GATE IN 2021 Question Paper (06-Feb-2021) (Shift 1)

An amplitude modulation (AM) scheme uses tone modulation, with modulation index of 0.6. The power efficiency of the AM scheme is _______ % (rounded off to one decimal place)

When the movable arm of a Michelson interferometer in vacuum (n = 1) is moved by 325 μm, the number of fringe crossings is 1000. The wavelength of the laser used in nanometers is ____.

Consider the function f(x) = −x² + 10x + 100. The minimum value of the function in the interval [5, 10] is ___.

Let $f(z)=\frac{1}{z^2+6z+9}$ defined in the complex plane. The integral ∮${}_c$ f(z)dz over the contour of a circle c with center at the origin and unit radius is ___.

The determinant of the matrix M is shown below is ____.

M=≤ft[ {*20c 1&2&0&0\\ 3&4&0&0\\ 0&0&4&3\\ 0&0&2&1 } ]