Math Chapter Wise

EnglishTGT 2011

Q341.The solution of differential equation tan y sec2 xdx+tan x sec2 ydy=0 is -

Atanx +tany = k Btan x –tan y = k Ctan x k tan y = Dtanx.tany = k

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EnglishTGT 2011

Q342.If equation of x(1–x2)dy+(2x2 y–y–ax3)dx=0 integrating factor(I.F.) pdx e∫, then value of p

A() 2 3 2 2x ax x 1 x − B2x3/–1 C2 3 2x 1 ax − D() 2 2x 1 x 1 x −

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EnglishUP PCS (Pre) 1998

Q343.The differential equation of parabolas having their axes parallel to the y-axis is

A2 d y dy y 0 dx + + = B2 d y y 0 dx + = C3 d y 0 dx = D3 dy d y. 0 dx dx =

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English(GIC) Lecture Exam, 2015

Q344.Equation of the curve passing through (1, 1) and satisfying the differential equation dy 2y = (x > 0, y > 0) dx x is

Ax = 2y By = x2 Cx = y2 Dy = 2x

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English(GIC) Lecture Exam, 2015

Q345.If y = cos(3 cos–1 x) then 3 d y dx is equal to

A3 B6 C12 D24

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English(GIC) Lecture Exam, 2015

Q346.Differential equation 3/2 2 d y dy = 1+ dx order and the sum of degree is equal to -

A3 B–3 C2 D4

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English(GIC) Lecture Exam, 2015

Q347.The solution of the differential equation dy (x + y +1) = 1is dx

Ax = cey +y+2 Bx = cey –y+2 Cx = cey –y–2 Dx = cey +y–2

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EnglishUP TGT-2016 (08-03-2019)

Q348.If y(x) is a solution of the differential equation 3 dy 4xy x dx + = + =, y(0) =0, then ((()) x 0 limy x → is

A0 B–2 C1 DNot existing

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EnglishUP TGT-2016 (08-03-2019)

Q349.The solution of the differential equation (((()))) 3 dy x 2y y dx + = + = is

Ax = y3 –cy2 Bx = y3 +cy Cy = x3 +cx Dy = x3 –cx2

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EnglishUP TGT-2016 (08-03-2019)

Q350.Solution of the differential equation (1+3x)dy– (1–3y)dx = 0, y (1) = 0 is

Ax+y +3xy = 1 Bx–y +3xy = 1 Cx–y –3xy = 1 Dx+y –3xy = 1

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EnglishKVS PGT 23-12-2018

Q351.If 2 y P(x) =, is a polynomial of degree 3, then 2 3 2 d d y 2. y. dx dx equals:

AP"'(x) P'(x)/+ BP"(x).P"'(x) CP(x).P"'(x) DA constant

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EnglishKVS PGT 23-12-2018

Q352.The order and degree respectively of the differential equation of all tangents to the parabola y2 =4ax is:

A2, 2 B3, 1 C1, 2 D4, 1

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EnglishUP PGT-2016 (02-02-2019)

Q353.Let V be a vector space over R consisting of solutions of 2 d y 4y 0. dx − = − = Dimension of V is

A0 B1 C2 D4

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EnglishUP PGT-2016 (02-02-2019)

Q354.What is the general solution of the differential equation (((()))) 2 ydx x 2y dy 0 − + = − + = − + = − + =?

Ax = y2 +cy Bx = 2cy2 Cx = 2y2 +cy Dx = 2y+cy2

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EnglishUP PGT-2016 (02-02-2019)

Q355.Solution of the differential equation 2 2 2 xdx ydy ydx xdy,y(0) 1 y x y + − = + is

A2 2 y x y 2x y + = + B2 2 x x y x y + = + C2 2 y x y x y + = + D2 2 x x y 2x y + = +

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EnglishUP PGT-2016 (02-02-2019)

Q356.The differential equation for the family of curves 2x 2x y Ae Be, − = + = + where A and B are arbitrary constants, is

A2 d y 4y 0 dx + = B2 d y 4y 0 dx − = C2 d y dy 4y 0 dx + − = D2 d y dy 4 y 0 dx + − =

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EnglishUP PGT-2016 (02-02-2019)

Q357.If a and b are arbitrary constants, then the partial differential equation of z =ax+a2 y2 +b is

Aq=2py Bp=2q2 y Cq=2p2 y Dp=xq2

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EnglishUP PGT-2016 (02-02-2019)

Q358.Solution of the differential equation (()))((()) dy y px p 1 p, p dx − − = − − = − − = − − = is

Ac y cx c 1 = + − B2 y x c = + Cy cx 2 = + D2 y cx 3 = + (Where c is an arbitrary constant)

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EnglishUP PCS (Pre) 1998

Q359.For the differential equation (D2 + 1)y = ex sin x the particular integral is:

A() x e 2cos x sin x 5 − − B() x e 2cos x sin x 4 + C() x e 2sin x cos x 4 + D() x e 2sin x cos x 5 +

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EnglishUP PCS (Pre) 1998

Q360.An integrating factor of the equation 3 2 dy xsin2y x cos y dx + = + = is:

A2 x 2 e sec y B−x 2/e sec y C2 x / 2 e D2 x / 2 e−

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