Math Chapter Wise

EnglishEMRS PGT-2023

Q01.The general solution of the differential equation () 2 2 xdy - ydx = x + y dy is:

A() y x tan x C = + B() x ytan x C = + C() x ytan y C = + D() y x tan y C = +

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EnglishEMRS PGT-2023

Q02.If a curve y = (x) f passes through the point () 1, -1 and satisfies the differential equation () y 1+ xy dx = x dy, then -1 2 f is equal to:

A−4/5 B2/5 C4/5 D−2/5

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EnglishBihar (TRE 1.0) -2023

Q03.The integral surface satisfying the equation ∂ ∂ 2 2 z z y + x = x + y x y and passing through the curve x = 1 – t, y = 1 + t, z = 1 + t2 is

Az = xy + () 2 2 2 1 x y 2 − Bz = xy + () 2 2 2 1 x y 4 − Cz = xy + () 2 2 2 1 x y 8 − DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q04.Let the general integral of the partial differential equation () () () ∂ ∂ 2 z z 2xy -1 + z - 2x = 2 x - yz z y be given by F(u, v) = 0, where F: R2 → → R is a continuously differentiable function. (R is the set of all real numbers and R2 = {(x, y): x, y ∈ R}) Then which of the following is true?

Au = x2 + y2 + z, v = xz + y Bu = x2 + y2 – z, v = xz – y Cu = x2 – y2 + z, v = yz + x DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q05.The partial differential equation () 2 2 2 ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂ 2 2 u u u 1 u u x + x - y - y + - = 0 x y 4 y x x y is

Ahyperbolic along the line x + y = 0 Belliptic along the line x - y = 0 Cparabolic along the line x + y = 0 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q06.Consider the wave equation ∂ ∂ 2 2 u u = 4,0 < x < π,t > 0 t x with u (0, t) = u (π, t) = 0, u(x, 0) = sin x and ∂ u = 0 t at t = 0. Then u π, 2 2 is

A2 B1 C– 1 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q07.The equation (αxy3 + y cos x)dx + (x2 y2 + βsinx) dy = 0 is exact for

Aα = 2, 1 3 β = Bα = 1, β = 3 2 Cα = 1, β = 2 3 DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q08.An integrating factor of x () -2x dy + 3x +1 y = xe dx is

Axe3x B3xex Cxex DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q09.The differential equation representing the family of circles touching y-axis at the origin is

Alinear and of first order Blinear and of second order Cnon-linear and of first order DMore than one of the above ENone of the above

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EnglishBihar (TRE 1.0) -2023

Q10.Let, f, g: [– 1, 1] → → → R, f(x) = x3, g(x) = x2 |x|. Then

Af and g are linearly independent on [– 1, 1] Bf and g are linearly dependent on [–1, 1] Cf(x) g'(x) – f'(x)g(x) is not identically zero on [– 1, 1] DMore than one of the above ENone of the above

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EnglishEMRS TGT-2023

Q11.If a and b are two odd prime numbers such that a > b, then a2 – b2 is:

Aan odd prime number Ban odd number Can even number Da prime number

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EnglishEMRS TGT-2023

Q12.3.13113111311113... is

Aan irrational number Ba whole number Can integer Da rational number

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EnglishKVS PGT 2023

Q13.Solution of the differential equation dy ycot x 4x cosecx dx + =, is:

A2 ysin x 2x c = + B2 ysin x x c = + C2 ysin x x c + = D2 ysin x 2x c + =

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EnglishKVS PGT 2023

Q14.The solution of the differential equation () 2 2 dy 1 x 1 y 0 dx + + + =, is:

A1 1 tan x tan y c − − − = B1 1 tan y tan x c − − ± = C1 1 tan y tan x c − − − = D1 1 tan x tan y c − − + =

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EnglishKVS PGT 2023

Q15.A solution of the differential equation x dy -y dx = 0 represents:

Aa rectangular hyperbola Bparabola whose vertex is at origin. Cstraight line passing through origin. DA circle whose centre is at the origin.

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EnglishKVS PGT 2023

Q16.Which of the following equation is homogeneous differential equation?

A(x2 +xy) dy = (x2 + y) dx By dy y x cos ycos x x dx x = + Cdy y x 1 xsin 0 dx x − + = D2 dy x x 2y xy dx = − +

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EnglishNVS PGT 2022

Q17.Which of the following is a linear differential equation?

A(y + x) y' + y = 1 B3y' + (x + 4) y = x2 + y'' Cy''' = cos (2y) D() 4 y y xy"' cosx e + + =

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EnglishNVS PGT 2022

Q18.The solution of the differential equation (x + y + 1) dy 1 dx = is:

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

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EnglishNVS PGT 2022

Q19.The order and degree of the differential equation y = dy 2 x dy dx + is:

A1, 2 B1, 3 C2, 1 D1, 1

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EnglishKVS PGT 2022

Q20.Solution of the differential equation (x+2y3)dy=y dx, is:

Ay=x3 +c Bx=y2 +c Cx=y3 +cy Dy=x2 +c

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