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Using binomial theorem indicate which is...

Using binomial theorem indicate which is larger `(1. 1)^(10000)or\ 1000 ?`

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Verified by Experts

We have:
`(1.1)^{10000} `
`=(1+0.1)^{10000} `
`={ }^{10000} C_{0} times(0.1)^{0}+{ }^{10000} C_{1} times(0.1)^{1}+{ }^{10000} C_{2} times(0.1)^{2}+ldots{ }^{10000} C_{10000} times(0.1)^{10000} `
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Using binomial theorem evaluate each of the following: (101)^4

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  2. Using binomial theorem evaluate each of the following: (98)^5

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  3. Using binomial theorem indicate which is larger (1. 1)^(10000)or\ 1000...

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  4. Write the general term in the expansion of (x^2-y)^6dot

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  5. Find the 10th term in the binomial expansion of (2x^2+1/x)^(12)dot

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  6. Find the constant term in the expansion of ((4x^2)/3+3/(2x))^9.

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  7. Find 13th term in the expansion of (9x-1/(3sqrtx))^(18),\ x!=0.

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  8. Find the 11th term from the end in the expansion of (2x-1/(x^2))^(25)d...

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  9. Find n, if the ratio of the fifth term from the beginning to the fifth...

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  10. Find a if 17th and 18th terms in the expansion of (2+a)^(50) are eq...

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  11. Show that the middle term in the expansion of (1+x)^(2n)\ is =frac{1....

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  12. Prove that the coefficient of the middle term in the expansion of (1+x...

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  13. Find the coefficient of x^(10) in the binomial expansion of (2x^2-1/x)...

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  14. Find the coefficient of x^6y^3 in the expansion of (x+2y)^9dot

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  15. Find the coefficient of x^(40) in the expansion of (1+2x+x^2)^(27)dot

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  16. Find the coefficient of x^5 in the expansioin of the product (1+2x)^6(...

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  17. Find the term independent of x in the expansion of: (x-1/x)^(14) .

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  18. Find the term independent of x in the expansion of: \ (2x^2-3/x^3)^(10...

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  19. In the binomial expansion of (1+a)^(m+n) , prove that the coefficient ...

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  20. Prove that the coefficients of x^n in (1+x)^(2n) is twice the coeffici...

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