Math Chapter Wise

EnglishDSSSB PGT 2021

Q41.Which of the following is not an integrating factor to the equation xdy – ydx = 0?

A1/xy B2 1 x C1/x D2 2 1 x y +

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EnglishDSSSB PGT 2021

Q42.The solution y = 0 of the equation 9yp2 +4 = 0, dy p = dx is -

ANodal-locus BSingular solution CTac-locus DCuspidal - locus

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EnglishDSSSB PGT 2021

Q43.The p- discriminate does not contain one of the following:

ANodal-locus BEnvelop CTac-locus DCuspidal - locus

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EnglishDSSSB PGT 2021

Q44.The integrating factor of the differential equation x dy dx –y = x cos x is

A1 x e B1/x Cx D2 1 – x e

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EnglishDSSSB PGT 2021

Q45.Two linearly independent solutions of the differential equation y" – 2y' + y = 0 are y1 = ex and y2 = xex then a particular solution of y" – 2y' + y = ex sin x is:

Ay2 (x cos x – sin x) – y1 cos x By1(x cos x + sin x) + y2 sin x Cy1 (x cos x + sin x) – y2 (cos x – x sin x) Dy1(x cos x – sin x) – y2 cos x

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EnglishDSSSB PGT 2021

Q46.Let y = x, y = e–x be two linearly independent solution of the corresponding homogeneous equation of () 2 d y dy 1+ x + x y = (1+ x). dx dx − − If yp = u(x)x + v(x) e–x be the particular solution of the non-homogenous equation, then:

Au(x) = x2,v(x) = ex (1 – x2) Bu(x) = x, v(x) = ex (1 – x) Cu(x) = x, v(x) = ex (1 +x) Du(x) = –x3, v(x) = ex (1 + 2x)

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EnglishDSSSB PGT 2021

Q47.The general solution of 2 d y dy = 1+ dx dx is (a, b are arbitrary constants)

Ay = cos (x + a) + bx By = cos (x + a) + b Cy = tan (x + a) + b Dy = sin (x + a) + bx

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EnglishDSSSB PGT 2021

Q48.For the differential equation (2x2 + 3x) y" + (6x + 3) y' + 2y = (x + 1) ex, which of the following is correct?

AThe equation is exact and its solution is y(2x + 3) = ex + c1 log x + c2 BThe equation is not exact and its solution is y2 (2x – 3) = y ex + c1 log x + c2 CThe equation is exact and its solution is y2 (2x – 3) = y ex + c1 log x + c2 DThe equation is not exact and its solution is y (2x + 3) = ex + c1 log x + c2

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EnglishDSSSB PGT 2021

Q49.A solution curve of the differential equation () 2 2 dy x + xy + 4x + 2y + 4 y = 0,x > 0, dx − − passes through the point (1, 3). Then the solution curve–

AIntersects y = x +2 exactly at two points BIntersects y = (x + 2)2 exactly at four points CIntersects y = x + 2 exactly at one point DIntersects y = (x + 2)2 exactly at six points

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EnglishDSSSB PGT 2021

Q50.If xh yk be the integration factor of (y3 – 2yx2) dx + (2xy2 – x3) dy = 0, then the value of (h, k) is:

A(–2, 3) B(2, –1) C(1, 1) D1, –2)

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EnglishDSSSB PGT 2021

Q51.The general solution of 3 2 d y dy dy = + dx dx dx is (a, b are arbitrary constants).

Alog cos (y + a) = x + b Blog sin (x + a) = y + b Clog sin (y + a) = x + b Dlog cos (x + a) = y + b

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EnglishDSSSB PGT 2021

Q52.The orthogonal trajectories of the system of coaxial circles x2 + y2 + 2λx + c = 0 is (taking µ as parameter)

Ax2 + y2 – 2µxy + c = 0 Bx2 + y2 + 2µy – c = 0 Cx2 + y2 +2µy + cx = 0 Dx2 + y2 – 2µx + cy = 0

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EnglishDSSSB PGT 2021

Q53.The complete primitive of p2 + px + py + xy = 0, where p =, dy dx is

A(2y + x2 – c) (x + log y – c) = 0 B(2y – x2 – c) (x – y log x – c) = 0 C(y + x2 – cxy) (x3 + 2 logy – c) = 0 D(2y2 – x2 – c) (x – y logy – c) = 0

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EnglishDSSSB PGT 2021

Q54.The three linearly independent solutions of 3 d y dy x 6x +12y = 0. dx dx − − of the form y = xr is –

Ax, x2, x3 Bx2, x3, x–2 C1, x, x2 D1, x2, x2

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EnglishDSE TGT 2019

Q55.If u = log v and v(x, y) is a homogenous function of degree n, then xux + yuy =

An(x+y) Bn Cn2 Dxy

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EnglishDSE TGT 2019

Q56.If y = sin(sin x), then y'' + (tan x) y' + y cos2 x =

A0 B1 Ctan x Dcos2 x

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EnglishDSE TGT 2019

Q57.If for 'A' and 'B' are two parameters, y = A cos 3x + B sin 3x, then

Ax dy/dx + y = 0 Bd2 y/dx2 + 9y = 0 Cd2 y/dx2 + x2 y= 0 D(x2 – y2) dy/dx - 2 xy = 0

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EnglishJSSC PGT 2018

Q58.The orthogonal trajectories on the sphere x2 + y2 + z2 + 1 upon its intersection with the family of planes z = k, –1 ≤ k ≤ 1 are given by:

A2 2 2 y c x and x y – z 1 = + = B2 2 2 y c z and x y z 1 = + + = C2 2 2 z c x andx y – z 1 = + = D2 2 2 y c x and x y z 1 = + + =

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EnglishJSSC PGT 2018

Q59.Find the rectangular coordinate of the point with cylindrical coordinate (2, 2π/3, 1).

A() –1, 3,1 B() 2, 3,–2 C() 1, 3,0 D() 1, 3,–1

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EnglishJSSC PGT 2018

Q60.The integrating factor for the differential equation y (xy + 2x2 y2) dx + x (xy – x2 y2) dy = 0 is:

A1/xy B2 2 1 x y C3 3 1 3x y D3 1 xy

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