PYQs Based test 25: Engineering Mathematics

Consider a function f(x, y, z) given by

f(x, y, z) = (x² + y² – 2z²)(y² + z²)

The partial derivative of this function with respect to x at the point x = 2, y = 1 and z = 3 is _______

Let p(z) = z³ + (1 + j) z² + (2 + j) z + 3, where z is a complex number.

Which one of the following is true?

Assume that in a traffic junction, the cycle of the traffic signal lights is 2 minutes of green (vehicle does not stop) and 3 minutes of red (vehicle stops). Consider that the arrival time of vehicles at the junction is uniformly distributed over 5 minute cycle. The expected waiting time (in minutes) for the vehicle at the junction is ___________ .

Consider the initial value problem below. The value of y at x = In 2, (rounded off to 3 decimal places) is

$\frac{dy}{dx}=2x-y,y\left(0\right)=1$

Let f(x) be a real -valued function such that f'(x₀) = 0 for some x₀ ∈ (0, 1), and f${}^{"}$ (x) > 0 for all x ∈ (0, 1). Then f(x) has