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GATE IN 2012

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Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr...
The maximum value of $$f\left( x \right) = {x^3} - 9{x^2} + 24x + 5$$ in the int...
The direction of vector $$A$$ is radially outward from the origin, with $$\left|...
Two independent random variables $$X$$ and $$Y$$ are uniformly distributed in th...
A fair coin is tossed till a head appears for the first time. The probability t...
With initial condition $$x\left( 1 \right)\,\,\, = \,\,\,\,0.5,\,\,\,$$ the solu...
If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/...
The unilateral Laplace transform of $$f(t)$$ is <br>$$\,{1 \over {{s^2} + s + 1...
Consider the differential equation <br>$${{{d^2}y\left( t \right)} \over {d{t^2...

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