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Q.

Column – 1

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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
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