Engineering Mathematics: GATE AE Comprehensive Syllabus & Solved PYQs

Calculus

Linear Algebra

Differential Equations

Numerical Methods

Consider the contour C shown in the figure below. For the vector F⃗ = (x + 2y)êx + (2x + 4y)êy, the integral ∮ F⃗ ⋅ dl⃗ C =________. Here dl⃗ represents an infinitesimal length along the contour C.

The number of independent elastic constants that a fully anisotropic linear elastic material can have is ______.

An n × n square matrix A satisfies AT = A-1. The determinant of this matrix may take which of the following value(s)?

The state of stress at a point in a^2-D body, in the x-y Cartesian coordinate system, is represented in matrix form as [$\sigma$]. The transformation matrix [Q] rotates the coordinate system to a new x'-y' Cartesian coordinate system. Select the CORRECT option(s) that represent(s) the state of stress in the new coordinate system.

If a matrix can be written as A = uvT, where both u and v are n-dimensional real- valued non-zero column vectors, then the rank of the matrix A is ________ (answer in integer).

For the matrix A = $\begin{bmatrix} a & b \\ c & d \end{bmatrix}$, if the relation a + b = c + d holds and a, b, c, d ≠ 0, then which one of the following statements about A is FALSE?

Consider the differential equation with the initial conditions given below. If y(x) is the solution of the equation, the value of the slope, $\frac{dy}{dx}$ , at x = ln(2) is ________ (rounded off to three decimal places). $\frac{d^2y}{dx^2}$ + 2 $\frac{dy}{dx}$ + y = 0 with y|x=0 = 0 and $\frac{dy}{dx}$| x=0 = 1

For any real symmetric matrix A, the transpose of A is ____ .