Math Chapter Wise

EnglishUP PCS (Pre) 1998

Q361.The general solution of the differential equation 2 x 2 d y y e dx − = − = is:

Ay = A cos (x + B) + ex Bx 1 y = A cosh (x + B) + xe 2 Cy = A cos h (x + B) + xex Dy = a cos (x + B) + xex

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EnglishUP PCS (Pre) 1998

Q362.Singular solutions of the differential equation xyp2 –(x2 +y2 –1)p+xy = 0 are:

AOnly x + y + 1 = 0, and x + y – 1 = 0 BOnly x – y + 1 = 0, and x – y – 1 = 0 COnly x + y + 1 = 0, x + y – 1 = 0, x – y + 1 = 0 and x – y – 1 = 0 Dnone of these

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EnglishUP PCS (Pre) 1998

Q363.The solution of the equations dy 1 y 0 dx 1 x + + = + is

A1 + x = c (1 + y) B2 2 y x y x c 2 2 + = + + C1 + x + y + xy = c Dnone of these

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EnglishUP PCS (Pre) 1998

Q364.The general solution of the differential equation y dx – x dy = xy.dx is

Ay = A xex BAx = yex Cy = Aex Dy = Ae–x

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EnglishUP PCS (Pre) 1998

Q365.The general solution of the differential equation 2 d y dy 3 4y 0 dx − − = − − = − − = − − = is:

Ay = c1e–x By = c2e4x Cy = c1e–x + c2e4x Dy = c1ex + c2e–4x

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EnglishUP PCS (Pre) 1998

Q366.If ax y e sinbx = then (((()))) 2 2 n 1 n 1 y a b y + − + + equals:

A2xyn B2ayn C2byn D2axyn

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EnglishUP PCS (Pre) 2005

Q367.The orthogonal trajectory of the family of straight lines y = mx, where m is a parameter, is:

Ay2 = 4ax Bx2 = 4ay Cx2 +y2 = a2 Dx2 –y2 = a2

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EnglishUP PCS (Pre) 2008

Q368.The particular integral of the differential equation − 2 4x 2 d y dy 5 + 6y = e dx is

A4x 1 e 4 B4x 1 e 2 C4x 1 e 12 D4x/4e

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EnglishUP PCS (Pre) 1994

Q369.The general solution of 2 dx 1 x dy 1 y is–

Ax y c (1 xy) − = + By x c (1 xy) Cy x c (1 xy) Dy x c (1 xy)

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EnglishUP PCS (Pre) 1994

Q370.The general solution of 3 2 (D 3D 3D 1)y 0 − + − = − + − = − + − = − + − = is

Ax x 2x/y ae be ce Bx 2/y ae bx cx C2 x/y (a bx cx )e DNone of these

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EnglishUP PCS (Pre) 1994

Q371.The solution of the differential equation 2 d x dx 3 2x 0 dt when t 0, x 0, and dx 0 dt is–

Ax t Bt/x e Cx 0 Dt/x e

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EnglishUP PCS (Pre) 1994

Q372.The family of conic represented by the solution of differential equation (4x 3y 1)dx (3x 2y 1)dy 0 is–

ACircles BParabolas CHyperbolas DEllipses

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EnglishUP PCS (Pre) 1994

Q373.Which of the following differential equations is linear?

A2 dy y x 1 dx B2 dy y sin x dx Cx dx x y e dy D2 3 dx y x y dy

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EnglishUP PCS (Pre) 1994

Q374.The general solution of the differential equation x y dy e dx is–

Ax y/e e c Bx y/e e c Cx y e e c − + = Dx y/e e c

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EnglishUP PCS (Pre) 1994

Q375.Solution of 2 2 (x y)dx 2xy dy 0 is–

A2 2/x(x 3y ) c B2 2/x (x 3y ) c C2 2/x(3x y ) c D2 2 2/x (3x y ) c

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EnglishUP PCS (Pre) 1994

Q376.The singular solution of 2 2 2 (x 1)p 2xyp y 1 0 is–

A2 2/x y 1 B2 2/x y 4 C2 2/x y 1 D2 2/x y 4

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EnglishUP PCS (Pre) 1994

Q377.Which one of the following does not satisfy the differential equation 3 d y y 0 dx?

Ax/e Bx/e Cx / 2 3 e sin x 2 Dx / 2 3 e cos x 2

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EnglishUP PCS (Pre) 1994

Q378.In the differential equation 3 2x (D 7D 6)y e, − + = − + = − + = − + = d D, dx the particular integral is–

A2x e 5 Bx xe 5 C5x/e Dnone of these

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EnglishUP PCS (Pre) 1994

Q379.In the differential equation 2 (D D 2)y x, the particular integral is–

A1 1 x 2 2 B1 1 x 2 2 C(x 1)/2 D(x 1)/2

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EnglishUP PCS (Pre) 1995

Q380.The complete primitive of the differential equation 2 1 y px, 4p where dy p dx is–

AA family of straight line whose envelope is 2 y 4x BA family of straight lines whose envelope is 2 y 8x CA family of straight lines whose envelope is 2 y x DNone of the above answer is correct

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