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

Let $\mathrm{f}\left(\mathrm{x}\right) = \frac{{\mathrm{\alpha x}}^2}{\mathrm{x} + 1}, \mathrm{x} \ne - 1$. The value of $\mathrm{\alpha }$ for which f (a) = a, ($\mathrm{a} \ne 0$) is

• 1 - $\frac{1}{\mathrm{a}}$

• $\frac{1}{\mathrm{a}}$

• $1 + \frac{1}{\mathrm{a}}$

• $\frac{1}{\mathrm{a}} - 1$

For a, b $\in$ R, define $\mathrm{a} * \mathrm{b} = \frac{\mathrm{a}}{\mathrm{a} + \mathrm{b}}$, where a + b $\ne$ 0. If a * b = 5,  then the value of b * a is

• 5

• - 5

• 4

• - 4

Let A = {x, y, z} and B = {a, b, c, d}. Which one of the following is not a relation from A to B ?

• {(x, a), (x, c)}

• {(y, c), (y, d)}

• {(z, a), (z, d)}

• {(z, b), (y, b), (a, d)}

The doamin of ${\sin }^{-1}\left[{\log }_2\left(\frac{\mathrm{x}}{12}\right)\right]$ is

• [2, 12]

• [- 1, 1]

• $\left[\frac{1}{3}, 24\right]$

• [6, 24]

If f(x) = x² - 1 and g(x) = (x + 1)², then (gof) (x) is

• (x + 1)⁴ - 1

• x⁴ - 1

• x⁴

• (x + 1)⁴

18.

If A = $\left[\begin{array}{cc}\mathrm{x}& - 2\\ 3& 7\end{array}\right]$ and A^{- 1} = $\left[\begin{array}{cc}\frac{7}{34}& \frac{1}{17}\\ \frac{- 3}{34}& \frac{2}{17}\end{array}\right]$, then the value of x is

• 2

• 3

• - 4

• 4

If $\left|\begin{array}{ccc}{\mathrm{x}}^2 + \mathrm{x}& 3\mathrm{x} - 1& - \mathrm{x} + 3\\ 2\mathrm{x} + 1& 2 + {\mathrm{x}}^2& {\mathrm{x}}^3 - 3\\ \mathrm{x} - 3& {\mathrm{x}}^2 + 4& 3\mathrm{x}\end{array}\right|$ = ${\mathrm{a}}_{0 }+ {\mathrm{a}}_1\mathrm{x} + {\mathrm{a}}_2{\mathrm{x}}^2 + ... + {\mathrm{a}}_7{\mathrm{x}}^7$, then the value of a₀ is

• 25

• 24

• 23

• 21

The value of the determinant $\left|\begin{array}{ccc}15!& 16!& 17!\\ 16!& 17!& 18!\\ 17!& 18!& 19!\end{array}\right|$ is equal to

• 15! + 16!

• 2(15!)(16!)(17!)

• 15! + 16! + 17!

• 16! + 17!