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If [x] and {x} represent the integral an...

If `[x]` and `{x}` represent the integral and fractional parts of `x ` respectively, then the value of `sum_(r=1)^(2000)({x+r})/(2000)` is

A

`(2001)/(2)x`

B

`x+2000`

C

`x`

D

`[x]+(2001)/(2)`

Text Solution

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The correct Answer is:
C
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OBJECTIVE RD SHARMA ENGLISH-REAL FUNCTIONS -Chapter Test
  1. The period of f(x)=sin((pix)/(n-1))+ cos ((pix)/(n)), n in Z, n gt 2,...

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  2. The function f(x)=((1)/(2))^(sinx), is

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  3. If [x] and {x} represent the integral and fractional parts of x respe...

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  4. Let f(x)={{:( 0,x=0),(x^(2) sin pi//2x,|x| lt 1),(x|x|, |x| ge 1):}. T...

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  5. Let f(x)=x+1 and phi(x)=x-2. Then the value of x satisfying |f(x)+phi(...

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  6. The domain of definition of the function f(x)=tan((pi)/([x+2])), is wh...

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  7. The range of the function f(x)=sin [log (sqrt(4-x^(2))/(1-x)) is :

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  8. The range of the function y=(x+2)/(x^2-8x-4)

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  9. The range of the function f(x)=1+sinx+sin^(3)x+sin^(5)x+…… when x in ...

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  10. The period of the function f(x)=|sin 3x|+| cos 3x| , is

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  11. The function f(x)={{:( 1, x in Q),(0, x notin Q):}, is

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  12. Which of the following functions has period pi ?

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  13. The function f(x)=x[x] , is

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  14. If f(x) and g(x) are periodic functions with the same fundamental per...

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  15. The range of the function f(x)=cosec^(-1)[sinx] " in " [0,2pi], where ...

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  16. If f(sinx)-f(-sinx)=x^(2)-1 is defined for all x in R , then the val...

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  17. Let f:[pi,3pi//2] to R be a function given by f(x)=[sinx]+[1+sinx]+[2...

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  18. Let the function f(x)=3x^(2)-4x+8log(1+|x|) be defined on the interval...

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  19. If f:[-4,0]->R is defined by f(x) = e^x + sin x, its even extension to...

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  20. Which one of the following is not periodic ?

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