The slope of the normal to the curve $y = 2x^2$ at $x = 1$ is:

For the function $f(x) = x^x, x > 0$, which of the following are TRUE?

(A) $f'(x) = x^x(1 + \log x)$

(B) $x = e$ is the critical point

(C) $f$ is increasing in $(\frac{1}{e}, \infty)$

(D) $f$ is increasing in $(0, \infty)$

Choose the correct answer from the options given below:

The revenue function is given by $R(x)=150x-2x^2-x^3$, where $x$ is the number of units demanded, then the marginal revenue when 5 units are sold, is :

The slope of normal to the curve $y = kx^2 - 3x + 2$ at $x = \frac{1}{2}$ is 5. The value of 'k' is

Consider the function $f(x) = \sin x$ in the interval $[\pi, 2\pi]$ then which of the following statements are correct?

(A) $x = \frac{3\pi}{2}$ is its stationary point.

(B) Its maximum value is 1

(C) Its minimum value is -1

(D) It attains its maximum value at $\pi$ and $2\pi$

Choose the correct answer from the options given below:

The maximum value of the function $f(x) = x^2(60 - x)$ in [20, 80] is:

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 :