The domain of the function $\mathrm{f}\left(\mathrm{x}\right) = {\sin }^{-1}\left(\frac{\mathrm{x} + 5}{2}\right)$ is

• [- 1, 1]

• [2, 3]

• [3, 7]

• [- 7, - 3]

If f(x) = x + 1 and g(x) = 2x, then f{g(x)} is equal to

• 2(x + 1)

• 2x(x + 1)

• x

• 2x + 1

The domain of the function f(x) = $\frac{{\log }_2\left(\mathrm{x} +\hspace{0.17em}3\right)}{{\mathrm{x}}^2 + 3\mathrm{x} +\hspace{0.17em}2}$ is

• R - {- 1, - 2}

• R - {- 1, - 2, 0}

• (- 3, - 1) ∪ (- 1, $\infty$)

• (- 3, $\infty$) - {- 1, - 2}

If * is defined by a * b = a - b² and $\oplus$ is defined by a $\oplus$ b = a² + b, where a and b are integers, then (3 $\oplus$ 4) * 5 is equal to

• 164

• 38

• - 12

• - 28

The image of the interval [- 1, 3] under the mapping f : R $\to$ R given by f(x) = 4x³ - 12x is

• [8, 72]

• [0, 72]

• [- 8, 72]

• [0, 8]

If the operation $\oplus$ is defined by a $\oplus$ b = a² + b² for all real numbers a and b, then (2 $\oplus$ 3) $\oplus$ 4 is equal to

• 120

• 185

• 175

• 129

The domain of the function f(x) = $\sqrt{7 - 3\mathrm{x}} + {\log }_{\mathrm{e}}\left(\mathrm{x}\right)$ is

• $0 < \mathrm{x} < \infty$

• $\frac{7}{3} \le \mathrm{x} < \infty$

• $0 < \mathrm{x} \le \frac{7}{3}$

• $- \infty < \mathrm{x} < 0$

If f(1) = 1, f(2n) = f(n) and f(2n + 1) = {f(n)}² - 2 for n = 1, 2, 3, ... , then the value of f(1) + f(2) + ... + f(25) is

• 1

• - 15

• - 17

• - 1

509.

In a class of 80 students numbered 1 to 80, all odd numbered students opt for cricket, students whose numbers are divisible by 5 opt for football and those whose numbers are divisible by 7 opt for hockey. The number of students who do not opt any of the three game is

• 13

• 24

• 28

• 52

A function f satisfies the relation f(n) = f(n²) + 6 for $\mathrm{n} \ge 2$  and f(2) = 8. Then, the value of f(256) is

• 24

• 26

• 22

• 28