List of top Engineering Mathematics Questions asked in GATE Biomedical Engineering

In the figure below, the Fourier series of v(t), in volts, is given as :
\(v(t) = v_0 + 2 cos(\omega_0t) + 5 cos(3\omega_0t) + cos (5\omega_0t)\)
The capacitor is a short circuit for all AC signals. The power absorbed by the 1Ω resistor is ________ W. Give your answer rounded off to the nearest integer.

If x[n] = u[n] - u[n -5], and h[n] = δ[n] - δ[n - 1] and y[n] = x[n] × h[n], then the value of \(\sum_{n=-\infin}^{\infin}\) y[n] is _________. Give your answer rounded off to the nearest integer.

For \(\vec{F}=(x+y)\hat{i}+(x+y)\hat{j}\) the value of \(\oint\vec{F}.d\vec{r}\) along the path shown in the figure is ________. Give your answer as an integer.

What is the value of the following integral using the residue integration method ?
\(\int\limits_{-\infin}^{\infin}\frac{dx}{1+x^4}\)

Consider a system of the following two partial differential equations :
\(\frac{∂\alpha}{∂x}=-2\frac{∂\beta}{∂t}\)
\(\frac{∂\beta}{∂x}=-2\frac{∂\alpha}{∂t}\)
Which one of the following choices is a possible solution for the system ?

If \(A=\begin{pmatrix} 1 & -1 \\ 2 & -2 \end{pmatrix}\), the eigenvalues of A are _____

A group of four people were residing together when a new virus was detected. If the probability of each person being infected is 0.1, then the probability that at least two of them are infected is ________. Give your answer rounded off to 3 decimal places.

A random noise signal with Gaussian distribution has a mean of zero and a standard deviation of 1 mV. The probability that an instantaneous measurement of this signal is greater than 2 mV or lesser than -2 mV is ________.
Give your answer as a percentage rounded off to the nearest integer.

The trigonometric Fourier series expansion of the periodic function in the figure has coefficients {a_n} and {b_n} for cosine and sine terms, respectively. The value of a₁/a₃ is ________.Give your answer rounded off to 1 decimal place.

The input x(t) and the output y(t) of a linear time invariant system are related as follows :
\(y(t)+\frac{dy(t)}{dt}+0.5\frac{d^2y(t)}{dt^2}=x(t)+0.1\frac{dx(t)}{dt}\)
What is the Laplace transform of the impulse response of the system ?

The Fourier transform of e^-|2t| is ________.

To solve the equation x = 2 cos x using Newton-Raphson's method, which one of the following iterations should be used ?

What is the value of the following complex line integral counter-clockwise ?
\(\oint_{|z|=3}\frac{8}{z(z-2)(z-4)}dz\)