Math Chapter Wise

EnglishUP PCS (Pre) 2006

Q441.The differential equation dx y y 1,y(0) 1 dy = − = − = − = − = has

Aunique solution Btwo solutions Cinfinite number of solution Dno solution

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EnglishUP PCS (Pre) 2006

Q442.The differential equation: (ay2 + x + x8) dx – (y8 –y+bxy) dy = 0 is exact if:

Aa=1, b=3 Ba=1, b=2 C2a+b=0 Da–b=0

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EnglishUP PCS (Pre) 2006

Q443.The solution of the differential equation (1+y2)dx = (tan–1 y–x)dy is:

A() 1 tan y 1 e x 1 tan y c − − − + − = B() 1 tan y 1 e x 1 tan y c − + − = C() 1 tan y 1 e x 1 tan y c − + + = D() 1 tan y 1 e x 1 tan y c − − − + − =

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EnglishUP PCS (Pre) 2006

Q444.The solution of the differential equation = + dy /dx e x 1, when x=0, y=3 is:

Ay= (x+1)loge(x+1)–x+3 By= loge (x+1)+x–3 Cy2 =(x+1)logex–x+3 Dy= (x+1)log (x+1)–x+3

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EnglishUP PCS (Pre) 2006

Q445.The solution of the differential equation y x y x dy e e dx + − = + = + is:

Ae–y =ex +ex +c Be–y =ex –e–x +c Ce–y =e–x –ex +c DNone of the above

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EnglishUP PCS (Pre) 2006

Q446.y=cx–c2 is the general solution of the differential equation:

A2 dy dy x y 0 dx dx + + = B2 d y 0 dx = Cdy c dx = D2 dy dy x y 0 dx dx − + =

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EnglishUP PCS (Pre) 2006

Q447.The singular solution of the differential equation − = − 2 2 dy dy x y 1, dx dx is:

Ax2 –y2 =1 By2 –x2 =1 Cx2 +y2 =1 DNone of the above

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EnglishUP PCS (Pre) 2006

Q448.A singular solution of the differential equation (())) ((()) 2 2 dy 9p 2 y 4 3 y,p, dx − = − = − = − = − = − = − = − = is:

Ay=2 By=3 Cy=0 DNone of the above

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EnglishUP PCS (Pre) 2006

Q449.The orthogonal trajectory of the curve xy=a2 is:

Ax2 +y2 =c2 Bx+y=c Cx2 –y2 =c2 D(x–y2)=c2

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EnglishUP PCS (Pre) 2006

Q450.The differential equation of the family of curves which are orthogonal to y = x+ce–x is:

A() dy 1 y x dx = − − Bx dy 1 ce dx − = − Cx dx 1 ce dy − = − Ddx y x 1 dy = − −

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EnglishUP PCS (Pre) 2006

Q451.The particular integral of the differential equation () + + = ≅ 2 2x d D 5D 6 y e, D dx is:

A10e2x B20e2x C2x 1 e 10 D2x 1 e 20

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EnglishUP PCS (Pre) 2006

Q452.Solution of the differential equation () + = ≅ 2 2 d D a y cosax, D dx, is

A2 1 2 x y c cosax c sinax sinax 2a = + + B1 2 x y c cosax c sinax cosax a = + + C1 2 x y c cosax c sinax sinax 2a = + + D1 2 2 x y c cosax c sinax cosax a = + +

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EnglishUP PCS (Pre) 2007

Q453.The differential equation of the family of circles 2 2 x y ax b 0 is–

A2/yy 2y 1 0 B2/yy 2y 1 0 C2/yy y 1 0 D2/yy 2y 1 0

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EnglishUP PCS (Pre) 2007

Q454.The order and degree of the differential equation 2 4 4 2 d y dy d y y dx dx dx = + + = + + = + + = + + are respectively–

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

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EnglishUP PCS (Pre) 2007

Q455.The particular integral of the differential equation 2 x (D D 2)y e is–

Ax 1 e 3 Bx/xe Cx 1 xe 3 Dx 1 xe 2

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EnglishUP PCS (Pre) 2007

Q456.The solution of the differential equation 3 dy (x 2y) y dx is–

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

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EnglishUP PCS (Pre) 2007

Q457.The solution of the differential equation 2 x 2 d y dy 2 y xe dx is

A3 x 1 a bx x e 6 B2 x 1 a bx x e 2 C3 x 1 a x e 6 D3 x 1 ax x e 6

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EnglishUP PCS (Pre) 2007

Q458.The general solution of y = px + p3, where dy p dx is–

A2 2/y cx c B3/y c x c C3 3/y cx c D3/y cx c

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EnglishUP PCS (Pre) 2007

Q459.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) 2007

Q460.The integrating factor of the differential equation xdy-(y+xy2) dx = 0 is–

A1/xy B2 2 1 x y C2 1 x D2 1 y

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