Mathematics Mock Test - 8

The co-factor of the element '4' in the determinant
$$\left|\begin{array}{cccc}1& 3& 5& 1\\ 2& 3& 4& 2\\ 8& 0& 1& 1\\ 0& 2& 1& 1\end{array}\right|$$

If $f(x)$ is an increasing function and $g(x)$ is a decreasing function, then which of the following is correct for the real values $p$ and $q$? Given that for these values of $x$, both functions are defined.

The function $f(x)=x^2-4x$, $x\in [0,4]$ attains minimum value at:

Let $f$ and $g$ be differentiable functions on $\mathbb{R}$ such that $f\circ g$ is the identity function. If for some $a,b\in \mathbb{R}$, $g^{\prime }(a)=5$ and $g(a)=b$, then $f^{\prime }(b)$ is equal to: