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B.Sc.I e Test 2018-19
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1.
The necessary and sufficient conditions for Mdx + Ndy = 0 to be exact is …………
1 point
∂M/∂x=∂N/∂Y
(∂^2 M)/(∂x^2 )+ (∂^2 N)/(∂y^2 )
∂M/∂y= ∂N/∂x
(∂^2 M)/∂x∂y
Clear selection
The integrating factor of the linear differential equation dy/dx+Py=Qis…..
1 point
e^(∫p dx)
e^(∫f(x) dx)
e^x
e^y
Clear selection
If((∂M/∂y-∂N/∂x))/N is a function of x, say f(x) then………….. is an integrating factor .
1 point
e^(∫f(y)dy)
e^(∫f(x)dx)
e^x
e^y
Clear selection
The degree of differential equation ((d^3 y)/ (dx^3 )) + (d^2 y)/(dx^2 )+ 5y = 0……
1 point
3
2
5
1
Clear selection
If (∂N/∂x-∂M/∂y)/M is a function of y, say f(y) then ………. is an integrating factor.
1 point
e ^∫f (y)dy
e ^∫f(x)dx
e^x
e^y
Clear selection
If the equation Mdx + Ndy = 0 is homogeneous equation in xand y, then I.F. = ………..
1 point
1 /Mx+Ny , provided Mx + Ny ≠ 0
e^(∫f(x)dx)
e^(∫f(y)dy)
1/(Mx-Ny), provided Mx – Ny ≠0
Clear selection
If y = px + exp (p) then its solution is ……………
1 point
Y = cx + exp(p)
y = cx + exp(c)
y = cx + p^c
y = cx + c^e
Clear selection
The differential equation y2 = pxy + f (py/x) can be reduced to clairaut’s form by standard substitution ………..
1 point
X= u and y = v
x2 = u and y2 = v
x – u2 and y = v
x = u and y = v2
Clear selection
The solution of p^2 -3p -10 = 0 is ………….
1 point
(y+ 2x –c) ( y +5x –c) =0
(y + 2x – c) (5y +x + c ) = 0
(y-2x – c) (y +5x – c) = 0
(y + 2x – c) (y – 5x – c) = 0
Clear selection
The value of 1/D^2+1 cosx is ----
1 point
xcosx
xsinx
( x/2) Sin x
-xcosx
Clear selection
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