IIT JEE 1982 Maths - 'Adapted' - Subjective to Multi-Correct Q13

If f(x) and g(x) are differentiable functions for $0≤x≤1$ such that f(0)=2, g(0)=0, f(1)=6, g(1)=2, then which of the following are definitely not false for some $0<c<1$ ? ('c' in one option may be different from 'c' in another.)

• (A) f'(c)-f(0)=g'(c)
• (B) f'(c)-g(0)=2g'(c)
• (C) f'(c)+f(1)=3g'(c)
• (D) f'(c)+2g(1)=4g'(c)

Enter your answer as a 4-digit string of 1s and 9s – 1 for correct option, 9 for wrong. For example: if $A$ and $B$ are correct, and $C$ and $D$ are incorrect, enter 1199. None, one or all may also be correct.

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