WBJEE PYQs for Continuity with Solutions: Practice WBJEE Previous Year Questions

The values of $a, b, c$ for which the function $f(x) = \begin{cases} \sin((a + 1)x) + \sin x, & x<0 \\ c, & x = 0 \\ \frac{(\sqrt{x + bx^2}) - \sqrt{x}}{bx^{1/2}}, & x > 0 \end{cases}$ is continuous at $x = 0$, are

Let \( f: [0, 1] \to \mathbb{R} \) and \( g: [0, 1] \to \mathbb{R} \) be defined as follows:
 
The function \( f(x) \) is defined as:
\[ f(x) = \begin{cases} 1 & \text{if } x \in \mathbb{Q} \cap [0, 1] \\ 0 & \text{if } x \in (\mathbb{R} \setminus \mathbb{Q}) \cap [0, 1] \end{cases} \]
The function \( g(x) \) is defined as:
\[ g(x) = \begin{cases} 0 & \text{if } x \in \mathbb{Q} \cap [0, 1] \\ 1 & \text{if } x \in (\mathbb{R} \setminus \mathbb{Q}) \cap [0, 1] \end{cases} \]
Then: