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if-f-x-gt-0-forall-x-epsilon-r-then-for-any-two-real-numbers-7



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Q1.
If f(x) be a continuous function defined for 1x3,f(x)ϵQxϵ[1,3],f(2)=10, (where Q a set of all rational numbers) then f(1.8) is 
  1. 20
  2. 1
  3. 10
  4. 5
Q2.
If f(x) be a polynomial of degree 8 such that f(x)=f(4x) xϵR, f(x) has 6 distinct real and equal roots then sum of roots of f(x)=0 is A. Then the number A is:
Q3.
Let f and g be real-valued functions such that
f(x+y)+f(xy)=2f(x)g(y)x,yϵR
if f is not identically zero and f|(x)|1,xϵR, then |g(y)|1,yϵR.
If true enter 1 else enter 0


  1. True
  2. False
Q4.
Let f and g be real valued functions such that f(x+y)+f(x-y)=2f(x).g(y)x,yϵR. Prove that, if f(x) is not identically zero and |f(x)|1xϵR, then |g(y)|1yϵR.
Q5.
Assertion :If f(x)=[x](sinxcosx+2) (where [.] denotes the greatest integer function) then f(x)=[x](cosx+sinx) for xϵZ Reason: f(x) does not exist for any xϵ integer
  1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
  2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
  3. Assertion is correct but Reason is incorrect
  4. Both Assertion and Reason are incorrect

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