Math Chapter Wise

EnglishPGT 2009 Rajasthan TGT 2015

Q301.The solution of x y 2 y dy e x e dx − − = + = + is

A3 y x x e e C 3 = + + B3 y x x e e C 3 − = + + C3 y x x e e C 3 − = + + D3 y x x e e C 3 − − = + +

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EnglishRajasthan TGT 2015

Q302.The solution of dy x y dx x y + = − is

A1 2 2 y tan log(x x) C x − = + + B2 2 y 2tan log(x y) C x = + + C1 2 2 y 2tan log(x y) C x − = + + D2 2 y tan 2log(x y) C x = + +

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EnglishRajasthan TGT 2015

Q303.The general solution of the differential equation(x+a)p2 +(x-y)p–y=0 (where dy p dx =) is

A2 ac y cx c 1 − = + B2 c a y cx c 1 + = + C2 2 ac y c x c 1 + = + D2 2 a c y cx 0 c 1 + + = +

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EnglishRajasthan TGT 2015

Q304.The solution of the differential equation 2 d y dy x 3x y 0 dx + + = + + = + + = + + = is

A1 2 (c c x) y x + = B1 2 (c c log x) y x + = C1 2 (c c x) y log x + = D1 2 y x(c c log x) = +

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EnglishRajasthan TGT 2013

Q305.The solution of the differential equation () () 4 2 2 3 2 y e dy y 2xsec y + y =log x e dx is-

Asec3 y2 = (loge x)2 + c, where c is arbitrary constant Bsec3 y2 = (loge x)2 + c, where c is arbitrary constant Ctan y2 =(loge x)2 + c, where c is arbitrary constant DNone of these

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EnglishRajasthan TGT 2013

Q306.What is the degree and order of the differential equation − 2 3 2 3 3 2 d y d y dy 3 +5 +4y=1 dx dx dx

A3, 3 B2 3, 3 C3, 2 D2,3

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EnglishRajasthan TGT 2013

Q307.If the solution of (4x + 6y + 5)dy – (3y + 2x + 4) dx = 0 be ()− 9 7x 2x + 3y logz= +c 14 2, then z equals to-

A14x + 21y B14x + 21y + 12 C14x+21y+22 D2x + 3y

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EnglishRajasthan TGT 2013

Q308.The solution of differential equation sin px cos y = cos px sin y + p, dy p= dx is-

Axy = sin–1 c By = x sin–1 c Cx = cy + sin–1 c Dy = cx – sin–1 c

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EnglishRajasthan TGT 2013

Q309.The particular integral of the differential equation () 2 x d D - 5D + 6 y = 5, D=, dx is-

A5x/loge 5 Bx e 5 2log 5 Cx e 5 3log 5 Dx e e 2 3 5 5 5 log.log e e

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EnglishRajasthan TGT 2013

Q310.The complementary function of the differential equation − 2 3 2 2 d y dy x 2x + 2xy=1 dx dx is

Ac1ex/+ c2e2x Bc1x+c2x2 Cc1e–x/+c2e–2x D1 2 2 c c x x +

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EnglishRajasthan TGT 2013

Q311.If one of the complementary function of the differential equation () 2 2 2 3 x 2 d y dy x - x + 2x +(x + 2)y = x e dx dx is c1x, then the second one is-

Ac2ex Bc2e–x Cc2xex Dc2xe–x

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EnglishRajasthan TGT 2013

Q312.Solution of partial differential equation 2 2 2 2 z z x + y =z, x y ∂ ∂ is

Az = c xcos α ysin α Bz = ax + 2 1 a − y + c Cloge z = a loge x + 2 1 a − y + c Dz = a log () x c y +

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EnglishRajasthan TGT 2013

Q313.For the partial differential equation, p2 + q2 – 2px –2qy + 2xy = 0 Charpit's auxiliary equations are-

Adp dq dx dy p y q x p x q y = − + − + − − Bdp dq dx dy p y q x x p q y = − − − − C() () dp dq dx dy p y q x x p y q = − + − + − − Ddp dq dx dy p y q x x p y q = − + − + − −

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EnglishRajasthan TGT 2011

Q314.If y x y x e − − =, then dy dx is equal to-

A2 e 1/(1 log x) + Be e log x /(1 log x) + C2 e e log x /(1 log x) + DNone of these

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EnglishRajasthan TGT 2011

Q315.If x3 +y3 =3xy, then dy dx is equal to

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

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EnglishRajasthan TGT 2011

Q316.if 2 2 y 2x = + = + 3x+4, then 2 3 2 d y y dx is equal to

AA constant BA function of x CA function of y DA function of both x,y

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EnglishRajasthan TGT 2011

Q317.The order of the differential equation of all circles of radius 5 is-

A2 B4 C3 D1

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EnglishRajasthan TGT 2011

Q318.The differential equation representing family of curves y acos t bsin t, = ω + ω = ω + ω = ω + ω = ω + ω where a and b are perimeters is/

A2 y y 0 + = B2 y y 0 ′′− ω = C2 y y 0 ′′+ ω = Dy y 0 ′′− =

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EnglishRajasthan TGT 2011

Q319.Solution of differential equation 3 dy x y x dx − = − = is-

A3 y x 2cx − = B3 2y x 2cx − = C2 2y x 2cx + = D2 y x 2cx + =

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EnglishRajasthan TGT 2011

Q320.Solution of differential equation (x+y)dy=ydx is

Ax / y y ce = By/ x y ce = Cy/ x x ce = Dx / y x ce =

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