Mathematics Mock Test - 11

Maximize $Z=4x+6y$ subject to $3x+2y\le 12$, $x+y\ge 2$, $x,y\ge 0$.

The number of straight lines that are equally inclined to the three-dimensional coordinate axes is:

Match List I with List II regarding the domain of functions:List I (Function)List II (Domain)A. $f(x)=\frac{1}{\sqrt{x-2}}+\frac{1}{\sqrt{3-x}}$ I. $[2,3]$ B. $f(x)=\sqrt{\frac{x-2}{3-x}}$ II. $(2,3]$ C. $f(x)=\sqrt{\frac{3-x}{x-2}}$ III. $[2,3)$ D. $f(x)=\sqrt{(x-2)(3-x)}$ IV. $(2,3)$ Choose the correct answer:

The solution of the differential equation $\cos (x+y)dy=dx$ is:

Let $\int \frac{\sqrt{x}}{\sqrt{1-x^3}}dx=\frac{2}{3}(g\circ f)(x)+c$. Then: