Math Chapter Wise

EnglishUP PCS (Pre) 2000

Q401.The general solution of the differential equation (1 + x)y dx + (1 – y)x dy = 0 is

Axy = c ex–y Bx + y = c exy Cxy = c ey–x Dx – y = c exy

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EnglishUP PCS (Pre) 2000

Q402.If 2y dy e dx − =, y = 0 when x = 5, then the value of x for y = 3 is:

A6 e 9 2 + Be5 C6 e log De6/+ 1

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EnglishUP PCS (Pre) 2000

Q403.An integrating factor of the differential equation (((()))) 2 dy 1 x 2xy cosx dx + + = + + = + + = + + = is:

A(1 + x2/) B2 1 1 x + Clog (1 + x2/) D–log (1 + x2/)

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EnglishUP PCS (Pre) 2001

Q404.If y=eax sin bx then 2 d y dx at x=0 is:

Azero Bab C2ab Da2/+b2

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EnglishUP PCS (Pre) 2001

Q405.The solution of dy dy dy y - x -1 = dx dx dx is:

A(yc–x)(c–1)=c B(y–cx)(c–1)=c C(y+cx)(c+1)=c D(yc+x)(c+1)=c

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EnglishUP PCS (Pre) 2001

Q406.The solution of (x–1) dy = y dx, y (0) = –5 is:

Ay = 5 (x–1) By = –5 (x–1) Cy = 5 (x+1) Dy = –5 (x+1)

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EnglishUP PCS (Pre) 2001

Q407.2 x y = 8 is a particular solution of the differential equation:

A2 d y dy 2 + x - y = 0 dx B2 dy dy 2 + x + y = 0 dx dx C2 dy dy 2 - x + y = 0 dx dx D2 dy dy 2 + x - y = 0 dx dx

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EnglishUP PCS (Pre) 2001

Q408.The differential equation xdx–ydy = 0 represents:

AA family of circles BA family of ellipsces CA family of rectangular hyperbolas DA family of cycloids

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EnglishUP PCS (Pre) 2001

Q409.The solutions of differential equation 2 dy dy - 5 + 6 = 0 dx dx are:

Ay = x + c, y = 6x + c By = –3x + c, y = –2x + c Cy = x + c, y = 5x + c Dy = 2x + c, y = 3x + c where c is an arbitrary constant.

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EnglishUP PCS (Pre) 2001

Q410.The solution of the differential equation 2 d y dy - 3 -4y = 0 dx is:

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

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EnglishUP PCS (Pre) 2001

Q411.If dy p = dx then the singular solution of 3 2 2 3 x p + x yp +a = 0 is:

Ax = 0 By = 0 Cxy2 =4a3 Dx2 y2 = 4a3

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EnglishUP PCS (Pre) 2001

Q412.The solution of the differential equation: (x+2y) dy–(2x–y)dx = 0 is:

Ay2 +x2 –2xy = c Bxy+ y2 +x2 = c Cx2 + 4xy + y2 = c Dxy+ y2 –x2 = c where c is an arbitrary constant.

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EnglishUP PCS (Pre) 2001

Q413.The solution of differential equation (D3 +3D2 +3D+1) y= e2x where d D = dx is:

AFormula option A (see source) B2 2x 1 2 3 1 y c c x c x e 27 + = + + C2 2x 1 2 3 x c c x c x e 27 + y = + + D2 2 2x 1 2 3 x y c c x c x e 27 + = + +

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EnglishUP PCS (Pre) 2002

Q414.The particular integral of the differential equation 2 -3x 2 d y dy + 4 + 3y = e dx is:

A3x 1 e 2 − B3x/xe− C3x 1 xe 6 − D3x 1 xe 2 −

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EnglishUP PCS (Pre) 2002

Q415.The singular solution of the differential equation 2 2 dy (xp - y) = p -1, p is: dx

Ax2 +y2 =1 Bx2 –y2 =1 Cx2 +y2 +1= 0 Dy2 –x2 =1

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EnglishUP PCS (Pre) 2002

Q416.The degree of the differential equation 2 1 + 2 d y dy dy + 2x + = 0 is: dx dx dx

A1 B2 C3 D4

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EnglishUP PCS (Pre) 2002

Q417.The integrating factor of the differential equation (x2 +y2 +1)dx-2xy dy = 0 is:

A−2/x B1/x C2 1 x D2/x

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EnglishUP PCS (Pre) 2003

Q418.The degree of the differential equation– 3/ 2 2 2 2 dy d y 1 dx dx is–

A1 B2 C3 D6

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EnglishUP PCS (Pre) 2003

Q419.Which of the following differential equations is linear:

An/y yy y 0 Bn/y sin y 0 Cn/y y ysin x 0 Dn/y y y 0

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EnglishUP PCS (Pre) 2003

Q420.The number of integrating factors of the non- exact differential equation 2 xy y x is–

Anone Bone Ctwo Dinfinite

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