GATE PI 2010 | GATE PI Year Wise Previous Years Questions

GATE PI 2010

MCQ (Single Correct Answer)

-0.6

The solution of the differential equation $${{dy} \over {dx}} - {y^2} = 1$$ satisfying the condition $$y(0)=1$$ is

$$y = {e^{{x^2}}}$$

$$y = \sqrt x $$

$$\,y = \cot \left( {x + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} \right)$$

$$y = tan\left( {x + {\raise0.5ex\hbox{$\scriptstyle \pi $} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 4$}}} \right)$$

GATE PI 2010

MCQ (Single Correct Answer)

-0.6

Which one of the following differential equations has a solution given by the function $$y = 5\sin \left( {3x + {\pi \over 3}} \right)$$

$${{dy} \over {dx}} - {5 \over 3}\cos \left( {3x} \right) = 0$$

$${{dy} \over {dx}} + {5 \over 3}\left( {\cos 3x} \right) = 0$$

$${{{d^2}y} \over {{d^2}\,x}} + 9y = 0$$

$${{{d^2}y} \over {d{x^2}}} - 9y = 0$$

GATE PI 2010

MCQ (Single Correct Answer)

-0.6

Two white and two black balls, kept in two bins, are arranged in four ways as shown below. In each arrangement, a bin has to be chosen randomly and only one ball needs to be picked randomly from the chosen bin. Which one of the following arrangements has the highest probability for getting a while ball picked?