An edge of a variable cube is increasing at the rate of 10 cm/s. How fast the volume of the cube will increase when the edge is 5 cm long?

• 750 cm³/ s

• 75 cm³/ s

• 300 cm³/ s

• 150 cm³/ s

The minimum value of f(x) = $\left|3 - \mathrm{x}\right| + 7$ is

• 0

• 6

• 7

• 8

The total revenue in rupees received from the sale of x units of a product is given by R(x) = 13x² + 26x + 15. Then, the marginal revenue in rupees, when x = 15 is

• 116

• 126

• 136

• 416

524.

If a tangent of the curve y = 2 + $\sqrt{4\mathrm{x} + 1}$ has slope $\frac{2}{5}$ at a point, then the point is

• (0, 2)

• $\left(\frac{3}{4}, 4\right)$

• (2, 5)

• (6, 7)

The points on the graph y = x³ - 3x at which the tangent is parallel to x-axis are

• (2, 2) and (1, - 2)

• (- 1, 2) and (- 2, - 2)

• (2, 2) and (- 1, 2)

• (1, - 2) and (- 1, 2)

The slope of the normal to the curve y² - xy - 8 = 0 at the point (0, 2) is equal to

• - 3

• - 6

• 3

• 6

If the straight line y - 2x+ 1 = 0 is the tangent to the curve xy + ax + by = 0 at x = i, then the values of a and b are respectively

• 1 and 2

• 1 and - 1

• - 1 and 2

• 1 and - 2

If the angle between the curves y = 2^x and y = 3^x is $\mathrm{\alpha }$, then the value of tan($\mathrm{\alpha }$) is equal to

• $\frac{\log \left({\displaystyle \frac{3}{2}}\right)}{1 + \log \left(2\right)\log \left(3\right)}$

• $\frac{6}{7}$

• $\frac{1}{7}$

• $\frac{\log \left({\displaystyle 6}\right)}{1 + \log \left(2\right)\log \left(3\right)}$

The function f(x) = 3x³ - 36x + 99 is increasing for

• $- \infty < \mathrm{x} < 2$

• $- 2 < \mathrm{x} < \infty$

• - 2 < x < 2

• x < - 2 or x > 2

The minimum value of the function $\mathrm{f}\left(\mathrm{x}\right) = \frac{1}{\sin \left(\mathrm{x}\right) + \cos \left(\mathrm{x}\right)}$ in the interval $\left[0, \frac{\mathrm{\pi }}{2}\right]$ is

• $\frac{\sqrt{2}}{2}$

• $- \frac{\sqrt{2}}{2}$

• $\frac{2}{\sqrt{3} + 1}$

• $-\frac{2}{\sqrt{3} + 1}$