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Q.

Match the following :

Column-IColumn-II
A) The value of ‘c’ in LMVT for f(x)=x25x on [0, 2] isp) 0
B) The value of ‘c’ in the Rolle’s Theorem for f(x)=log(x2+3613x) on [4, 9] isq) 1
C) The value of ‘c’ in the Rolle’s Theorem for f(x)=x2 on [1,1] isr) 3
D) The value of ‘c’ in the Rolle’s Theorem for f(x)=cosx on (π2,π2)s) 6

The correct matching

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a

A-p, B-q, C-s, D-p

b

A-s, B-q, C-r, D-s

c

A-q, B-s, C-p, D-p

d

A-r, B-q, C-s, D-p

answer is B.

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Detailed Solution

f(x)=x25z,x[0,2]

f(x) is continuous and differentiable

f(2)f(0)20=f(c) for some c(0,2) i.e.,

62=f(c) 2c5=3 c=1

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