GATE IN 2011 Question Paper (13-Feb-2011) (Shift-2)

The series ${\sum }_{m=0}^{\infty }\frac{1}{4^m}(x-1{)}^{2m}$ converges for

Consider the differential equation $\ddot{y}+2\dot{y}+y=0$ with boundary conditions $y(0)=1,y(1)=0$. The value of $y(2)$ is

The box $1$ contains chips numbered $3,6,9,12$ and $15$. The box $2$ contains chips numbered $6,11$, $16,21$ and $26$. Two chips, one from each box, are drawn at random. The numbers written on these chips are multiplied. The probability for the product to be an even number is

The extremum (minimum or maximum) point of a function $f(x)$ is to be determined by solving $\frac{df(x)}{dx}=0$ using the Newton-Raphson method. Let $f(x)=x^3-6x$ and $x_0=1$ be the initial guess of $x$. The value of $x$ after two iterations ($x_2$) is

The unit-step response of a negative unity feedback system with the open-loop transfer function $G(s)=\frac{6}{s+5}$ is