GATE 2016 Instrumentation
8 questions across 1 session
A straight line of the form $$y=mx+c$$ passes through the origin and the point $$(x, y)=(2,6).$$ The value of $$m$$ is
$$\mathop {\lim }\limits_{n \to \infty } \left( {\sqrt {{n^2} + n} - \sqrt {{n^2} + 1} } \right)\,\,$$ is ________.
Let $$\,\,f:\left[ { - 1, - } \right] \to R,\,\,$$ where $$\,f\left( x \right) = 2{x^3} - {x^4} - 10.$$ The minimum value of $$f(x)$$ is _______.
In the neighborhood of $$z=1,$$ the function $$f(z)$$ has a power series expansion of the form $$f\left( z \right) = 1 + \left( {1 - z} \right) + {\left( {1 - z} \right)^2} + ........
The value of the integral $${1 \over {2\pi j}}\int\limits_c {{{{z^2} + 1} \over {{z^2} - 1}}} dz$$ where $$z$$ is a complex number and $$C$$ is a unit circle with center at $$1+0j$...
Consider the matrix $$A = \left( {\matrix{ 2 & 1 & 1 \cr 2 & 3 & 4 \cr { - 1} & { - 1} & { - 2} \cr } } \right)$$ whose eigen values are $$1, -1$$ and $$3$$. Then trace of $$\left(...
An urn contains $$5$$ red and $$7$$ green balls. A ball is drawn at random and its colour is noted. The ball is placed back into the urn along with another ball of the same colour....
The vector that is NOT perpendicular to the vectors $$\,\,\left( {i + j + k} \right)\,\,$$ and $$\,\left( {i + 2j + 3k} \right)\,\,$$ is _________.