List of top Engineering Mathematics Questions asked in GATE Production and Industrial Engineering

The annual profit of a company depends on its annual marketing expenditure. The information of the preceding 3 years' annual profit and marketing expenditure is given in the table. Based on linear regression, the estimated profit (in units) of the 4th year at a marketing expenditure of 5 units is ............ (Rounded off to two decimal places)

A bag contains 5 red, 7 green, and 3 blue balls. Two balls are drawn at random from the bag one-by-one. The probability of the second drawn ball being red is:
The eigenvalues of the matrix \( A = \begin{bmatrix} 0 & -1 \\ 1 & 0 \end{bmatrix} \) are:
The solution of the linear differential equation \[ \frac{dy}{dx} + y = e^x, \] when \( y(0) = 0 \), is:
If \( F(s) \) denotes the Laplace transform of some function \( f(t) \), then the Laplace transform of \( e^{bt} f(t) \), where \( b \) is a real constant, is:
If \( i, j, k \) are the orthogonal unit vectors in Cartesian \( x \)-\( y \)-\( z \) coordinate system, the curl of the vector \( -2y\hat{i} + x\hat{j} \) is:
Which one of the following equations is a linear differential equation?