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GATE 2019: Engineering Mathematics Test 3
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Question 1
Which of the following methods do the Newton-Raphson method of finding roots of nonlinear equations falls under the category?
Question 2
The differential equation 
is discretised using Euler’s numerical integration method with a time step ΔT > 0. What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation?
is discretised using Euler’s numerical integration method with a time step ΔT > 0. What is the maximum permissible value of ΔT to ensure stability of the solution of the corresponding discrete time equation? Question 3
Which of the following is the suitable response of the system s(n+2) – 3s(n+1)+2s(n) = δ(n), when all the initial conditions are zero?
Question 4
Determine the displacement function y(t) of the weight if 16lb weight is attached to a spring constant equal to 2 lb/ft. Neglect damping. The weight is released from rest at 3 ft below the equilibrium position. At t=2π sec, it is struck with a hammer, providing an impulse of 4lb-sec?
Question 5
A differential equation 
has to be solved using trapezoidal rule of integration with a step size h = 0.01 s. Function u (t) indicates a unit step function. If x (0–) = 0, then value of x at t = 0.01s will be given by:
has to be solved using trapezoidal rule of integration with a step size h = 0.01 s. Function u (t) indicates a unit step function. If x (0–) = 0, then value of x at t = 0.01s will be given by: Question 6
Only one of the real roots of f(x) =x6 -x -1 lies in the interval 1≤x≤2 and bisection method is used to find its value. For achieving an accuracy of 0.001, the required minimum number of iterations is _________.
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Jun 25ESE & GATE EE
