Given: A one-one function from set $\{1,2,3\}$ to set $\{a,b,c,d,e\}$

Step 1: One-one (injective) function means no two elements map to the same output.

We choose 3 different elements from 5 and assign them to 3 inputs in order.

So, total one-one functions = $P(5,3) = 5 \times 4 \times 3 = 60$

✅ Final Answer: $\boxed{60}$

Given:
$$f\left(\frac{1 - x}{1 + x}\right) = x + 2$$

To Find: $f(1)$

Let $\frac{1 - x}{1 + x} = 1 \Rightarrow x = 0$

Then, $f(1) = f\left(\frac{1 - 0}{1 + 0}\right) = 0 + 2 = 2$

Answer: $$\boxed{2}$$

? Function with Greatest Integer and Cosine

Given:

$$f(x) = \cos\left([\pi^2]x\right) + \cos\left([-\pi^2]x\right)$$

Find: $$f\left(\frac{\pi}{2}\right)$$

Step 1: Estimate Floor Values

$$\pi^2 \approx 9.8696 \Rightarrow [\pi^2] = 9,\quad [-\pi^2] = -10$$

Step 2: Plug into the Function

$$f\left(\frac{\pi}{2}\right) = \cos\left(9 \cdot \frac{\pi}{2}\right) + \cos\left(-10 \cdot \frac{\pi}{2}\right) = \cos\left(\frac{9\pi}{2}\right) + \cos(-5\pi)$$

Step 3: Simplify

$$\cos\left(\frac{9\pi}{2}\right) = 0,\quad \cos(-5\pi) = -1$$

✅ Final Answer:

$$\boxed{-1}$$