Math Chapter Wise

EnglishPGT 2003

Q281.Find the solution of the equation 2 d x x dt − = − = which satisfies the condition 3 = dx dt when x = 1 and t = 2 when x = –1

A2 − = t x e B2 1 − + = t x e C2 2 − + = t x e DNone of these

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EnglishPGT 2003

Q282.Solve 2 2 12 12, d y dy x x y dx dx + − = + − = + − = + − = satisfying (1) 0, '(1) 0 y y =

A() 4 3 1 1 3 4 7 − = + + y x x B() 4 3 1 1 3 4 7 − = − + + y x x C() 4 3 1 1 3 4 7 − = − − + y x x DNone of these

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EnglishPGT 2003

Q283.Solve ((()) 2 3 5 3 2 5 0 dy x y x y dx + − + + − = + − + + − = + − + + − = + − + + − =

A2 2 3[(1) (1) ] 4(1)(1) − + − + − − = y x x y c B2 2 3[(1) (1) ] − + − + y x c C2 2 3[(1) (1) ] 4(1)(1) + + + + − − = y x x y c DNone of the above

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EnglishPGT 2002

Q284.Solution of the differential equation 2 dy y 2x 3x 4 dx x − = + + − = + + − = + + − = + + is:

Ay= x3 +3x2 +4x logx + cx By=x2 +3x2 +4xlogx+c Cy=x3 +3x2 +4logx+c DNone of these

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EnglishPGT 2002

Q285.Solution of the equation dy 1 cos2y 0 dx 1 cos2x + + = − is

Atan y+cot x= c Btan y –cot x= c Ccot x + tan y = c Dnone of these

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EnglishPGT 2002

Q286.Equation of the curve passing through (1,1) and satisfying the differential equation: (()) dy 2y: x 0,y 0 dx x = > > = > > = > > = > > is given by:

Ax2 =y Bx=y2 Cx = 2y Dy = 2x

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EnglishPGT 2000

Q287.Solve y (a – z) dx+ x (a – z) dy + xydz = 0?

Axy = c(a – z) Bxy = ac Cx = c(a – z) Dy = c(z – a)

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EnglishPGT 2000

Q288.The degree of the differential equation 2 2 d y dy d y xsin dx dx dx + =

A2 B1 C3 DNone of these

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EnglishPGT 2000

Q289.The solution of 2 d y dy (5 2x) 6(5 2x) 8y 0 dx + − + + = + − + + = + − + + = + − + + = is

A2 1 2 y (5 2x) C cosx 2 log(5 2x) C = + + + By = (5+2x)3 C1cosx+sinxc3 Cy = (5+2x)2 C1cosx+c1sinx Dy = (3+5x)2 C1sinx

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EnglishPGT 2000

Q290.The solution of (D2 –5D+6)y=4ex +5 is:

A2x 3x x 1 2 5 y c e c e 2e 6 = + + + B3x 1 2 3 y c e c x c = + + C4x 1 2 3 y c e c x c = + + D3x 1 2 3 y c e 4c x 4c = + +

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EnglishPGT 2000

Q291.The value of M y ∂ and N x ∂ from (x2 –2xy+3y2) dx +(4y3 +6xy-x2) dy = 6 is

A–2x+6y and 6y–2x B8y+7 and 9x+8 C–2x+7y and 9x+8 DNone of these

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EnglishPGT 2000

Q292.The value of dx+xdy = e–y log y dy is:

Ac+xlogx–y Bc+ylogy–y Clogx+y–c Dy–logy+c

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EnglishPGT 2000

Q293.The correct answer dy 2x y 1 dx x 2y 3 − + = + − is:

Axy+3y+4x–3 = c Bxy–x2 +4y+4 = c Cxy+x2 –y2 –3y+3 = c Dxy+y2 –3y–x2 –x= c

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EnglishRajasthan TGT 2016

Q294.General solution of differential equation (((()))) 3 dy x 2y y dx + = + = is

Ax=cy+y2 Bx=cy–y2 Cx=cy+y3 Dx=cy–y3

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EnglishRajasthan TGT 2016

Q295.The solution of differential equation dy xp 2y pxy; p dx + = + = + = + = is

Axy2 =cey Bxy2 =cex Cx2 y=cey Dxy=cey

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EnglishRajasthan TGT 2016

Q296.The general solution of the differential equation ((()) 2 d y dy 3i 1 3iy 0 dx dx + − − = + − − = + − − = + − − = is

Ax 3ix 1 2 y c e c e = + Bx 3ix 1 2 y c e c e − = + Cx 3ix 1 2 y c e c e− = + Dx 3ix 1 2 y c e c e − − = +

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EnglishRajasthan TGT 2016

Q297.If 3 2 2/ 3 2 dy 1 dx d y dx + λ =, then the degree and order of the above differential equation are respectively

A2, 2 B9, 2 C2, 4 D3, 2

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EnglishRajasthan TGT 2015

Q298.Which of the following differential equation is a linear equation of order 3?

A3 2 2 3 2 d y dy y x dx dx + + = B3 2 x 3 2 d y d y x e dx dx + = C3 2 d y d y dy. y x dx dx dx + + = DNone of these

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EnglishRajasthan TGT 2015

Q299.The solution of dy 1 dx x y 1 = + + is

Ay log(x y 2) C 1 = + − + + By 1 log(x y 2) C + = + + + Cy log(x y 2) C + + − = D2y 1 log(x y 2) C + + + + =

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EnglishRajasthan TGT 2015

Q300.Integrating factor of 3 dy x(x 1) (x 2)y x (2x 1) dx − = − + − − = − + − − = − + − − = − + − is

A3 x 1 x − B2 x x 1 − C2 x 1 x − D3 x 2x 1 −

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