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The coefficient of x^p in the expansion ...

The coefficient of `x^p` in the expansion of `(x^2+(1)/(x))^(2n)` is

A

`((2n)!)/(((4n-p)!)/(3!).((2n-p)!)/(3!))`

B

`((2n)!)/(((4n-p!)/(3))!.((2n+p!)/(3))!`

C

`((2n)!)/(((4n+p!)/(3))!.((2n-p!)/(3))!`

D

`((2n)!)/(((4n+p!))/(3!).((2n+p!))/(3!)`

Text Solution

Verified by Experts

The correct Answer is:
B
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DIPTI PUBLICATION ( AP EAMET)-BINOMIAL THEOREM-EXERCISE 1A (BINOMIAL THEOREM WITH INTEGRAL INDEX)
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  2. If P and Q are the sum of odd terms and the sum of even terms respecti...

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  3. The coefficient of x^p in the expansion of (x^2+(1)/(x))^(2n) is

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  4. If T0, T1, T2, … Tn represent the terms in the expansion of (x+a)^n, t...

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  5. The expansion [x+(x^3-1)^(1//2)]^5+[x-(x^3-1)^(1//2)]^5 is a polynomia...

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  6. If (1)/(sqrt(4x+1)){(1+(sqrt(4x+1))/(2))^n-(1-(sqrt(4x+1))/(2))^n}=a0+...

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  7. (sqrt2+1)^6+(sqrt2-1)^6=

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  8. Larger of 99^50+100^50 and 101^50

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  9. Larger of 199^100+200^100 and 201^100 is

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  10. 11^9+9^11 is divided by

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  11. If n is a positive integer then 11^n-10n-1 is divided by

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  12. If n is a positive integer then 49^n + 16n-1 is divided by

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  13. The remainder when 2^2000 is divided by 17 is

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  14. The remainder left out when8^(2n)-(62)^(2n+1) is divided by 9 is

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  15. If (3+sqrt8)^n - I+F where In are positive integer , 0 lt F lt 1 then ...

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  16. If (4+sqrt15)^n=I+F when I, n are positive integers, 0 lt F lt 1 then ...

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  17. If (7+4sqrt3)^n=I+F where I and n are +ve integers and F is +ve proper...

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  18. Let R=(5 sqrt5+11)^(2n+1) , f=R-[R]. Then Rf=

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  19. If (6 sqrt6+14)^(2n+1)=R and F=[R], where [R] denotes the greatest int...

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

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