Math Chapter Wise

EnglishUP PCS (Pre) 2003

Q421.The differential equation y px f(p)is of–

ANewtonian form BEuler’s form CGaussian form DClairaut form

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EnglishUP PCS (Pre) 2003

Q422.The differential equation ydx 2xdy 0represents:

Aa family of straight lines Ba family of parabolas Ca family of ellipses Da family of circles

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EnglishUP PCS (Pre) 2003

Q423.An integrating factor of the differential equation dy 1 y x dx x is–

A1/x Bx C1 x e Dlog x

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EnglishUP PCS (Pre) 2003

Q424.The solution of the differential equation (y2 +x)dx+xydy is–

Ax2 (3y2 +2x) = c Bx2 (2y2 +3x)= c Cy2 (3x2 +2y)= c Dnone of the above

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EnglishUP PCS (Pre) 2003

Q425.The solution of the differential equation (x-y2)dx + 2xydy = 0 is–

A2 y x ye c B2 y x xe c C2 y ye c DNone of these

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EnglishUP PCS (Pre) 2003

Q426.The singular solution of dy dy log x y dx dx is–

Ay x(log x 1) By x log x 1 Cy x log x DNone of the above

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EnglishUP PCS (Pre) 2004

Q427.The orthogonal trajectory of the family of the parabolas 2 x 4 y, being the parameter, is–

A2 2/x y c B2 2/x 2y c C2 2/2x y c D2 2/x 2y c

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EnglishUP PCS (Pre) 2004

Q428.Solution of the differential equation dy 2x y 3 dx represents a family of–

Astraight line Bcircles Cparabolas Dellipses

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EnglishUP PCS (Pre) 2004

Q429.If d D dx ≡ ≡, then 2 2 1 D a cos a x is equal to–

Ax sina x 2a Bx sin a x 2a Cx (sin ax cosax) 2a Dx cosax 2a

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EnglishUP PCS (Pre) 2004

Q430.Which of the following differential equations is linear?

A2 dy x y sin y dx B2 dy x y sin x dx Cdy (1 y) sin x 0 dx D2 dy y(y x) x dx

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EnglishUP PCS (Pre) 2004

Q431.The order and degree of the differential equation 4 d y dy y dx are respectively:

A2,4 B2,2 C4,2 D4,1

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EnglishUP PCS (Pre) 2004

Q432.Integrating factor of the linear differential equation dy y 1 log x dx x x is–

A1/x B1/ x/e C1 log x x e Dlog x/e

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EnglishUP PCS (Pre) 2004

Q433.The solution of y =px + 2p2, where dy p is dx

A2/y 5x c B2/y 2cx c C2/y 6x 2c D2/y cx 2c

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EnglishUP PCS (Pre) 2004

Q434.(x,y) is a point of inflexion of the curve y = f(x), if

A2 d y 0 dx but 3 d y 0 dx B2 d y 0 dx and 3 d y 0 dx but 4 d y 0 dx C2 d y 0 dx but 3 d y 0 dx Ddy 0 dx but 2 d y 0 dx

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EnglishUP PCS (Pre) 2005

Q435.The solution of the differential equation (D3 +a2 D)y =sin ax, where ≡ d D dx, is:

A1 2 3 2 x y c c cosax c sinax sinax 2a = + + − B1 2 3 2 x y c c cosax c sinax sinax 2a = + + + C1 2 3 2 x y c c cosax c sinax cosax 2a = + + − D1 2 3 2 x y c c cosax c sinax cosax 2a = + + −

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EnglishUP PCS (Pre) 2005

Q436.Which of the following differential equation is linear:

A2 dy x y y dx + = Bn dy sin x x y dx − = Cdy (1 y) P(x)y Q(x) dx + + = D2 dy y x y dx + =

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EnglishUP PCS (Pre) 2005

Q437.The differential equation ≡ dy y = px +f(p),P, dx is known as:

AClairaut's differential equation BLagrange's differential equation CCauchy's differential equation DEuler's differential equation

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EnglishUP PCS (Pre) 2005

Q438.The differential equation (x2 – ay)dx–(ax–y2 –ey)dy = 0 is:

AHomogeneous BLinear CExact DBernoulli's equation

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EnglishUP PCS (Pre) 2005

Q439.The solution of the differential equation ydx –xdy +(1+x2)dx+x2 sin ydy = 0 is:

Ax2 –y+1+x cos y = cy Bx2 –y+1+x cos y = cx Cx2 –y–1–x cos y = cx Dnone of these

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EnglishUP PCS (Pre) 2006

Q440.The degree of the differential equation dy dy 3y x sin dx dx = + is:

A0 B1 C2 Dcannot be determined

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