List of top Mechanical Engineering Questions on Engineering Mathematics

A vector field \[ \mathbf{B}(x, y, z) = x \mathbf{\hat{i}} + y \mathbf{\hat{j}} - 2z \mathbf{\hat{k}} \] is defined over a conical region having height \(h = 2\), base radius \(r = 3\) and axis along z, as shown in the figure. The base of the cone lies in the x-y plane and is centered at the origin. If \(\mathbf{n}\) denotes the unit outward normal to the curved surface S of the cone, the value of the integral \[ \iint_S \mathbf{B} \cdot \mathbf{n} \, dS \] equals ................ (Answer in integer)

The figure shows the plot of a function over the interval [-4, 4]. Which one of the options given CORRECTLY identifies the function?

The smallest perimeter that a rectangle with area of 4 square units can have is ............... units. (Answer in integer)

Consider the second-order linear ordinary differential equation \[ x^2 \frac{d^2y}{dx^2} + x \frac{dy}{dx} - y = 0, x \ge 1 \] with the initial conditions \[ y(x = 1) = 6, \frac{dy}{dx}\bigg|_{x=1} = 2. \] The value of y at x = 2 equals ................ (Answer in integer)

The initial value problem \[ \frac{dy}{dt} + 2y = 0, y(0) = 1 \] is solved numerically using the forward Euler's method with a constant and positive time step of \(\Delta t\). Let \(y_n\) represent the numerical solution obtained after n steps. The condition \(|y_{n+1}| \le |y_n|\) is satisfied if and only if \(\Delta t\) does not exceed ................ (Answer in integer)

A linear transformation maps a point \((x, y)\) in the plane to the point \((\hat{x}, \hat{y})\) according to the rule \[ \hat{x} = 3y, \hat{y} = 2x. \] Then, the disc \(x^2 + y^2 \le 1\) gets transformed to a region with an area equal to ................ (Rounded off to two decimals)
Use \(\pi = 3.14\).

The value of k that makes the complex-valued function \[ f(z) = e^{-kx} (\cos 2y - i \sin 2y) \] analytic, where \(z = x + iy\), is ................ (Answer in integer)

A machine produces a defective component with a probability of 0.015. The number of defective components in a packed box containing 200 components produced by the machine follows a Poisson distribution. The mean and the variance of the distribution are