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Q.

Column-II contains the number of solutions of the functions given in Column-I.  Match them correctly.

 Column-I Column-II
A)fx=sin2x+sin2x+π3+cosxcosx+π3   &  g54=1thengfx=P)2
B)If f(x)=[x]+r=12019xr[xr]2019, then f(4)=____, where [.] denotes GREATEST INTEGER FUNCTION AND {.} denotes FRACTIONAL PART FUNCTIONQ)6
C)Number of solutions of sinxsec2x1=23 in x(5π2,7π2) are____R)1
D)The number of values of 'x' such that x,[x],{x} are in arithmetic Progression, where [.] denotes GREATEST INTEGER FUNCTION and {.} denotes FRACTIONAL PART FUNCTION are_____ S)4

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a

A-R, B-S, C-Q, D-P

b

A-Q, B-S, C-Q, D-P

c

A-Q, B-R, C-P, D-Q

d

A-R, B-R, C-P, D-Q

answer is B.

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Detailed Solution

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(B) f(x)=[x]+{x}=x

(C) sin|tanx|=23sinx>0

If xQ1,we get cosx=23 which gives 1 solution

If xQ2,we get cosx=23 which gives 1 solution

(D) 2[x]=x+{x}[x]=2{x}[x]=0,1

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