Consider the function f(x) = g(x) + h(x)

Where $\mathrm{g}\left(\mathrm{x}\right) = \sin \left(\frac{\mathrm{x}}{4}\right) \mathrm{and} \mathrm{h}\left(\mathrm{x}\right) = \cos \left(\frac{4\mathrm{x}}{5}\right)$

What is the period of the function f(x) ?

• 10$\mathrm{\pi }$

• 20$\mathrm{\pi }$

• 40$\mathrm{\pi }$

• $80\mathrm{\pi }$

Consider the function f(x) = g(x) + h(x)

Where $\mathrm{g}\left(\mathrm{x}\right) = \sin \left(\frac{\mathrm{x}}{4}\right) \mathrm{and} \mathrm{h}\left(\mathrm{x}\right) = \cos \left(\frac{4\mathrm{x}}{5}\right)$

What is the period of the function h(x) ?

• $\mathrm{\pi }$

• $\frac{4\mathrm{\pi }}{5}$

• $\frac{5\mathrm{\pi }}{2}$

• $\frac{3\mathrm{\pi }}{2}$

Consider the function f(x) = g(x) + h(x)

Where $\mathrm{g}\left(\mathrm{x}\right) = \sin \left(\frac{\mathrm{x}}{4}\right) \mathrm{and} \mathrm{h}\left(\mathrm{x}\right) = \cos \left(\frac{4\mathrm{x}}{5}\right)$

What is the period of the function g(x) ?

• $\mathrm{\pi }$

• $2\mathrm{\pi }$

• 4$\mathrm{\pi }$

• $8\mathrm{\pi }$

74.

Let f(x) = x², g(x) = tan(x) and h(x) = ln(x). What is [fo(fof)](2) equal to ?

• 2

• 8

• 16

• 256

Let f(x) = x², g(x) = tan(x) and h(x) = ln(x). For x = $\frac{\sqrt{\mathrm{\pi }}}{2}$, What isvalue of  [ho(gof)](x) equal to ?

• 0

• 1

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{2}$

Let S = {1, 2, 3, ...}. A relation R on S × S is defined by x Ry if log_a(x) > log_a(y) when $\mathrm{a} = \frac{1}{2}$, Then the relation is

• reflexive only

• symmetric only

• transitive only

• both symmetric and transitive

If 1.5 ≤ x ≤ 4.5, then which one of the following is correct ?

• (2x – 3) (2x – 9) > 0

• (2x – 3) (2x – 9) < 0

• (2x – 3) (2x – 9) ≥ 0

• (2x – 3) (2x – 9) ≤ 0

If, x = log_c (ab), y = log_a(bc), z = log_b(ca), then which of the following is correct ?

• xyz = 1

• x + y + z = 1

• (1 + x)^-1 + (1 + y)^-1 + (1 + z)^-1 = 1

• (1 + x)^-2 + (1 + y)^-2 + (1 + z)^-2 = 1

What is the value of $\frac{1}{10}{\log }_5\left(1024\right) - {\log }_5\left(10\right) + \frac{1}{5}{\log }_5\left(3125\right) ?$

• 0

• 1

• 2

• 3

The number (1101101 + 1011011)₂ can be written in decimal system as

• (198)₁₀

• (199)₁₀

• (200)₁₀

• (201)₁₀