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Let R=(2+sqrt3)^(2n) and f=R-[R] where [...

Let `R=(2+sqrt3)^(2n) and f=R-[R]` where [ ] denotes the greatest integer function , then `R(1-f)=`

A

1

B

`2^2n`

C

`2^(2n)-1`

D

`""^(2n) C_n`

Text Solution

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The correct Answer is:
A
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1A (BINOMIAL THEOREM WITH INTEGRAL INDEX)
  1. If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest int...

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  2. If R=(5 +sqrt21)^(2n+1) and f=R-[R], where [R] denotes the greatest in...

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  3. Let R=(2+sqrt3)^(2n) and f=R-[R] where [ ] denotes the greatest intege...

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  4. For natural numbers m, n if (1-y)^m (1+y)^n=1+a1 y +a2 y^2 + …, and a1...

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  5. The middle term in the expansion of (x+(1)/(x))^10 is

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  6. The middle term of (a//x-x//a)^10 is

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  7. Middle term in the expansion of (2x-(3)/(x))^15 is

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  8. The middle term of (x+(1)/(x))^(2n) is

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  9. The middle terms of ((x^(3//2)y)/(2)+(2)/(xy^(3//2)))^13 are

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  10. The middle terms of (3x^2+5//x^3)^11 are

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  11. The middle term of (1-3x+3x^2-x^3)^(2n) is

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  12. If the middle term of (1+x)^ (2n) is (1.3.5….(2n-1)k)/(n!) then k=

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  13. The greatest coefficient of (1+x)^10 is

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  14. The greatest coeff. of (x//y+y//x)^(2n+1) is

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  15. The value of the greatest term in sqrt3(1+1//sqrt3)^(20) is

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  16. The coefficient of the middle term in the binomial expansion in powers...

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  17. If the middle term in the expansion of (1+x)^(2n) is the greatest term...

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  18. Which term is the numerically greatest in (1-3x)^10 when x=1//2 ?

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  19. Which term of (2x-3y)^12 when x=1, y=5//2 numerically greatest ?

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  20. The numerically greatest term of (3x+2y)^11 when x=2//3, y=3//4 is

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