List of top Engineering Mathematics Questions asked in GATE Biomedical Engineering

Two systems \( U \) and \( V \) are defined as shown below. Which of the following statement(s) is/are CORRECT? \[ x(t) \quad {System} \, U \quad y(t) = x(t)^2 + 1 \] \[ x(t) \quad {System} \, V \quad y(t) = x(t) + 1 \]
Which of the following is/are CORRECT about the value of \( y = \log_e(-e^x) \), where \( x \) is a real number.
Gelatin solutions P and Q of concentrations 3.5% and 0.5%, respectively, need to be mixed to obtain a 3% solution R. How much volume (in ml) of P needs to be mixed with 100 ml of Q to obtain R? (Choose the correct option)
The elements of the dataset \( \{-5, 1, a, 5, b\} \) are in ascending order. If both the mean and median of the dataset are equal to 3, what is the value of \( b \)?
The eigenvalues of the matrix: \[ \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix} \] are ________
\( N \) independent trials of a binomial random variable yield an expectation value of 16 and variance of 12. What is the value of \( N \)?
The function \( f(Z)=\dfrac{1}{Z-1} \) of a complex variable \(Z\) is integrated on a closed contour in an anti-clockwise direction. For which of the following contours, does this integral have a non-zero value?
Calculate the reciprocal of the coefficient of \(z^3\) in the Taylor series expansion of the function \(f(z)=\sin(z)\) around \(z=0\). (Provide the answer as an integer.)
For the function \(f(x) = x^4 - x^2\), which of the following statements is/are TRUE?
Using divergence theorem, evaluate the integral \(\iint_{S} \vec{F} \cdot \vec{n}\, dA\), where \(S\) is the surface of the cone \(x^{2}+y^{2} \le z^{2},\ 0 \le z \le 3\). If \(\vec{F} = 4x\hat{i} + 3z\hat{j} + 5y\hat{k}\) is a vector function with outer unit normal vector \(\vec{n}\), the value of the integral is ______ (rounded off to the nearest integer).
In a biological study, the experimental values measured from 6 subjects are given in the table below. Using this data, the linear regression coefficient for estimating the weight of the heart based on the systolic pressure is ________ (rounded off to two decimal places).
If $g(t)=\dfrac{df(t)}{dt}$, and $F(s)=\dfrac{1+s}{s^{2}+12s+32}$ where $F(s)$ is the Laplace transform of $f(t)$, then the value of $g(t)$ at $t=0$ is _________.

If the given matrices \[ A = \begin{bmatrix} 3 & -2 \\ 4 & -2 \end{bmatrix}, \quad I = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} \] satisfy \( A^{2} = kA - 2I\), \(\text{ the value of coefficient }\) k \(\text{ is}\) _________.

Solution of the differential equation \[ \frac{dy}{dx} - y = \cos x \] is
In the complex z-domain, the value of the integral \[ \oint_{C} \frac{z^{3} - 9}{3z - i} \, dz \] is
Due to the current COVID pandemic conditions, assume that positive or negative status of any individual are equally likely. There are 3 members in a family. If one of the members has tested COVID positive, the conditional probability that at least 2 members are COVID positive is ______ (rounded off to three decimal places).
Given $x$ is real, identify all the even-functions among the following:
If \(\vec{V} = a\hat{i} + b\hat{j} + c\hat{k}\), identify the INVALID operation on \(\vec{V}\).
Evaluation of the integral \[ \int \frac{dx}{\sqrt{2x - x^2}} \] results in