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Using binomial theorem , Prove that 2^(3...

Using binomial theorem , Prove that `2^(3n)-7n-1` is divisible by 49.

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KUMAR PRAKASHAN-BINOMIAL THEOREM -PRACTICE WORK
  1. Using binomial theorem , Evaluate the following : (98)^(5)

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  2. Find (x+y)^(5)+(x-y)^(5) . Hence evaluate (sqrt(2)+1)^(5)+(sqrt(2)-1)^...

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  3. Using binomial theorem , Prove that 2^(3n)-7n-1 is divisible by 49.

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  4. Using binomial theorem ,Prove that 3^(3n)-26n -1 is divisible by 676.

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  5. Using binomial theorem , Prove that a^(n)-b^(n) is divisible by (a-b)

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  6. Prove that , (101)^(50) gt 100^(50)+99^(50)

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  7. Evaluate : (1.01)^(10)+(1-0.01)^(10)

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  8. Find the coefficient of : x^(4) " in " (2x+5)^(8)

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  9. Find the coefficient of : y^(5) " in " (3y^(2)+1/(3y))^(10)

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  10. Find the coefficient of : x^(10) " in " (x^(2)-2)^(11)

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  11. Find the coefficient of : x^(40) " in " (1^(2)+2x)^(20)

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  12. Find the coefficient of : x^(11) " in " (x^(3)-2/(x^(2)))^(12)

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  13. Find the general term in the expansion of (5x-3)^(12)

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  14. Find the general term in the expansion of (z^(2)-3/(z^(2)))^(35)

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  15. Find the general term in the expansion of (x+3y)^(10)

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  16. Find the general term in the expansion of (y^(2)+6y+9)^(20)

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  17. Find the general term in the expansion of (3y+6z)^(9)

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  18. Find the 6^(th) term in expansion of ((x^(3))/2-2/(x^(2)))^(9)

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  19. Find the 7^(th) term in the expansion of (x+3y)^(8)

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  20. Find the 7^(th) term in the expansion of (3x - (2y)/3)^(10)

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