zero
Solution of differential equation siny.dydx+1xcosy=x4cos2y is
  • xsecy=x6+C
  • 6xsecy=x+C
  • 6xsecy=x6+C
  • 6xsecy=6x6+C
The general solution of the differential equation dydx=ex+y  is : 
  • ex+ey=c
  • ex+ey=c
  • ex+ey=c
  • ex+ey=c
The solution of the differential equation 2x2ydydx=tan(x2y2)2xy2 given y(1)=π2 is
  • sin (x2y2)1=0
  • cos(π2+x2y2)+x=0
  • sin(x2y2)=ex1
  • sin(x2y2)=e2(x1)
The solution of the equation (x2+xy)dy=(x2+y2)dxis 
  • logx=(xy)+yx+c
  • logx=2log(xy)+yx+c
  • logx=log(xy)+xy+c
  • none of these above
Solve the given differential equation dydx=(cosxsinx),
  • y=sinx+cosx+c
  • y=sinxcosx+c
  • y=tanx+secx
  • None  of  these
The solution of the differential equation xdydx=y(logylogx+1) is
  • y=xecx
  • y+xecx=0
  • y+ex
  • none of these
Which of the following functions is differentiable at x=0?
  • e|x||x|
  • e|x|+|x|
  • |x|e|x|
  • |x|e|x|
Solution of the differential equation of (y2x3)dxxydy=0 is
  • y2+2x3+cx2=0
  • y22x3+cx2=0
  • y2+2x3cx2=0
  • y2+3x3+cx2=0
The integrating factor (I.F) of differential equation \cfrac { dy }{ dx } \left( 1+x \right) -xy=1-x is _____
  • \left( 1+x \right) { e }^{ x }
  • \left( x-1 \right) { e }^{ x }\quad
  • \left( 1+x \right) { e }^{ -x }
  • \left( 1-x \right) { e }^{ -x }\quad
If \cos { x } \cfrac { dy }{ dx } -y\sin { x } =6x,(0<x<\cfrac { \pi  }{ 2 } ) and \quad y\left( \cfrac { \pi  }{ 3 }  \right) =0\quad then y\left( \cfrac { \pi  }{ 6 }  \right) is equal to:
  • -\cfrac { { \pi }^{ 2 } }{ 4\sqrt { 3 } }
  • -\cfrac { { \pi }^{ 2 } }{ 2 }
  • -\cfrac { { \pi }^{ 2 } }{ 2\sqrt { 3 } }
  • \cfrac { { \pi }^{ 2 } }{ 2\sqrt { 3 } }
Let f(x) be a function such that f(0)=f'(0)=0, f''(x)=\sec^{4}x+4, then the function is
  • \log (\sin x)+\dfrac{1}{3}\tan^{3}x+xb
  • \dfrac{2}{3}\log (\sec^2 x)+\dfrac{1}{6}\tan^{2}x+2x^{2}
  • \log (\cos x)+\dfrac{1}{6}\cos^{2}x+\dfrac{x^{2}}{5}
  • None\ of\ these
if y = y(x) and \dfrac{ 2 + sinx }{y + 1}(\dfrac{dy}{dx}) = -cosx, y(0) = 1, then y(\pi/2) equals
  • 1/3
  • 2/3
  • -1/3
  • 1
If x\dfrac{dy}{dx} = y(\log y - \log x + 1) , then the solution of the equation is 
  • \log \dfrac{x}{y} = cy
  • \log \dfrac{y}{x} = cy
  • \log \dfrac{x}{y} = cx
  • None of these
Solution of \dfrac{dy}{dx} + 2xy = y is 
  • y = ce^{x-x^{2}}
  • y = ce^{x^{2}-x}
  • y = ce^{x}
  • y = ce^{-x^{2}}
The solution of differential equation yy' = x\big(\dfrac{y^{2}}{x^{2}} + \dfrac{f (y^{2}/x^{2})}{f' (y^{2}/x^{2})}\big) is
  • f(y^{2}/x^{2}) = cx^{2}
  • x^{2}f(y^{2}/x^{2}) = c^{2}y^{2}
  • x^{2}f(y^{2}/x^{2}) = c
  • f(y^{2}/x^{2}) = cy/x
The solution of \dfrac{dv}{dt} + \dfrac{k}{m}v = -g is
  • v = ce^{-\dfrac{k}{m}t} - \dfrac{mg}{k}
  • v = c - \dfrac{mg}{k}e^{-\dfrac{k}{m}t}
  • ve^{-\dfrac{k}{m}t} = c - \dfrac{mg}{k}
  • ve^{-\dfrac{k}{m}t} = c - \dfrac{mg}{k}
The solution of the equation (x^{2}y + x^{2})dx + y^{2}(x-1)dy = 0 is given by
  • x^{2} + y^{2} + 2(x-y) + 2 ln \dfrac{(x-1)(y+1)}{c} = 0
  • x^{2} + y^{2} + 2(x-y) + ln \dfrac{(x-1)(y+1)}{c} = 0
  • x^{2} + y^{2} + 2(x-y) - 2 ln \dfrac{(x-1)(y+1)}{c} = 0
  • None of these
Solution of 2y sin x \frac {dv}{dx}= 2 sin x cos x -y^2 cos x, for x = \frac { \pi}{2} , y = 1 is 
  • y^2 = sin x
  • y = sin^2 x
  • y^2 = 1 +cos x
  • None of these
If \phi(x) =\int \left\{ \phi (x) \right\}^{-2} dx and \phi ( 1) =0 then \phi (x) =
  • \left\{ 2(x -1) \right\}^{1/4}
  • \left\{ 5(x -2) \right\}^{1/5}
  • \left\{ 3(x -1) \right\}^{1/3}
  • None of these
Solution of differential equation dy - \sin x \sin y dx = 0 is
  • e^{\cos x}\tan \dfrac{y}{2} = c
  • e^{\cos x}\tan y = c
  • \cos x \tan y = c
  • \cos x \sin y = c
if integrating factor of x(1-x^{2})dy + (2x^{2}y - y -ax^{3})dx=0 is e^{\int pdx} , then P is equal to 
  • \dfrac{2x^{2} - ax^{3}}{x(1-x^{2})}
  • 2x^{3} - 1
  • \dfrac{2x^{2} - a}{ax^{3}}
  • \dfrac{2x^{2} - 1}{x(1-x^{2})}
The solution of differentiation equation (2y+xy^{3})dx+(x+x^{2}y^{2})dy=o is 
  • x^{2}y+\dfrac{x^{3}y^{3}}{3}= c
  • xy^{2}+\dfrac{x^{3}y^{3}}{3}= c
  • x^{2}y+\dfrac{x^{4}y^{4}}{4}= c
  • None of these
The solution of differential equation \dfrac{x+y\dfrac{dy}{dx}}{y-x\dfrac{dy}{dx}} = \dfrac{x\cos^{2}(x^{2} + y^{2})}{y^{3}} is
  • \tan(x^{2}+y^{2})=\dfrac{x^{2}}{y^{2}}+c
  • \cot(x^{2}+y^{2})=\dfrac{x^{2}}{y^{2}}+c
  • \tan(x^{2}+y^{2})=\dfrac{y^{2}}{x^{2}}+c
  • \tan(x^{2}+y^{2})=\dfrac{y^{2}}{x^{2}}+c
0:0:1


Answered Not Answered Not Visited Correct : 0 Incorrect : 0

Practice Class 12 Commerce Maths Quiz Questions and Answers