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Let f (x) =||x^(2)-4x+3|-2|. Which of th...

Let `f (x) =||x^(2)-4x+3|-2|.` Which of the following is/are correct ?

A

`f (x)=` m has exactly two real solutios of different sign `AA m gt2`

B

`f (x)=m` has exactly two real solution `AA m in (2,oo) uu{0}`

C

`f (x)=m` has no solutions `AA m lt 0`

D

`f(x)=m` has four distinct real solution `AA m in (0,1)`

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The correct Answer is:
A, B, C
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VK JAISWAL-FUNCTION -ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT
  1. f (x) is an even periodic function with period 10 In [0,5], f (x) = {{...

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  2. Let f (x) =||x^(2)-4x+3|-2|. Which of the following is/are correct ?

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  3. Let f (x) =cos &^(-1) ((1=-tan ^(2)(x//2))/(1+ tan ^(2) (x//2))) Whi...

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  4. |log (e)|x|| =|k -1| -3 has four distict roots then k satisfies : (whe...

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  5. Which of the following funjctions are difined for all x in R ? (Wher...

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  6. Let f (x)= {{:(x ^(2),0lt x lt2),(2x-3, 2 le x lt3),(x+2, x ge3):} the...

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  7. Let f: [(2pi)/(3), (5pi)/(3)]to[0,4] be a function difined as f (x) =s...

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  8. Let f (x) be invertible function and let f ^(-1) (x) be is inverse. Le...

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  9. Find the value of cos^(-1)((x)/(2)+(sqrt(3-3x^(2)))/(2))

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  10. Let f:R rarr R defined by f(x)=cos^(-1)(-{-x}), where {x} denotes fra...

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  11. Which option (s) is/are ture ?

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  12. If f (x) =[ln (x)/(e) +[ln (e)/(x)], where [.] denotes greatest interg...

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  13. If f (x0= {{:(x ^(3), , x ne Q),(-x ^(3),,x ne Q):}, then :

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  14. Let f(x) be a real valued function such that f(0)=1/2 and f(x+y)=f(x)f...

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  15. f (x) is an even periodic function with period 10 In [0,5], f (x) = {{...

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  16. For the equation (e ^(-x))/(1+x)= lamda which of the following stateme...

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  17. . For x in R^+, if x, [x], {x} are in harmonic progression then the va...

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  18. The equation ||x-1|+a | =4,a in R, has :

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  19. Let f (n)(x) = (sin x )^(1//pi) , x in R, then:

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  20. If the domain of f (x) =1/picos ^(-1)[log (3) ((x^(3))/(3))] where, x ...

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