PYQs Based Test - 17 : Engineering Mathematics

The partial derivative of the function

$f\left(x,y,z\right)=e^{1-x\cos y}+xz{e}^{-1/\left(1+y^2\right)}$

With respect to x at the point (1, 0, e) is

The value of the integral $\underset{0}{\overset{\pi }{\int }}\underset{y}{\overset{\pi }{\int }}\frac{\sin x}{x}dxdy,$ is equal to _______.

Consider matrix = ≤ft[ {*20c &{2}\\ {{^2} - }&{{^2}} } ] and vector = ≤ft[ {*20c {{_1}}\\ {{_2}} } ]. The number of distinct real values of k for which the equation Ax = 0 has infinitely many solution is________

Consider the differential equation given below:

$\frac{dy}{dx}+\frac{x}{1-x^2}y=x\sqrt{y}$

The integrating factor of the differential equation is:

The vector function F(r) = -x î + yĵ is defined over a circular are C shown in the figure.



The line integral of ∫${}_C$ F(r) ⋅ dr is