Match List I with List II

LIST I	LIST II
A. Maximum value of $f(x) = -\lvert x+1 \rvert + 3$	I. 6
B. Minimum value of $f(x) = (2x-1)^2 + 5$	II. 5
C. Maximum value of $f(x) = 6 - x^2$	III. no maximum value
D. Maximum value of $f(x) = x^3 + 1$	IV. 3

Choose the correct answer from the options given below:

An angle $\theta, 0<\theta<\frac{\pi}{2}$, which increases twice as fast as its sine, is

The function $f(x) = \sin x + \cos x$; $0 \leq x \leq 2\pi$ is

(A) Increasing in $\left(0, \frac{\pi}{4}\right)$

(B) Decreasing in $(0, \pi)$

(C) Increasing in $\left(\frac{5\pi}{4}, 2\pi\right)$

(D) Decreasing in $\left(\frac{\pi}{4}, \frac{5\pi}{4}\right)$

(E) Neither increasing Nor decreasing in $\left(0, \frac{\pi}{4}\right)$

Choose the correct answer from the options given below:

The side of an equilateral triangle is increasing at the rate of 2 cm/sec. The rate at which the area of the triangle is increasing, when the side of the triangle is 5 cm, is

In a sphere the rate of change of volume with respect to(w.r.t) time is

If the sum of the lengths of hypotenuse and a side of a right angled triangle is given, then the area of the triangle is maximum when angle between them is:

A spherical ice ball is melting at the rate of 100 $\pi$ cm³/min. The rate at which its radius is decreasing when its radius is 15 cm, is