Math Chapter Wise

EnglishKVS PGT 2022

Q21.Solution of the differential equation x y dy e dx + = is:

Ae−x +ey =c Bex +e−y =c Cex +ey =c De−x +e−y =c

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EnglishKVS PGT 2022

Q22.Which of the following is a homogeneous differential equation?

A(4x+6y+5)dy−(2y+3x+3)dx=0 Bxy dx−(x3 +y3)dy=0 C(x2 +2y3)dx+2xy dy=0 Dy2 dx+(x2 −xy+y2)dy=0

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EnglishKVS PGT 2022

Q23.The differential equation for y=a cos (αx)+b sin (αy), where a and b are arbitrary constants is:

A2 d y a y 0 dx + = B2 d y a y 0 dx − = C2 d y ay 0 dx − = D2 d y ay 0 dx + =

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EnglishRPSC PGT 2022

Q24.Geometrical meaning of Lagrange's linear partial differential equation Pq + Qp = R is -

ANormal at point (x,y,z) of any surface f(x,y,z) = 0 is perpendicular to a line whose direction ratio's are P,Q,R BNormal at point (x,y,z,) of any surface f(x,y, z) =0 is parallel to line whose direction ratio's are P,Q,R CNormal at point (x,y,z) of any surface f(x,y,z) = 0 make an angle of 45° to a line whose direction ratio's are P,Q,R DNormal at any point (x,y,z) of any surface f(x,y,z) = 0 is perpendicular to a line whose direction ratio's are P,q,–1

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EnglishRPSC PGT 2022

Q25.If y = 1 msin x e −, then 3 d y 3 dx x=0 will be equal to-

Am (m+1) Bm2 C(m2/+1)m D0

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EnglishRPSC PGT 2022

Q26.If D = d dx, then value of 1 -1 (x) (xD -1) is -

A−log x/x B−1/2x Clog x Dlog x 2 x −

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EnglishRPSC PGT 2022

Q27.If Z = 1/2 x + y 1/3 1/4 x + y, then ∂ z x (8,0) is equal to -

A2/3 B∞ C1/3 D5/3

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EnglishRPSC PGT 2022

Q28.If y = y(x), then which of the following differential equation is linear?

Ady 2 1/2 x y y dx + = Bdy m sin x x y dx − = Cdy (1 y) p(x)y Q(x) dx + + = Ddy y x y dx + = +

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EnglishRPSC PGT 2022

Q29.If Pn(x) is Legendre polynomial, then P′ ′ ′n(1) is -

A2 2n 1 + B2n 1 2 + Cn(n 1) 2 + D2 n(n 1) +

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EnglishRPSC PGT 2022

Q30.For the differential equation x dy - y dx = 0 which of the following cannot be an integrating factor?

A1 2 x B1 2 y C1/xy D1 x y +

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EnglishRPSC PGT 2022

Q31.The general solution of the partial differential equation z – px – qy = c 2 2 (1 + p + q) is-

Az = ax – by + c 2 2 (1 a b) − − Bz = ax + by + c 2 2 (1 a b) + + Cz = ax – by – c 2 2 (1 a b) + + Dz = ax + by + c 10 −π

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EnglishRPSC PGT 2022

Q32.if Jn(x) is Bessel’s function, then d 2 [(J (x)) ] n dx is -

Ax 2 2 [(J (x)) (J (x)) ] n 1 n 1 2n + − + Bx 2 2 [(J (x)) (J (x)) ] n 1 n 1 2n − − + C2Jn(x)[Jn–1(x) – Jn+1(x)] D2Jn(x)[Jn+1(x) – Jn–1(x)]

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EnglishRPSC PGT 2022

Q33.Solution of equations dx dy = -ωy; = ωx,is - dt dt

Ax = c1 cos ωt + c2 sin ωt y = c1 sin ωt – c2 cos ωt Bx = c1 cos ωt + c2 sin ωt y = c1 sin ωt + c2 cos ωt Cx = c1 sin ωt – c2 cos ωt y = c1 sin ωt + c2 cos ωt Dx = c1 cos ωt + c2 sin ωt y = c1 cos ωt – c2 sin ωt

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EnglishRPSC PGT 2022

Q34.The solution of differential equation sin px cos y = cos px sin y + p is:

Ay = cx2 – cos–1 P By = cx–sin–1 c Cy = cx–cos–1 c Dy = cx2 – sin–1 P

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EnglishDSSSB PGT 2021

Q35.A solution-curve of the equation xy' = 2y, passing through (1, 2) also passes through

A(24, 5) B(0, 0) C(4, 12) D(2, 3)

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EnglishDSSSB PGT 2021

Q36.The singular solution p = log(px–y) is

Ay = log x By = x logx Cy = x(log – 1) Dy = logx – 1

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EnglishDSSSB PGT 2021

Q37.The singular solution of (xp – y)2 = p2 – 1, where p = dy dx is -

Ax2 + y2 = 2 Bx2 – y2 = 1 Cx2 – y2 = 2 Dx2 + y2 = 1

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EnglishDSSSB PGT 2021

Q38.Which one of the following is a solution of the differential equation 2 dy dy + x – y = 0 dx dx

Ax2 + 4y = 0 By2 – 4x = 0 Cy = x + 1 Dy = x –1

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EnglishDSSSB PGT 2021

Q39.The differential equation ydx – 2xdy = 0, represents

AA family of parabolas BA family of catenaries CA family of straight lines DA family of circles

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EnglishDSSSB PGT 2021

Q40.If the equation Mdx + Ndy = 0 has one and only one solution, then the number of integrating- factor is

ATwo BOne CInfinite DFinite

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