GATE 2011 Instrumentation

The series $$\,\,\sum\limits_{m = 0}^\alpha {{1 \over {{4^m}}}{{\left( {x - 1} \right)}^{2m}}\,\,\,} $$ converges for

Consider the differential equation $$\mathop y\limits^{ \bullet \bullet } + 2\,\mathop y\limits^ \bullet + y = 0\,\,$$ with boundary conditions $$y(0)=1$$ & $$y(1)=0.$$ The value o...

The matrix $$M = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & 6 \cr { - 1} & { - 2} & 0 \cr } } \right]$$ has eigen values $$-3, -3, 5.$$ An eigen vector corresponding to the e...

The box $$1$$ contains chips numbered $$3, 6, 9,$$ $$12$$ and $$15$$. The box $$2$$ contains chips numbered $$6, 11, 16, 21$$ and $$26$$. Two chips, one from each box are drawn at...