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Consider the equation x+y-[x][y]=0, wher...

Consider the equation x+y-[x][y]=0, where `[*]` is the greatest integer function.
The number of integral solutions to the equation is

A

(a) `x+y=-1`

B

(b) `x+y=0`

C

(c) `x+y=1`

D

(d) `x+y=5`

Text Solution

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The correct Answer is:
b
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ARIHANT MATHS-FUNCTIONS-Exercise (Passage Based Questions)
  1. Let f:R rarr R be a continuous function such that f(x)-2f(x/2)+f(x/4...

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  2. Consider the equation x+y-[x][y]=0, where [*] is the greatest integer ...

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  3. Consider the equation x+y-[x][y]=0, where [*] is the greatest integer ...

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  4. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

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  5. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

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  6. Let f(x)=1/2[f(xy)+f(x/y)] " for " x,y in R^(+) such that f(1)=0,f'(1)...

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  7. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  8. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  9. If f:R rarr R and f(x)=g(x)+h(x) where g(x) is a polynominal and h(x) ...

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  10. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

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  11. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3)andf(x)=sqrt(g(x)),f(x) have it...

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  12. Let g(x)=a(0)+a(1)x+a(2)x^(2)+a(3)x^(3) " and " f(x)=sqrt(g(x)), f(x) ...

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  13. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

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  14. Let f :[2,oo)to {1,oo) defined by f (x)=2^(x ^(4)-4x ^(3))and g : [(pi...

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  15. Let f:[2,infty) rarr [1, infty) defined by f(x)=2^(x^(4)-4x^(2)) and g...

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  16. Let P(x) be a polynomial of degree at most 5 which leaves remainders -...

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  17. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

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  18. Let P(x) be polynominal of degree atmost 5 which leaves remainders -1 ...

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  19. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

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  20. Consider alpha gt 1 and f:[1/alpha,alpha] rarr [1/alpha,alpha] be bije...

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