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If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x when ...

If `f(x)=sin[pi^(2)]x+sin[-pi^(2)]x` when `[x]` is the step function, then `f(pi//6)=`

A

`-1+sqrt3//2`

B

`1+sqrt3//2`

C

`1-sqrt3//2`

D

1

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DIPTI PUBLICATION ( AP EAMET)-FUNCTIONS-EXERCISE 1A(FUNCTIONS)
  1. For any integer n ge1, the number of positive divisors of n is denoted...

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  2. If NN denotes the set of all positive integers and if f:NN rarrN is d...

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  3. If f(x)=sin[pi^(2)]x+sin[-pi^(2)]x when [x] is the step function, then...

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  4. If f(x) is a polynomial fin x( gt0) satisfying the equation f(x)+f(1//...

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  5. If f(x) is a polynomial function x>0 such that f(x)f(1//x)=f(x)+f(1//x...

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  6. If f(x) is a polynomial function such that f(x)f((1)/(x))=f(x)+f((1)/(...

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  7. If f(x) is a function such that f(x+y)=f(x)f(y) and f(5) =125 " then "...

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  8. If f(x) is a function such that f(xy)=f(x)+f(y) and f(2)=1 then f(x)=

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  9. If f(x)=cos(logx), then show that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/...

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  10. If f(x)=sin(logx), then f(xy)+f(x//y)-2f(x)cos (logy)=

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  11. If f(n)(x)-(tan.(x)/(2))(1+secx)(1+sec 2x)……(1+sec2^(n)x) then which o...

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  12. If f:A rarrR is defined as f(x)=x^(3)+1 and A={1, 2, -1, -2, 0} then t...

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  13. If f:ArarrR is defined as f(x)=cosx and A={0, pi//6, pi//4, pi//3} the...

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  14. If f:ArarrR is defined as f(x)=tan(x//2) and A{pi//2, pi//3, 2pi//3} t...

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  15. If A={3, 0, 1, 2} and f:A rarr B is an onto function defined by f(x)=3...

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  16. If f:[2, oo)rarrB defined by f(x)=x^(2)-4x+5 is a bijection, then B=

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  17. If f:RR rarr RR is defined by f(x)=x-[x] -(1)/(2)" for "x in RR, where...

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  18. If f:RR rarr RR is defined by f(x)=[(x)/(2)] for x in RR, where [y] de...

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  19. A={1,2,3,4,5}, B={1, 4, 7, 10, 13}. If f from A into B defined by f(x)...

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  20. A={-1, 0, 2, 5, 6, 11}, B={2, -1, 1, 0, 11, 108} and f(x)=x^(2)-x-2, t...

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