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Question

Match the entries of col. I with those of col. II.
ColumnIColumnII(a)f(x)=1x+x21+xx2 on [0,1](p)Greatest value of f=1(b)f(x)=2tanxtan2x on [0,π2](q)Least value of f=35(c)f(x)=2π(sin2xx) on [π2,π2](r)Least value of f=1(d)f(x)=12,(x33x2+6x2) on (1,1)(s)Least value of f=6


A

(a)(p),(b)(q),(c)(r),(d)(s)

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B

(a)(p,q),(b)(p),(c)(p,r),(d)(p,s)

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C

(a)(q),(b)(p),(c)(p),(d)(s)

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D

(a)(s),(b)(q),(c)(p,r),(d)(r,s)

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Solution

The correct option is B

(a)(p,q),(b)(p),(c)(p,r),(d)(p,s)


(a)(p,q),(b)(p),(c)(p,r),(d)(p,s)
(a)f(x)=2(2x1)(1+xx2)2 by quotient formula
f(x)=0x=12f(0)=1,f(1)=1butf(12)=35
Greatest value =1 (p), Least value =35(q)
(b)f(x)=2sec2x(1tanx)=0
tanx=1 or x=π4andf(π4)=21=1
(b)(p).(c)f(x)=2π(2cos2x1)=0cos2x=12=cosπ3x=π6f(c2)=1,f(π2)=1andf(π6)=3π13<1
greatest value =1 and least value =-1
(C)(p,r)(d)f(x)=32(x22x+2)=32[(x1)2+1]0
But f(-1)=-6,f(1)=1
Least value is -6 and greatest value is 1.
(d)(p,s)


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