Section 3 (Maximum Marks: 12)

• This section contains TWO (02) List-Match Sets.

• Each List-Match set has TWO(02) Multiple Choice Questions.

• Each List-Match set has two lists: List-I and List-II.

• List-I has Four entries (I), (II), (III) and (IV) and List-II has Six entries (P), (Q), (R), (S), (T) and (U).

• FOUR options are given in each Multiple Choice Question based On List-I and List-II and ONLY ONE of these four options satisfies the condition asked in the Multiple Choice Question.

• Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the option corresponding to correct combinatioin is chosen;

Zero Marks : 0 If none of the options is chosen (i.e., the question is unanswered);

Zero Marks : -1 In all other cases.

Answer the following by appropriately matching the lists based on the information given in the paragraph

Let f(x) = sin( cosx) and g(x) = cos(2 sinx) be two functions defined for x > 0. Define the following sets whose elements are written in the increasing order:

X = {x : f(x) = 0}, Y = {x : f (x) = 0},

Z={x:g(x) = 0},W={x:g'(x) = 0}

List -I contains the set X, Y, Z and W. List - II contains some information regarding these sets. List -I List - II

(I) X (P)

(II) Y (Q) an arithmetic progression

(III) Z (R) NOT an arithmetic progression

(IV) W (S)

(T)

(U)

(i) Which of the following is the only CORRECT combination?