Mathematics Tes...

The area of the region\(\left\{(x, y): 0 \leq x \leq \frac{9}{4}, \quad 0 \leq y \leq 1, \quad x \geq 3 y, \quad x+y \geq 2\right\}\)is:

A light ray emerging from the point source placed at \(P(2,3)\) is reflected at a point \(Q\) on the \(y\) -axis. It then passes through the point \(R(5, 10)\). The coordinates of \({Q}\) are:

The number of real roots of the equation \(5+\left|2^x-1\right|=2^x\left(2^x-2\right)\) is:

If \(\left[\begin{array}{ccc}1 & -3 & 2 \\ 2 & -8 & 5 \\ 4 & 2 & \lambda\end{array}\right]\) is not an invertible matrix, then what is the value of \(\lambda\)?

Find the distance between the planes \(2 x+y-2 z+6=0\) and \(4 x+2 y-4 z-6=\) \(0\) .

What is \(\int_{-\frac{\pi}{6}}^{\frac{\pi}{6}} \frac{\sin ^{5} x \cos ^{3} x}{x^{4}} d x\) equal to?

If \(\sqrt{1-{x}^{2}}+\sqrt{1-{y}^{2}}={a}\), then what is \(\frac{{dy}}{{dx}}\) equal to ?

What is the coefficient of the middle term in the expansion of \(\left(1+4 x+4 x^{2}\right)^{5} ?\)

Let \(f: R \rightarrow R\) be defined as \(f( x )=2 x -1\) and \(g : R -\{1\} \rightarrow R\) be defined as \(g ( x )=\frac{ x -\frac{1}{2}}{ x -1}\). Then the composition function \(f( g ( x ))\) is: