Engineering Mathematics GATE-2003
Q 1: A box contains 6 red balls and 4 green balls; one ball is randomly picked and then a second ball is picked without replacement of the first ball. The probability that both are green is
Q 2: The directional derivative of f(x,y,z)=x^2+y^2+z^2 at the point (1, 1, 1) in the direction \underline i-\underline k is
Q 3: The Taylor series expansion of the function: F(x)=x/(1+x) around x = 0 is
Q 4: The range of values for a constant ‘K’ to yield a stable system in the following set of time-dependent differential equations is
\frac{dy_1}{dt}=-5y_1+(4-K)y_2 \frac{dy_2}{dt}=y_1-2y_2Q 5: The value of y as t → ∞ for the following differential equation for an initial value of y(1) = 0 is
(4t^2+1)\frac{dy}{dt}+8yt-t=0Q 6: The most general complex analytical function f(z)=u(x,y)+i\;v(x,y) for u=x^2-y^2 is
Q 7: The differential equation \frac{d^2y}{dt^2}+10\frac{dy}{dt}+25x=0 will have a solution of the form NOTE: C1 and C2 are constants