The integral

$$ \frac{1}{\pi} \int\limits_0^{\infty} \frac{x^{2026}}{\left(1+x^{2026}\right)\left(1+x^2\right)} d x $$

evaluates to $\_\_\_\_$

(Round off to two decimal places)

Let $f(t)$ be a real-valued function whose second derivative is positive for $- \infty < t < \infty$. Which of the following statements is/are always true?

Consider the function $f(t) = (\text{max}(0,t))^2$ for $- \infty < t < \infty$, where $\text{max}(a,b)$ denotes the maximum of $a$ and $b$. Which of the following statements is/are true?

Consider the following equation in a 2-D real-space.

$$|{x_1}{|^p} + |{x_2}{|^p} = 1$$ for $$p > 0$$

Which of the following statement(s) is/are true.