The rate of change in area of a triangle having sides 10 cm and 12 cm when the variable angle between them is $\theta = 60°$, is :

If an edge of a variable cube is increasing at the rate of 0.8 cm/sec, at what rate its surface area is increasing when its edge is 10 cm?

The function $f(x) = 2x^3 - 3x^2 - 36x + 7$ is :

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

B. Decreasing in $(-2,3)$

C. Neither increasing nor decreasing in $(-2,3)$

D. Increasing in $(3,\infty)$

Choose the correct answer from the options given below:

A balloon, which always remains spherical on inflation, is being inflated by pumping in 900 cubic centimeters of gas per second. The rate at which the radius of the balloon increases when the radius is 15 cm, is:

If $\alpha$ and $\beta$ are absolute maximum and absolute minimum values of a function $f(x)=\dfrac{x}{2}+\dfrac{2}{x}$ on the interval $[1,2]$, then the value of $\alpha+\beta$ is:

If it is given that at $x = 1$, the function $f(x) = x^4 - 62x^2 + 2ax + b$ attains its maximum value on the interval [0, 2], then the value of a is:

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