The appropriate change in the volume V of a cube of side $x$ metres caused by increasing the side by 2% 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 semi vertical angle of a right circular cone of maximum volume of a given slant height is

For the function $f(x)=x^3-2x^2-4x-5$, which of the following statement is not correct ?

If $f(x) = x^2 - 4x + 13, x \in \mathbb{R}$, then which of the following are correct?

(A) $x = 2$ is a stationary point of $f(x)$.

(B) $f(x)$ is increasing function on $(2, \infty)$

(C) $f(x)$ have maxima at $x = 2$

(D) $f(2) = 9$

Choose the correct answer from the options given below:

The value of C which satisfies Rolle's Theorem for $f(x) = \sin^4 x + \cos^4 x$ in $\left[0, \frac{\pi}{2}\right]$. Then C is :

Rate of change of area of a circle with respect to radius

(A) When r = 2 cm is $4\pi$ cm²/cm.

(B) When r = 6 cm is $12\pi$ cm²/cm.

(C) When r = 12 cm is $6\pi$ cm²/cm.

(D) When r = 16 cm is $8\pi$ cm²/cm.

Choose the correct answer from the options given below: