, , and and differentiate at x = 0 if a = 0 and b = 1

, will result in - 2 marks, as a wrong option is also darkened. Let a, b R and f : R R be defined by f(x) = a cos(|x 3 - x|) + b|x| sin(|x 3 + x|). Then f is differentiate at x = 1 if a = 1 and b = 0

and and NOT differentiate at x = 0 if a = 1 and b = 0

. ONE OR MORE THAN ONE of these four option(s) is(are) correct. • For each question, marks will be awarded in one of the following categories : Full Marks : +4 If only the bubble(s) corresponding to the correct option(s) is(are) darkened. Partial Marks : + 1 For darkening a bubble corresponding to each correct option, provided NO incorrect option is darkened. Zero Marks : 0 If none of the bubbles is darkened. Negative Marks : -2 In all other cases. • For example, if are all the correct options for a question, darkening all these three will result in +4 marks; darkening only will result in +2 marks; and darkening NOT differentiate at x = 1 if a = 1 and b = 1