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Q.

Let  f1(x)  andf2(x) be continuous and differentiable functions. If  f1(0)=f1(2)=f1(4),f1(1)+f1(3)=f2(0)=f2(2)=f2(4)=0  and if  f1(x)=0andf21(x)=0
  do not have common root, then the minimum number of zeros of  f11(x)f21(x)+f1(x)f211(x)in[0,4],is

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a

2

b

1

c

3

d

4

answer is C.

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Detailed Solution

f1(x)=0  has mini two solutions in  [0,4]
f2(x)=0  has mini 3 solutions in  [0,4]
f2'(x)=0  has mini 2 solutions in  [0,4]
f1(x)f2'(x)=0  has minimum 4 solutions in   [0,4]
ddx(f1(x)f2'(x))=0  has minimum 3 solutions in  [0,4]

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