Mathematics Mock Test - 7

A water filling Pipe $P$ is 5 times as fast as a second Pipe $Q$. If $P$ fills a cistern in 30 minutes, how long will it take to fill the tank when both pipes are operated simultaneously?

The number of vectors of unit length perpendicular to vectors $\vec{a}=(1,1,0)$ and $\vec{b}=(0,1,1)$ is:

If $A=\left[\begin{array}{ccc}1& -2& 2\\ 0& 2& -3\\ 3& -2& 4\end{array}\right]$, then $A\cdot \text{adj}(A)$ is equal to:

The area bounded by the curves $y=|x|-1$ and $y=-|x|+1$ is:

The real values of $x$ satisfying the inequality: ${\log }_{0.5}(x^2-25)-{\log }_{0.5}(x-5)<{\log }_{0.5}3$ is: