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?