If the interval in which the function f(x) = $\frac{x}{x^2+1}$ is strictly increasing is (-a, a), then a is equal to

If $f(x) = \sin x - \cos x$, $x \in [0, 2\pi]$ then

(A) $f(x)$ is increasing in $(0, \frac{3\pi}{4})$

(B) $f(x)$ is decreasing in $(0, \frac{3\pi}{4})$

(C) $f(x)$ is decreasing in $(\frac{3\pi}{4}, \frac{7\pi}{4})$

(D) $f(x)$ is decreasing in $(\frac{7\pi}{4}, 2\pi)$

Choose the correct answer from the options given below:

A cylindrical drum of radius 7 cm and height 2 m is being kept in a vertical position filled with milk. If the milk is leaking at 14 cm³/sec from its lower base, then the rate of decrease in the level of milk is:

[Take $\pi = \frac{22}{7}$]

The function $f(x) = 2x^3-15x^2+36x+4$ has local maxima at $x=$

The tangent to the curve $y = e^{3x}$ at the point $(0, 1)$, meets the x-axis at :

The function $f(x) = x + \frac{a^2}{x}$, $a > 0$, $x \neq 0$ has a local maxima at

The function $f(x) = -x^3 + 12x^2 - 36x + 21$ is

A. Increasing on $(-\infty, 2)$

B. Decreasing on $(-\infty, 2)$

C. Increasing on $(2, 6)$

D. Decreasing on $(6, \infty)$

Choose the correct answer from the options given below: