GATE EC 2018 Question Paper (10-Feb-2018) (Shift 1)

A lossy transmission line has resistance per unit length R = 0.05 Ω/m. The line is distortionless and has a characteristic impedance of 50 Ω. The attenuation constant (in Np/m, correct to three decimal places) of the line is _________.

Consider matrix = ≤ft[ {*20c &{2}\\ {{^2} - }&{{^2}} } ] and vector = ≤ft[ {*20c {{_1}}\\ {{_2}} } ]. The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________

Let X₁, X₂, X₃ and X₄ be independent normal random variables with zero mean and unit variance. The probability that X₄ is the smallest among the four is _________.

Taylor series expansion of $\mathrm{f}\left(\mathrm{x}\right)=\underset{0}{\overset{\mathrm{x}}{\int }}{\mathrm{e}}^{-\left(\frac{{\mathrm{t}}^2}{2}\right)}\mathrm{dt}$ around x = 0 has the form

f(x) = a₀ + a₁x + a₂x² + ….

The coefficient a₂ (correct to two decimal places) is equal to ________

The ABCD matric for a two-port network is defined by:

≤ft[ {*20c {{_1}}\\ {{_1}} } ] = ≤ft[ {*20c &\\ &} ]≤ft[ {*20c {{_2}}\\ { - {_2}} } ]



The parameter B for the given two-port network (in ohms, correct to two decimal places) is ________.