IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q7

If the following function $f(x)$ is continuous at $x=0$ , then which of the option/s can be true (not necessary simultaneously)?

$f(x)=\begin{cases} \Large \frac{\sin[a(x+1)]+\sin x}{x}, \normalsize x<0 \\ c, x=0\\ \Large \frac{(x+bx^2)^{1/2}-x^{1/2}}{bx^{3/2}}, \normalsize x>0 \end{cases}$

• (A) a = 1/2
• (B) b = 2
• (C) c = 1/2
• (D) f(1) = 1/3

Enter your answer as a 4 digit string of 1s and 9s - 1 for correct option, 9 for wrong. Eg. 1199 indicates A and B are correct, C and D are incorrect. None, one or all may also be correct.

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