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Find the 6th term in the expansion of (x...

Find the 6th term in the expansion of `(x^2+a^4/y^2)^10`.

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6th term i.e. (5+1)th term in the expansion of
`(x^2+a^4/y^2)^10` is `"^10C_5(x^2)^10-5(a^4/y^2)^5`
`= 10!/5!5!x^10(a^20/y^10) `
` = 10.9.8.7.6/5.4.3.2.1(x^10a^20)/y^10= 252x^10a^20/y^10`
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MBD PUBLICATION-Elements of Mathematics-QUESTION BANK
  1. Find the middle term in the expansion of the (x+1/x)^9

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  2. Find the middle term in the expansion of the (x^(3/2)-y^(3/2))^8

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  3. Find the 6th term in the expansion of (x^2+a^4/y^2)^10.

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  4. Find the fifth term in the expansion of (6x-a^3/x)^10

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  5. Find the coefficient of 1/y^10 in the expansion of (y^3+a^7/y^5)^10

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  6. In the expansion of (y^3+a^7/y^5)^10, Does there exist a term indepen...

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  7. Find the coefficient of x^4 in the expansion of (1+3x+10x^2)(x+1/x)^10

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  8. Find the term independent of x in the above expansion. (1+3x+10x^2)(x+...

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  9. Show that the coefficient of a^m and a^n in expansion of (1+a)^(m+n) a...

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  10. An expression of the form (a+b+c+d+ .... ) consisting of sum of many d...

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  11. State and prove a multinomial Theorem.

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  12. Prove that "^(2n)C0 + ^(2n)C2 + .... + ^(2n)C(2n) = 2^(2n-1)

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  13. Prove that "^(2n)C1 + ^(2n)C3 + .... + ^(2n)C(2n-1) = 2^(2n-1)

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  14. Find the sum of C1 + 2C2 + 3C3 + .... + nCn

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  15. Find the sum of C0 + 2C1 + 3C2 + .... + (n+1)Cn

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  16. Compute ((1+k)(1+k/2) ..... (1+k/n))/((1+n)(1+n/2) ..... (1+n/k))

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  17. Show that C0 C1 + C1 C2 + C2 C3 + .... + C(n-1) Cn = (2n!)/((n-1)!(n...

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  18. C0 C1 + C1 C2 + .... + C(n-1) Cn = (2^n.n.1.3.5... (2n-1))/(n+1)

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  19. Show that 3C0-8C1 + 13C2 - 18C3 + ..... + (n+1)^(th) term = 0

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  20. Show that C0 n^2 + C1 (2-n)^2 + C2 (4-n)^2 + .... + Cn (2n-n)^2 = n.2^...

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