Math Chapter Wise

EnglishUP PCS (Pre) 1995

Q381.The exact differential equation is–

A(4x 6y 5)dx (2x 3y 4)dy B2 2 2/(6x 2y )dx (x 4xy)dy Cy y (e 1)cos x.dx e sin x.dy D1 y 1 sin y dx x(1 cos y)dy x

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EnglishUP PCS (Pre) 1995

Q382.The integrating factor of 2 2 dy (1 x) 2yx 4x 0 is dx

A2x B4x2 C1+x2 D–4x2

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EnglishUP PCS (Pre) 1995

Q383.The solution of the differential equation 2 d y y cos2x dx is–

A1 Acosx Bsin x cos2x 3 B1 Acosx Bsin x sin 2x 3 C1 Acosx Bsin x cos2x 3 D1 Acosx Bsin x sin 2x 3

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EnglishUP PCS (Pre) 1995

Q384.The equation dy y x dx = represents a family of–

ACircles BHyperbolas CParabola DEllipses

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EnglishUP PCS (Pre) 1995

Q385.The degree of the differential equation– 3 2 2 2 2 d y dy 3 1 dx

A1 B2 C3 DNone of these

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EnglishUP PCS (Pre) 1995

Q386.The solution of the differential equation x y 2 y dy e x e dx is–

Ay x 3 1 e e x c 3 By x 3 1 e e x c 3 Cy x 3 1 e e x c 3 Dy x 3 1 e e x c 3

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EnglishUP PCS (Pre) 1996

Q387.Solution of the differential equation (x + 2y3) dy dx = y is:

Ay = x3 + cx Bx = y3 - cy Cy = x2 + cy3 DNone of these where C is an arbitrary constant

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EnglishUP PCS (Pre) 1996

Q388.Solution of the differential equation y – 2px = f(xp2), where p ≡ ≡ dy dx is:

Ay = 2cx + f (c2) By = cx + f(c2 x) Cy = 2c x + f (cx2) Dy = 2c x + f (c2)

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EnglishUP PCS (Pre) 1996

Q389.Solution of the differential equation x 2 2 (2D 1) y 4e

Ay = (c1 + c2x) e–x/2 By = 2 x / 2 1 2 1 c c x x e 2 − + + Cy = 2 x / 2 1 2 1 c c x x e 4 − + + DNone of these where c1 and c2 are arbitrary constants.

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EnglishUP PCS (Pre) 1996

Q390.If m is the degree and n the order of the following differential equation 3 2 2 d y dy + 4 + 3y + y = 0 dx then:

Am = n Bm > n Cm < n Dm ≥ n

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EnglishUP PCS (Pre) 1996

Q391.Particular solution of the differential equation 2 d y dx + m2 y = a sin mx, is:

Ac1 cos mx Bc2 sin mx Ca 2m − x cos mx Da 2m − x sin mx

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EnglishUP PCS (Pre) 1996

Q392.The differential equation P dx + Q dy = 0 is exact, if:

A2 P x y ∂ − ∂ ∂ = 0 BaP Q x y ∂ = ∂ ∂ CP Q y x ∂ ∂ = ∂ ∂ DNone of these

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EnglishUP PCS (Pre) 1996

Q393.Solution of the differential equation (tan-1 y – x) dy – (1 + y2) dx = 0 is:

Ax = c tan–1y + tan x e −1 Bx = c tan y e −1 + 1 tan y 1 − Cy = tan–1 x + c tan x e −1 DNone of these

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EnglishUP PCS (Pre) 1999

Q394.An integrating factor for making the differential equation (xy+1) y dx+ (xy–1) x dy = 0 exact is:

Axy B1/xy Cy/x Dx/y

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EnglishUP PCS (Pre) 1999

Q395.The solution of the equation 2 dy dy x - y +a = 0 dx dx is

Ac y ax a = + Ba y ax c = + Ca y cx c = + Dc y cx a = +

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EnglishUP PCS (Pre) 1999

Q396.With C1 and C2 as arbitrary constants, the general solution of the differential equation (D2 –1)y = x2 is:

Ay = c1ex +c2e–x –x2 By = c1ex +c2e–x +(x2 +2) Cy = c1ex +c2e–x –2 Dy = c1ex +c2e–x –(x2 +2)

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EnglishUP PCS (Pre) 1999

Q397.The particular integral of (D2 +1) = e–x is:

Ax 1 x e 4 2 − Bx 1 x e 4 2 − + Cx 1 e 2 − Dx 1 e 2 −

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EnglishUP PCS (Pre) 1999

Q398.The solution of (xy2 +1) dx+(x2 y+1)dy = 0

Ax2 y2 +2x2 +2y2 = c Bx2 y2 +x2 +y2 = c Cx2 y2 +x2 +y2 = c Dx2 y2 +2x+2y = c

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EnglishUP PCS (Pre) 1999

Q399.The differential equation ydx + xdy = 0 represents a family of:

Acircles Bellipses Ccycloids Drectangular hyperbolas

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EnglishUP PCS (Pre) 2000

Q400.The singular solution of the differential equation a y px p = + = + is:

Aa y cx c = + By2 = 4 ax Cy = 2x2 DNone of these

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