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Let f (x) =x ^(2) -4x +c AA x in R, wher...

Let `f (x) =x ^(2) -4x +c AA x in R,` where c is a real constant, then which of the following is/are true ?

A

`f (0) gt f (1) gt f (2)`

B

`f (2) gt f (3) gt f(4)`

C

`f (1) lt f (4) lt f (-1)`

D

`f (0) =f (4) gt f(3)`

Text Solution

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The correct Answer is:
A, C, D
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VK JAISWAL ENGLISH-QUADRATIC EQUATIONS -EXERCISE (ONE OR MORE THAN ONE ANSWER IS/ARE CORRECT)
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  2. Given a,b, c are three distinct real numbers satisfying the inequality...

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  3. Let f (x) =x ^(2) -4x +c AA x in R, where c is a real constant, then w...

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  5. If satisfies |x-1| + |x-2|+|x-3|gt6, then :

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  6. If both roots of the quadratic equation ax ^(2)+x+b-a =0 are non real ...

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  7. If a,b are two numbers such that a ^(2) +b^(2) =7 and a ^(3) + b^(3) =...

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  8. The number of non-negative integral ordered pair(s) (x,y) for which (x...

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  9. If alpha, beta, gamma and delta are the roots of the equation x ^(4) -...

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  11. For which of the following graphs the quadratic expression y=ax^(2)+bx...

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  12. If a x^2+b x+c=0,a ,b ,c in R has no real zeros, and if c<o , then wh...

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  13. If alpha and beta are the roots of the equation ax ^(2) + bx + c=0,a,b...

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  14. The equation cos ^(2) x - sin x+lamda = 0, x in (0, pi//2) has roots t...

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  15. If the equation ln (x^(2) +5x ) -ln (x+a +3)=0 has exactly one solutio...

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  16. The number of non-negative integral ordered pair (s) (x,y) for which ...

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  17. For a<0, determine all real roots of the equation x^2-2a|x-a|-3a^2=0.

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  18. If 0 lt a lt b lt c and the roots alpha,beta of the equation ax^2 +...

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  19. Solve : | x - 1| + |x - 2| + | x - 3 | gt 6

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