Which of the following functions is not periodic?
(a) `|sin 3x| +sin^(2)x " (b) " cos sqrt(x)+cos^(2)x`
(c ) `cos 4x +tan^(2)x " (d ) " cos 2x + sinx`

Explanation

To determine which of the given functions is not periodic, we need to analyze each option one by one. A function is periodic if it repeats its values at regular intervals, which is not the case for all functions.

### Step-by-Step Solution:

1. **Option (a): \( | \sin(3x) | + \sin^2(x) \)**
- The function \( | \sin(3x) | \) is periodic with a period of \( \frac{2\pi}{3} \).
- The function \( \sin^2(x) \) is also periodic with a period of \( \pi \).
- Since both components are periodic, their sum \( | \sin(3x) | + \sin^2(x) \) is periodic.

2. **Option (b): \( \cos(\sqrt{x}) + \cos^2(x) \)**
- The function \( \cos(\sqrt{x}) \) is not periodic because as \( x \) increases, \( \sqrt{x} \) increases without bound, and thus \( \cos(\sqrt{x}) \) does not repeat its values.
- The function \( \cos^2(x) \) is periodic with a period of \( \pi \).
- However, since one part is not periodic, the entire function \( \cos(\sqrt{x}) + \cos^2(x) \) is not periodic.

3. **Option (c): \( \cos(4x) + \tan^2(x) \)**
- The function \( \cos(4x) \) is periodic with a period of \( \frac{\pi}{2} \).
- The function \( \tan^2(x) \) is periodic with a period of \( \pi \).
- Since both components are periodic, their sum \( \cos(4x) + \tan^2(x) \) is periodic.

4. **Option (d): \( \cos(2x) + \sin(x) \)**
- The function \( \cos(2x) \) is periodic with a period of \( \pi \).
- The function \( \sin(x) \) is also periodic with a period of \( 2\pi \).
- Since both components are periodic, their sum \( \cos(2x) + \sin(x) \) is periodic.

### Conclusion:
From the analysis above, the function that is not periodic is **Option (b): \( \cos(\sqrt{x}) + \cos^2(x) \)**.