Math Chapter Wise

EnglishUPPSC Polytechnic Lecturer 2021(II)

Q141.The Fourier transform of -a|x| e, where a > 0 and ∈ ∞ ∞ x (-,), is –

A2 2 a a s + B2 2 2a a s + C2 2 2a a s − D2 2 a a s −

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q142.The value of ∞ ∫ -3t 0 te sint dt is –

A1/50 B3/50 C7/50 D9/50

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EnglishUPPSC Polytechnic Lecturer 2021(II)

Q143.The integral equation corresponding to differential equation 2 d y + y dx = cosx with the initial condition y(0) = 0, y'(0) = 1 is –

Aφ(x) = (cosx + x) + x 0 (x t) (t)dt − φ ∫ Bφ(x) = (cosx – x) + x 0 (2x t) (t)dt − φ ∫ Cφ(x) = (cosx – x) – x 0 (x t) (t)dt − φ ∫ Dφ(x) = (cosx – x) – x 0 (2x t) (t)dt − φ ∫

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EnglishUP PGT 2021

Q144.If y = –1 when x = 0 then the solution of the differential equation (1+e 2x) dy + (1+y 2) e x dx = 0 is –

Atan –1 y + tan –1 e x = 0 Btan –1 xy + tan –1 e x = 0 Ctan –1 y + tan –1 (xe x) = 0 DNone of the above

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EnglishUP PGT 2021

Q145.The differential equation of y = ae–bx (a and b are parameters) is – y = ae–bx

Ay 2 dy d y dx dx = By 2 d y dy dx = Cy 2 2 2 dy d y dx dx = Dy 2 d y dy dx =

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EnglishUP PGT 2021

Q146.The solution of differential equation 2 dy dy – 7 12 0 dx dx + = is –

A(y – 4x + c) (y – 3x + c) = 0 B(y + x + c) (y – x + c) = 0 C(y + 4x + c) (y + 3x + c) = 0 D(y + 2x + c) (y + 3x + c) = 0

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EnglishUP PGT 2021

Q147.The general solution of the partial differential equation 2 z x y ∂ = + ∂ ∂ is of the form z =

A() () () 1 xy x – y + F x + G y 2 B() () () 1 xy x + y + F x + G y 2 C() () () 1 xy x – y + F x.G y 2 D() () () 1 xy x + y + F x.G y 2

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EnglishUP PGT 2021

Q148.The orthogonal trajectories to the family of straight lines y = k (x – 1), k ∈ R, are given by–

A(x – 1)2 + y2 = c2 B(x – 1)2 + (y – 1)2 = c2 Cky + x – 1 = 0 Dx2 + y2 = c2

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EnglishUP PGT 2021

Q149.Equation of the curve passing through (1, 1) and satisfying the differential equation 2 dy y + = d x x x is -

Axy = x4 + 3 B4xy + x4 = 3 Cyex = x4 + 3 D4xy = x4 + 3

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EnglishUP PGT 2021

Q150.The order and degree of the differential equation 3/2 2 d y dy K = 1+ dx are

AOrder 2 degree 3 BOrder 2 degree 2 COrder 3 degree 2 DNone of the above

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EnglishUP PGT 2021

Q151.The solution of PDE u u y 0 y ∂ ∂ + = ∂ ∂ x of the form u =

Af(x + y) Bf(x – y) Cf y x Df(x y)

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EnglishUP PGT 2021

Q152.The solution of the partial differential equation () () ∂ ∂ z z mz – ny + n – z = y – m y x l l x x.

Af(x2 + xz, y2 + yz) = 0 Bf(z2 + xy, y2 + xz) = 0 Cf(x2 + y2, lx + my) = 0 Df(x2 + y2 + z2, lx + my + nz) = 0

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EnglishUP PGT 2021

Q153.General solution of x2 (y – px) = p2 y where dy p = dx is –

Ay2 – c2 = 2cx3 Bx2 (y – cx) = c2 y Cxy2 = cx4 + c2 Dy2 = cx2 + c2

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EnglishUP PGT 2021

Q154.Solution of the differential equation () e dy log = 2x – y, y 0 = 0 dx

Aey = 2e2x + 1 Bey = 2e2x + 1 Cey = 2e2x + 3 D2ey = e2x + 1

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EnglishUPPSC GIC 2021

Q155.An integrating factor of the differential equation dy y tan x 2sin xis dx = − −

Asec x Bcos x Csin x Dtan x

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EnglishUPPSC GIC 2021

Q156.The solution of the differential equation 3 dy y x dx x − = is-

A3y = x (x3 + c) By = x (x3 + c) Cy2 = x (x3 + c) Dy = x2 (x3 + c)

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EnglishUPPSC GIC 2021

Q157.The order and degree of the differential equation- () () P q m m 1 m m 1 d y d y f x, y x, y....... 0 dx dx − + φ + = are respectively-

Ap and m Bm and p Cp and q Dq and p

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EnglishUPPSC GIC 2021 Rajasthan TGT 2015 UP PGT 2009 UP PCS (Pre) 1995

Q158.The general solution of differential equation x y 2 y dy e x e dx − − = + is

A3 y x x e e c 3 = + + B3 y x x e e 3 = + C3 x 3 y x e c = + + D3 x y y e e c 3 = + +

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EnglishUP TGT 2021

Q159.The order of the differential equation 3 2 2 dy dy y – x = a y + dx dx is

A3 B1 C2 D4

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EnglishUP TGT 2021

Q160.Solution of the differential equation dy log = ax + by dx is

Abeax + ae–by + C = 0 Bax –by e e – C 0 a b + = Ceax + e–by + C = 0 Deax + by = C(ax + by)

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