Math Chapter Wise

EnglishUP PCS (Pre) 2007

Q461.Which of the following is the singular solution of the differential equation– dy 5 y x? dy dx = +

A2/y 20x By cx 5/ c Cy = x + 5 Dx2 = 20y

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EnglishUP PCS (Pre) 2008

Q462.The whole length of an arc of the cycloid x = a (θ+sin θ), y = a (1–cos θ) is:

A8 B8a C4a D8πa

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EnglishUP PCS (Pre) 2008

Q463.If y = axn+1 +bx–n then 2 2 2 x d y dx is equal to

An(n–1)y Bn(n+1)y Cny Dn2/y

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EnglishUP PCS (Pre) 2008

Q464.Differential equation of the orthogonal trajectories of the family of parabolas y = ax2 is

A2x y' y = B2x y' y = − Cx y' 2y = Dx y' 2y − =

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EnglishUP PCS (Pre) 2008

Q465.Complementary function of the solution of the differential equation 2 d y dy - 4 + y = sin x is dx

A() 2x A cos h 3x + Bsin h 3x e B() -2x A cos h 3x + Bsin h 3x e C( ) 2x/A cos 3x + Bsin 3x e D( ) 2x/A cos 3x + Bsin 3x e

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EnglishUP PCS (Pre) 2008

Q466.The particular integral of the differential equation 2 d y + y = cos x dx is

A2 cos x 3 B2 sin x 3 − C2 sin x 3 D2 cos x 3 −

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EnglishUP PCS (Pre) 2008

Q467.In the following differential equation non– linear differential -equation is

A2 d y dy x y 0 dx + + = B2 d y dy xy 0 dx + + = C2 d y dy xy 0 dx + + = D2 d y dy x x y 0 dx + + + =

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EnglishUP PCS (Pre) 2008

Q468.The solution of the differential equation n dy y x dx x + = is

Ay = Cx By +x = C Cn 2 x yx c n 2 + = + + Dn x y c n 2 = + +

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EnglishUP PCS (Pre) 2008

Q469.Solution of the differential equation sec2 x tan y dx+sec2 y tan x dy= 0 is

Atan x + tan y = C Btan x tan y = C Ctan x – tan y = C Dtan x + sec y = C

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EnglishUP PCS (Pre) 2008

Q470.Given x dy ye dx = such that when x = 0, y = e. The value of y (y>0) when x = 1 will be

Ae B1/e Cee Dnone of the above

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EnglishUP PCS (Pre) 2008

Q471.The integrating factor of the differential equation x2 ydx-(x3 +y3)dy = 0 is

Ax4 B-x4 Cy4 Dy–4

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EnglishUP PCS (Pre) 2008

Q472.The general solution of 2 dy xp + 2px- y = 0,where p =,is dx

Ay2 = 4cx Bx+y2 = c Cxy+(x+y)2 = c D(y-c)2 = 4cx

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EnglishUP PCS (Pre) 2008

Q473.The general solution of ≡ 2 2 2 dy x p +(2x + y)yp + y = 0, p, is dx

A(1-cxy)2 =cy2 B(1+cxy)2 =cy2 C(xy+c)2 =c2 y2 D(xy-c)2 =c2 y2

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EnglishUP PCS (Pre) 2008

Q474.The general solution of the differential equation e dy p = log (px - y), p =, is dx

Ax2 y2 =cep By2 = xep +ec Cy = cx-ec Dy2 = cx2 -e logec

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EnglishUP PCS (Pre) 2009

Q475.If dy (1+ t) -ty = 1 dt and y (0) = –1, then y (1) is equal to

A1 e 2 + B1 e 2 − C−1/2 D1/2

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EnglishUP PCS (Pre) 2009

Q476.2x 4 d 1 If D =, then (e)is equal to dx (D- 2)

A3 2x x e 6 B4 2x x e 16 C4 2x x e 8 D4 2x x e 24

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EnglishUP PCS (Pre) 2009

Q477.General solution of the differential equation 2 d y x + y = sin, 2 dx is y equal to

A2 x sin x 2cos x + c,sin x + c +1 2 B1 2 x sin x c cos x + c, sin x - 2 C1 2 x sin x c cos x + c sin x +1- 2 D1 2 x sin x c cos x + c sin x +1- 2

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EnglishUP PCS (Pre) 2009

Q478.The particular integral of the differential equation 2 x 2 d y dy - 3 + 2y = xe is dx

Ax 1 xe (x 1) 2 + Bx 1 xe (x 2) 2 − + Cx 1 xe (x 2) 2 + Dx 1 xe (x 1) 2 +

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EnglishUP PCS (Pre) 2009

Q479.The order and degree of the differential equation 3 4 2 2 -1 dy x + x y = tan x + 4 dx are respectively

A1, 3 B2, 4 C3, 4 D4, 1

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EnglishUP PCS (Pre) 2009

Q480.An integrating factor for the differential equation dy 1 + y = x is dx x

A1/x Bx Ccx/d) logcx Dlog_c x

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