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GATE 2019: Engineering Mathematics Test 5
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Question 1
If 
,where 0, then is 
is
,where 0, then is is Question 2
If the characteristic equation of the differential equation
has two equal roots, then the values of a are
has two equal roots, then the values of a are
Question 3
The ordinary differential equation
Is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is______
Is to be solved using the forward Euler method. The largest time step that can be used to solve the equation without making the numerical solution unstable is______
Question 4
If u = sin (x2 + y2) where a2x2 + b2y2 = c2 & x and y both are variablethen value of (du/dx) will be?
Question 5
The circuit shown in Figure has initial current iL(0–) = 1A through the inductor and an initial voltage Vc (0–) = –1V across the capacitor. For input v(t) = u(t), the Laplace transform of the current i(t) for t ≥ 0 is
Question 6
A function n(x) satisfied the differential equation 
where L is a constant. The boundary conditions are : n(0) = K and n(∞) -0. The solution to this equation is
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