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Using binomial theorem, indicate which i...

Using binomial theorem, indicate which is larger `(1. 1)^(10000)or1000 ?`

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Let,`(1.1)^10000=(1+0.1)^10000`
=`10000_(C_0)​​+10000_(C_1)​​(1.1) + `other positive terms
=`1+10000 xx 1.1 + `other positive terms
=`1+11000 +` other positive terms
...
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RD SHARMA-BINOMIAL THEOREM-Solved Examples And Exercises
  1. Find the 9th term in the expansion of (x/a-(3a)/(x^2))^(12) .

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  2. Find the 4th term from the end in the expansion of (3/(x^2)-(x^3)/6)^7...

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  3. Using binomial theorem, indicate which is larger (1. 1)^(10000)or1000 ...

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  4. Show that 2^(4n+4) -15n-16, where n in N is divisible by 225.

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  5. Show that the middle term in the expansion (1+x)^(2n)i s (1. 3. 5 (2n...

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  6. Find the coefficients of x^(32) in the expansion of (x^4-1/(x^3))^(15)...

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  7. Find the middle term in the expansion (2/3x^2-3/(2x))^(20) .

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  8. Find the middle terms in the expansion (3x-(x^3)/6)^7 .

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  9. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(6)dot

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  10. The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)...

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  11. Prove that there is no term involving x^6 in the expansion of (2x^2-3...

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  12. Find the term independent of x in the expansion of (3x^2-1/(2x^3))^(10...

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  13. Find the coefficient of x^(50) after simplifying and collecting the li...

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  14. Find the coefficient of x^n in the expansion of (1+x)(1-x)^ndot

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  15. If a1,a2, a3, a4 be the coefficient of four consecutive terms in the e...

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  16. Find the number of integral terms in the expansion of (5^(1/2)+7^(1/8)...

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  17. Find the coefficients of x^7 in (a x^2+1/(b x))^(11)a n dx^(-7)in(a x^...

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  18. Find the coefficient of x^5 in the expansion of (1+x)^(21)+(1+x)^(22)+...

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  19. If the middle term in the binomial expansion of (1/x+xsinx^(10)) is eq...

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  20. Find the greatest value of the term independent of x in the expansion ...

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