GATE IN 2005 | GATE IN Year Wise Previous Years Questions

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

The general solution of the differential equation $$\left( {{D^2} - 4D + 4} \right)y = 0$$ is of the form (given $$D = {d \over {dx}}$$ and $${C_1},{C_2}$$ are constants)

$${C_1}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{ - 2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,{e^{2x}}$$

$${C_1}\,{e^{2x}} + {C_2}\,x\,{e^{2x}}$$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

Consider the circle $$\left| {z\, - 5\, - 5i} \right|\, = \,2$$ in the complex number plane (x, y) with z = x + iy. The minimum distance from the origin to the circle is

$$5\sqrt 2 - 2$$

$$\sqrt {54} $$

$$\sqrt {34} $$

$$5\sqrt 2 $$

GATE IN 2005

MCQ (Single Correct Answer)

-0.3

Let $${z^3}\, = \,\overline z $$, where z is a complex number not equal to zero. Then z is a solution of

$${z^2} = 1$$

$${z^3} = 1$$

$${z^4} = 1$$

$${z^9} = 1$$

GATE IN Papers

2017