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Last three digit of 27^(27)...

Last three digit of `27^(27)`

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PATHFINDER-BINOMIAL THEOREM-QUESTION BANK
  1. If (1+x)^n = ^nC0+ ^nC1x+…….+^nCnx^n then find the value of ^nC1 ^2+2^...

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  2. Let R=(5 sqrt 5+11)^(2n+1) and f=R-[R] where [] is the greatest intege...

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  3. Last three digit of 27^(27)

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  4. Find remainder when 7^(103) is divided by 25.

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  5. If n in I^+ show 2^(3n+3) -7n -8 is divisible by 49.

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  6. Find the coefficient of x^7 in (1+3x-2x^3)^10

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  7. Find the coefficient of a^3b^4c^5 in (ab+bc+ca)^6

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  8. Expand (x^2+(3/x))^4 , xne0

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  9. Compute (98)^5

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  10. Using binomial theorem prove that 6^n-5n always leaves remainder I whe...

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  11. Find a, if 17th and 18th terms in the expansions of (2+a)^50 are equal...

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

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  13. Use the principle of mathematical induction to show that 5^(2+1)+3^(n+...

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  14. Prove by mathematical induction that sum(r=0)^n "^nCr = n cdot 2^(n-1)

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  15. For ninN, prove that ((n+1)/2)^ngt n!

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  16. Using mathematical induction to show that p^(n+1) +(p+1)^(2n-1) is div...

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  17. Prove by induction that the integer next greater than (3+sqrt5)6n is d...

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  18. Using the principle of mathematical induction show that tan^(-1)(x/(1+...

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  19. Prove by induction that (1+x1)(1+x2)(1+x3)…….(1+xn) ge 1+x1+x2+……+xn

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  20. Use induction to prove that 3^(2n)-1 is not exactly divisible by 2^(n+...

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