Tiêu đề K-2517 (Physical Science).pdf ✅

Paper III 2 K-2517 Total Number of Pages : 16 PHYSICAL SCIENCE PAPER – III Note : This paper contains seventy-five (75) objective type questions. Each question carries two (2) marks. All questions are compulsory. 1. A solution of the differential equation 2 2 dy y dx x = − is (A) xy = constant (B) y/x = constant (C) 1 1 y x − = constant (D) 1 1 y x + = constant 2. The general solution of the equation 2 2 2 22 y 1y x ct ∂ ∂ = ∂ ∂ is (A) y = F(x + ct) + ( ) G t x c + (B) y = F(x + ct) + G(x – ct) (C) y = F(xc + t) + G(xc – t) (D) y = ( ) ( ) x x F tG t c c ++ + Where F and G are arbitrary differentiable functions. 3. The general solution of the Laplace equation in cylindrical co-ordinates 2 2 22 2 1 u 1u u r 0 rr r r z ∂∂ ∂ ∂ ⎛ ⎞ + += ⎜ ⎟ ∂ ∂ ∂θ ∂ ⎝ ⎠ is (A) = ∑[ θ + θ m m m kz u e (A cosm B sinm ) + e–kz × (Cm cosm θ + D sinm )] m θ J m(kr) (B) = ∑[ θ + θ m m m kz u e (A coshm B sinhm ) + e–kz × (Cm coshm θ + D sinhm )] m θ J m(kr) (C) { m m u A coshm (coskz sinkz) = θ+ ∑ + B m sinhm θ (coskz – sinkz)} J m(kr) (D) = ∑{ + − θ m im u Am coskz e B m sinkz } +imθ e J m(kr) Where A m, Bm, Cm, Dm and k are constants and J m(kr) is Bessel function of order m.