GATE IN 2016 Question Paper (31-Jan-2016) (Shift 2)

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 ________.

$\underset{n\to \infty }{\lim }\left(\sqrt{n^2+n}-\sqrt{n^2+1}\right)$ is _________.

A voltage V₁ is measured 100 times and its average and standard deviation are 100 V and 1.5 V respectively. A second voltage V₂, which is independent of V₁, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V₃is computed as: V₃ + V₁ + V₂. Then the standard deviation of V₃ in volts is ________

The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is ______.

In the neighbourhood of z = 1, the function f(z) has a power series expansion of the form

𝑓(𝑧) = 1 + (1 − 𝑧) + (1 − 𝑧)² + ...∞

Then f(z) is