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In the expansion of (x +a)^n, the sums o...

In the expansion of `(x +a)^n`, the sums of the odd and the even terms are O and E respectively, prove that : `O^2-E^2= (x^2-a^2)^n`.

A

`(a^2-x^2)^n`

B

`(a^2-x^2)^(2n)`

C

`(a^2+ x^2)^(2n)`

D

`(a^2+ x^2)^(n)`.

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MODERN PUBLICATION-BINOMIAL THEOREM-EXERCISE
  1. If the three consecutive coefficients in the expansion of (1 + x)^n ar...

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  2. Let (1 + x)^n= C0+C1x+C2x^2+.....+Cn x^n and C1/C0+2 C2/C1+3 C3/C2+......

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  3. In the expansion of (x +a)^n, the sums of the odd and the even terms a...

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  4. The 5th term from the end in the expansion of (x^3/2-2/x)^12 is :

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  5. In the binomial expansion of (a -b)^n, nge5, the sum of the 5th and 6t...

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  6. The value of C (47, 4) + underset (r=1) overset (5) sum (52-r,3) is:

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  7. 7^9+9^7 is divisible by :

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  8. Find the term independent of x in the expansion of : ((x+1)/(x^(2//3)-...

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  9. Product of any r consecutive natural numbers is always divisible by :

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  10. If C0,C1,C2,........, Cn denote the coefficients in the expansion of (...

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  11. A polygon has 44 diagonals. The number of the sides is :

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  12. Find 'a' if the coefficients of x^(2) and x^(3) in the expanion of (3 ...

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  13. Using binomial theorem. the value of (0.999)^3,correct to 3 decimal pl...

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  14. The coefficient of x^n, where n is any positive integer, in the expans...

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  15. If ""^(2n+1)P(n-1): ""^(2n-1)Pn =3:5 then the value of n equals :

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  16. If|x|<1, then the coefficient of x^6 in the expansion of (1+x + x^2)^-...

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  17. ""^15C0.""^5C5+""^15C1.""^5C4+""^15C2.""^5C3+ ""^15C3.^5C2+""^15C4.""^...

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  18. Every body in a room shakes hand with every body else. The total numbe...

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  19. ""^15C8+""^15C9-""^15C6-""^15C7=

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  20. If the rth term in the expansion of (x/3-2/x^2)^10 contains x^4, then ...

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