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With the help of bionomial theorem expan...

With the help of bionomial theorem expansion, show that `(4^(n)-3n)` is always leaves remainder 1, when divided by 9.

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AAKASH INSTITUTE-BINOMIAL THEOREM-Try Yourself
  1. What is the last entry of any row of pascle's triangle?

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  2. What is the 6th sicth entry in row 5 of pascle's triangle?

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  3. Expand (i) (x/3+3y/2)^(5) ,(ii) (x^(2)+2/x)^(4) using pascle's trian...

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  4. Expand (2x^(2) + 4y^(2))^(6) using pascals triangle.

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  5. Expand (i) (x+1/x)^(7) , (ii) (x^(2)+2/x)^(4) using binomial theorem.

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  6. Expand (i) ((2x)/3-(3)/(2x))^(6) , (ii) (2/x-x/2)^(5)

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  7. Byusing binomial theorem evaluate (i) (101)^(3) , (ii) (47)^(4)

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  8. Byusing binomial theorem evaluate (i) (107)^(5) , (ii) (55)^(3)

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  9. Using bionomial theorem, show that (9^(n)-8n-1) is always divisible by...

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  10. With the help of bionomial theorem expansion, show that (4^(n)-3n) is ...

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  11. Find (1+x)^(4) + (1-x)^(4). Hence evaluate (sqrt2+1)^(4) + (sqrt2-1)^(...

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  12. Find (1+x)^(6) - (1-x)^(6). Hence evaluate (1+sqrt3)^(6) - (1-sqrt3)^(...

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  13. Find the fifth expansion of (a/3-3b)^(7)

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  14. Find the fifth expansion of (2x^(2)-1/(3x^(2)))^(10)

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  15. Write down the general term in the expansion of (x^(2)-y^(3))^6. (ii...

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  16. Find the middle term in the expansion of (i). (9/x+x/9)^(8) (ii). (1...

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  17. In the expansion of (1+a)^(34) , if the cofficient of (r-5)^(th) and (...

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  18. (x+sqrt(x^2-1))^6+(x-sqrt(x^2-1))^6

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  19. if (1+a)^(n)=.^(n)C(0)+.^(n)C(1)a++.^(n)C(2)a^(2)+ . . .+.^(n)C(n)a^(n...

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  20. If (1+a)^(n)=.^(n)C(0)+.^(n)C(1)a+.^(n)C(2)a^(2)+ . . +.^(n)C(n)a^(n),...

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