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If n be a positive integer, then by usin...

If n be a positive integer, then by using binomial theorem show that `3^(2n+2)-8n-9` is always divisible by 64.

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PATHFINDER-BINOMIAL THEOREM AND PRINCIPLE OF MATHEMATICAL INDUCTION-QUESTION BANK
  1. Show that the middle term in the expansion of (x+1)^(2n) is (1.3.5.......

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  2. The first three terms in the binomial expansion of (x+y)^n are 1,56 an...

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  3. If n be a positive integer, then by using binomial theorem show that 3...

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

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  5. Find the coefficient of x in the expansion (1-x^2+2x^4)(1-1/x)^6.

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  6. If (1+x+x^2)^n=a0+a1x+a2x^2+.......+a(2n)x^(2n), then prove that a0+a2...

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  7. If the coefficients of 2nd, 3rd and 4th terms in the expansion of (1+x...

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  8. If the coefficients of four consecutive terms in the expansion of (1+x...

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  9. The 3rd,4th and fifth terms in the expansion of (x+a)^n are 252, 1512,...

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  10. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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

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  12. Show that the integral part of the value of (9+4sqrt5)^n is odd for po...

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  13. If the 3rd, 4th. 5th and sixth term in the expansion of (x+alpha)^n ar...

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  14. If coefficient of x^2 and x^11 are 27 and -192 respectively of (1+ax+2...

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

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  16. Determine the x-independent term in the expansion of (1+4x)^p(1+1/(4x)...

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  17. For ninN , 2^(3n)-1 is divisible by

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  18. For ninN , n^3+2n is divisible by

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  19. ForninN , 3^(2n-1)+2^(n+1) is always divisible by

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  20. For ninN 2^(3n)-7n-1 is always divisible by

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