Q.1 Find the rank of matrix [1 2 3 2 / 2 3 5 1 / 1 3 4 5] Q.2 Find the solution of system of equations , 2 x + 3 y + 4 z = 11 , x + 5 y + 7 z = 15, 3 x + 11 y + 13 z = 25 Q.3 Find the rank of the matrix by reducing it to normal form [ 1 2 -1 / 3 -1 2 / 4 1 3] Q.4 Show that the equations 2x+6y=-11,6x+20y-6z=-3,6y-18z=-1 are not consistent. RGPV NOV 2018 Q.5 Find the characteristic roots of matrix A=[6 -2 2 , -2 3 -1,2 -1 3] RGPV NOV 2018 Q.6 Solve the equation x^2p^2+y^2q^2=z^2 RGPV NOV 2018 Q.7 Show that the equation (5x4 – 3x2y2 – 2xy3) dx + (2x3y – 3xy2 – 5y4) dy = 0) is an exact differential equation. Find its solution. RGPV NOV 2018 Q.8 Solve the differential equation dy/dx + 2y tan x = sinx. RGPV NOV 2018 Q. 9 Solve the differential Equation (D^4-3D^2-4)y=5sin2x - e^-2x RGPV NOV 2018 Q. 10 Solve x d^2/dx^2 -(2x-1) dy/dx+(x-1)y=0 Given that y = e^x is an integral included in the complementary function. RGPV NOV 2018 Que 11 : Solve : (1 + x2) dy / dx + 2xy = 2cos x RGPV NOV 18 Q 12 : Solve : x2 p3 + y(1+x2y) p2+y3 p = 0, where p = dy/dx RGPV NOV 18 Q 13 : Solve : d3y / dx3 -3 d2y / dx2 + 3 dy / dx - y = ex + 2 RGPV NOV 18 Q 14 : Solve : x2 d2y / dx2 - 2x dy / dx - 4y = x2 + 2log x RGPV NOV 18 Q 15 : Solve : (1-x2) d2y / dx2 + x dy / dx - y = x (1-x2)3/2 RGPV NOV 18 Q 16 : Solve in series the equation (1+x2) d2y / dx2 + x dy / dx - y = 0 about the point x = 0. RGPV NOV 18 Q 17 : Form a partial differential equation by eliminating arbitrary function from z = f(x2 = y2) RGPV NOV 18 Q 18 : Solve the following differential equation RGPV NOV 18 Q 19 : Solve x2 p2 + y2 q2 = 1, where p=∂z / ∂x and q = ∂z / ∂y RGPV NOV 18 Q 20 : Solve the linear partial differential equation ∂2z / ∂x2+2 ∂2z / ∂x∂y + ∂2z / ∂y2 = e3x+2y RGPV NOV 18