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MATHEMATICS-2
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 + x
2
) dy / dx + 2xy = 2cos x
RGPV NOV 18
Q 12 : Solve : x
2
p
3
+ y(1+x
2
y) p
2
+y
3
p = 0, where p = dy/dx
RGPV NOV 18
Q 13 : Solve : d
3
y / dx
3
-3 d
2
y / dx
2
+ 3 dy / dx - y = e
x
+ 2
RGPV NOV 18
Q 14 : Solve : x
2
d
2
y / dx
2
- 2x dy / dx - 4y = x
2
+ 2log x
RGPV NOV 18
Q 15 : Solve : (1-x
2
) d
2
y / dx
2
+ x dy / dx - y = x (1-x
2
)
3/2
RGPV NOV 18
Q 16 : Solve in series the equation (1+x
2
) d
2
y / dx
2
+ 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(x
2
= y
2
)
RGPV NOV 18
Q 18 : Solve the following differential equation
RGPV NOV 18
Q 19 : Solve x
2
p
2
+ y
2
q
2
= 1, where p=∂z / ∂x and q = ∂z / ∂y
RGPV NOV 18
Q 20 : Solve the linear partial differential equation ∂
2
z / ∂x
2
+2 ∂
2
z / ∂x∂y + ∂
2
z / ∂y
2
= e
3x+2y
RGPV NOV 18
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