GATE IN 2005

## GATE IN

Identity which one of the following is an eigen vectors of the matrix $$A = \left[ {\matrix{
1 & 0 \cr
{ - 1

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Let $$A$$ be $$3 \times 3$$ matrix with rank $$2.$$ Then $$AX=O$$ has

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The value of the integral $$\int\limits_{ - 1}^1 {{1 \over {{x^2}}}dx} \,\,\,$$ is

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$$f = {a_0}\,{x^n} + {a_1}\,{x^{n - 1}}\,y + - - + \,{a_{n - 1}}\,x\,{y^{n - 1}} + {a_n}\,{y^n}$$
where $$\,\,{a_i}\

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If a vector $$\overrightarrow R \left( t \right)$$ has a constant magnitude then

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A scalar field is given by $$f = {x^{2/3}} + {y^{2/3}},$$ where $$x$$ and $$y$$ are the Cartesian coordinates. The deriv

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The probability that there are $$53$$ Sundays in a randomly chosen leap year is

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The general solution of the differential equation $$\left( {{D^2} - 4D + 4} \right)y = 0$$ is of the form (given $$D =

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

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

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