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

The following differential equation governs the evolution of variable \(x(t)\) with time \(t, t \geq 0\).
\(\frac {d^2x}{dt^2} + 4x = e^{-t}\)
Given the initial conditions \(x = 0\) and \(\frac {dx}{dt} = 0\) at \(t = 0\), the value of \(x\) at \(t =\frac {\pi}{8}\) is _____  . (Rounded off to 3 decimal places)

The values of function \(y(x)\) at discrete values of \(x\) are given in the table. The value of \(∫_0^4y(x)dx\), using Trapezoidal rule is _____ . (Rounded off to 1 decimal place)

x	0	1	2	3	4
y(x)	1	3	6	9	12

Which of the following statement(s) is/are TRUE for a given acceptance sampling plan?

Seven cards numbered 1 to 7 are placed in a box. After thoroughly mixing all the cards, one card is drawn at random.
If it is known that the number on the card drawn is odd, then the probability that the number on the card drawn is greater than 4 is _____ %. (Answer in integer)

If \(\lim\limits_{x \to1}(\frac {x^2-2ax+b}{x-1})=8\)
then \((a-b)\) is _____ . (Answer in integer)

If \(A=\begin{bmatrix} a & b\\[0.3em] c & -a \\[0.3em] \end{bmatrix}\)is a matrix such that \(A^2=I\), where \(I\) is an identity matrix, then which of the following is TRUE?

In a complex function
\(f(x, y) = u(x, y) + i v(x, y),\)
\(i\) is the imaginary unit, and \(x, y, u(x, y)\) and \(v(x, y)\) are real.
If \(f(x, y)\) is analytic then which of the following equations is/are TRUE?

If \(X\) is a continuous random variable with the probability density function
\(f(x) =   \begin{cases}     \frac K4      & ; 0\leq x \leq 1\\     0 & ; \text{otherwise}    \end{cases}\)
Then the value of \(K\) is _____ . (Answer in integer)

A vector field is given as \(F(x, y) = (100x + 100y) i + (−50x + 200y) j\), where \(i\) and \(j\) are the unit vectors along the \(x\) and \(y\) axes in the Cartesian frame, respectively. Then the value of
\(∮F(x, y). dl\)
where \(dl = dx i + dy j\) is an elemental path taken over an anticlockwise circular contour \(C\) of radius \(r = 2\) is

In the Taylor series expansion of sin z around \(z = 0\), the coefficient of the term \(z^3\) is

A uniform cantilever beam of length L and flexural rigidity EI is loaded by a force F as shown in the figure. Assuming that the Euler-Bernoulli beam theory is applicable here, the magnitude of the static deflection at the free end of the beam is