List of top Engineering Mathematics Questions asked in GATE Instrumentation Engineering

Choose the correct statement(s) from the following options, regarding Cauchy's theorem on complex integration \( \oint_C f(z)\,dz \), where \( C \) is a simple closed path in a simply connected domain \( D \).
Let the difference equation \( y[n] = \alpha y[n-1] + x[n] \), where \( \alpha>1 \) and \( \alpha \) is real, represent a causal discrete-time linear time invariant system. The system is initially at rest. If \( x[n] = -\delta[n-p] \), where \( p>10 \), the value of \( y[p+1] \) is:
The value of the integral \( \int_{-\pi}^{\pi} (\cos^6 x + \cos^4 x) \, dx \) is:
Newton-Raphson method is used to compute the inverse of the number 1.6. Among the following options, the initial guess of the solution that results in non-convergence of the iterative process is:
Consider the function \( f(z) = \frac{2z + 1}{z^2 - 2z} \), where \( z \) is a complex variable. The sum of the residues at singular points of \( f(z) \) is:
If one of the eigenvectors of the matrix
\[ A = \begin{bmatrix} 1 & 1 \\ -4 & x \end{bmatrix} \] is along the direction of
\[ \begin{bmatrix} 2\alpha \\ \alpha \end{bmatrix} \] where \( \alpha \) is any non-zero real number, then the value of \( x \) is ________ (in integer).
The solution of the differential equation \(\dfrac{dy}{dx} = \dfrac{y}{x}\) represents:
A \( 2n \times 2n \) matrix \( A = [a_{ij}] \) has its elements defined as: \[ a_{ij} = \begin{cases} \beta(i + j), & \text{if } i + j \text{ is odd} \\ -\beta(i + j), & \text{if } i + j \text{ is even} \end{cases} \] where \( n \) is an integer greater than 2, and \( \beta \) is any non-zero real number. What is the rank of matrix \( A \)?
Choose the eigenfunction(s) of stable linear time-invariant continuous-time systems from the following options.
The probability of a student missing a class is \( 0.1 \). In a total number of 10 classes, the probability that the student will not miss more than one class is _______ (rounded off to two decimal places).
The value of the surface integral $\iint_S (2x + z) dy dz + (2x + z) dz dx + (2z + y) dx dy$ over the sphere $S: x^2 + y^2 + z^2 = 9$ is