1
GATE EE 2011
+2
-0.6
Solution, the variable $${x_1}$$ and $${x_2}$$ for the following equations is to be obtained by employing the Newton $$-$$ Raphson iteration method
equation (i) $$10\,{x_2}\,\sin \,{x_1} - 0.8 = 0$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ $$10\,x_2^2\, - 10\,{x_2}\cos \,{x_1} - 0.6 = 0$$
Assuming the initial values $${x_1} = 0.0$$ and $${x_2} = 1.0$$ the Jacobian matrix is
A
$$\left[ {\matrix{ {10} & { - 0.8} \cr 0 & { - 0.6} \cr } } \right]$$
B
$$\left[ {\matrix{ {10} & 0 \cr 0 & {10} \cr } } \right]$$
C
$$\left[ {\matrix{ 0 & { - 0.8} \cr {10} & { - 0.6} \cr } } \right]$$
D
$$\left[ {\matrix{ {10} & 0 \cr {10} & { - 10} \cr } } \right]$$
2
GATE EE 2008
+2
-0.6
A differential equation $${{dx} \over {dt}} = {e^{ - 2t}}\,\,u\left( t \right)\,\,$$ has to be solved using trapezoidal rule of integration with a step size $$h=0.01$$ sec. Function $$u(t)$$ indicates a unit step function. If $$x(0)=0$$ then the value of $$x$$ at $$t=0.01$$ sec will be given by
A
$$0.00099$$
B
$$0.00495$$
C
$$0.0099$$
D
$$0.0198$$
3
GATE EE 1998
+2
-0.6
The value of $$\,\,\,\int\limits_1^2 {{1 \over x}\,\,\,dx\,\,\,\,}$$ computed using simpson's rule with a step size of $$h=0.25$$ is
A
$$0.69430$$
B
$$0.69385$$
C
$$0.69325$$
D
$$0.69415$$
EXAM MAP
Medical
NEET