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a
A-P,Q,R, B-S,T, C- P,Q, D-R
b
A-P,B-Q,C-R,D-T
c
A-P,Q,R,B-P,C-S,T,D-P
d
A-PQRS, B-P.Q.R, C-P,Q,R,S,T, D- P, Q
answer is D.
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Detailed Solution
(A) I=∫0π4sin3x·cos3xcdx=18∫0π4sin32xdx=116∫0π2sin3x dx=124 BI =∫02π2 sinxdx =∫02π2 sin2π-xdx =∫02π-2sinxdx I+I =∫02π2sinx+-2sinxdx I+I=∫02π-1dx since x+-x=-1 if x is not an integer I=-π⇒I=4 , (C) I=∫-31sgnx dx=∫-30-1dx+∫011dx=-3+1=-2 (D) I=∫01x3+1-2x+1dx=∫01x2-x+1-2x+1dx =13-12+1-2 log2=56-log 4 now -2I-log 16=-53=-2=2