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Consider the following statements : S...

Consider the following statements :
`S_(1):` The function `y=(2x^(2)-1)/(x^(4))` is neither increasing nor decreasing
`(S_(2):` if f(x) is strictly increasing real function defined on R and C is a real constant then number of Solutions of f(x) =c is always equal to one.
`S_(3):` Let f(x) =x : `x in (0,1)` , f(x) does not has any point of local maxima`//`minima
`S_(4):` f(x)={x} has maximum at x=6 (here{} denotes fractional part function)
State , in order ff whether `S_(1),S_(2),S_(3),S_(4)` are true or false

A

TTFT

B

FTFT

C

TFTF

D

TFFT

Text Solution

Verified by Experts

The correct Answer is:
C
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RESONANCE-APPLICATION OF DERIVATIVES-Exersise-2 Part I
  1. "Let "f(x) ={ underset( x^(2) +8 " "." "x ge0)(-x^(2)" "." "x lt0)...

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  2. Minunun distance between the curves f(x)=e^x and g(x)=ln x is

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  3. The point(s) on the parabola y^2 = 4x which are closest to the circlex...

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  4. If f(x)= a^({a^(|x|)sgn x }),g(x)=a^([a^(|x|)sgn x] for a gt 1, a!=1...

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  5. If f:[1,10]->[1,10] is a non-decreasing function and g:[1,10]->[1,10] ...

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  6. If f(x)=|ax-b|+c|x| is stricly increasing at atleast one point of non ...

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  7. If g(x) is a curve which is obtained by the reflection of f(x) = (e^x...

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  8. The set of values of p for which the points of extremum of the functio...

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  9. The values of parameter a for which the point of minimum of the functi...

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  10. Consider the following statements : S(1): The function y=(2x^(2)-1)...

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  11. Q. Let f (x)=sin^3x+ lambdasin^2x where (pi)/2 ltxlt (pi)/2. The inte...

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  12. "Let "f(x) ={underset(-2x + log(2) (b^(2)-2), x gt1)(x^(3) -x^(2) +10 ...

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  13. Four points A, B, C, D lie in that order on the parabola y = ax^2 +bx+...

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  14. The base of prism is equilateral triangle. The distance from the centr...

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  15. The maximum area of the rectangle whose sides pass through the vertice...

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  16. Statement 1: ABC is given triangle having respective sides a,b,c. D,E,...

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  17. if f'(x)=(x -4) (x-5) (x-6) (x-7) then.

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  18. Show that the square roots of two successive natural numbers greater ...

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  19. If Rolle's theorems applicable to the function f(x)=ln x/x, (x> 0) ove...

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  20. if f(x) be a twice differentiable function such that f(x) =x^(2) " fo...

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