Which of the following are NOT correct regarding the equation of tangent and normal to the curve $y = \frac{x-11}{(x-2)(x-3)}$ at the point, where it cuts the $x$-axis?

(A) The point of contact is (11, 0).

(B) The equation of tangent is $x - 72y - 11 = 0$

(C) The equation of normal is $72x + y - 11 = 0$

(D) The slope of the tangent at the given point of contact is $\frac{1}{88}$

Choose the correct answer from the options given below:

If the function $f(x)=\sin x+\cos x, 0 \le x \le 2\pi$ is increasing in the interval $(\alpha,\beta) \cup (\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to:

The interval(s), where the function $f(x) = \begin{cases} \frac{1-e^x}{e^{2x}-1} & : x \neq 0 \\ \frac{-1}{2} & : x = 0 \end{cases}$ is increasing, is/ are:

The maximum value of $f(x)=\dfrac{1}{3(x^2-x+1)}$ is :

The function $f(x) = x^2 - 4x + 6$ is

(A) Strictly decreasing on $(-\infty, 2) \cup (2, \infty)$

(B) Strictly increasing on $(2, \infty)$

(C) Strictly increasing on $(-\infty, \infty)$

(D) Strictly decreasing on $(-\infty, 2)$

Choose the correct answer from the options given below:

The maximum area of a rectangle inscribed in a circle of radius $3\sqrt{2}$ cm, is:

The equation of the tangent line to the curve $y = x^2 - 2x + 5$ which is parallel to the line $4x - y + 1 = 0$ is