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Find the remainder when 3^(37) is divide...

Find the remainder when `3^(37)` is divided with 80 ?

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AAKASH SERIES-BINOMIAL THEOREM-EXERCISE - 1.4 (Level-2)
  1. Find the range of values of the term independent of x in (x sin^(-1)p+...

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  2. The remainder when 5^(99) is divided by 13 is

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  3. Find the remainder when 3^(37) is divided with 80 ?

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  4. Find the remainder when 2^(60) is divided with 7.

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  5. Find the number of distinct terms in the expansion (x + 2y + 3z + ...

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  6. Find the number of distinct terms in the following expansions. (x^(2...

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  7. Find the number of distinct terms in the following expansions. (p+q)...

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  8. Find the number of distinct terms in the expansion (x+ y + z)^10+ ...

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  9. Prove that, C(0) *""^(2n)C(n)-C(1)*""^((2n-2))C(n)+C(2) *""^((2n-4))C(...

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  10. If (1+x)^(n)=sum(r=0)^(n)""^(n)C(r )x^(r ) and if sum(r=0)^(n) (1)/(""...

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  11. Prove that C(0)-(1)/(3)*C(1)+(1)/(5)*C(2) - …+(-1)^(n)*(1)/(2n+1)C(n) ...

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  12. If a, b, c, d be 3^(rd), 4^(th), 5^(th) and 6^(th) terms of the expans...

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  13. Show that sum(r=0)^(n) (-1)^(r ). ""^(n)C(r ) {(1)/(2^(r )) +(3^(r ))/...

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  14. If sum(r = 0)^(2n) a(r ) (x-2)^(r ) = sum(r = 0)^(2n) b(r ) (x-3)^(r )...

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  15. Show that the coefficient of x^(n)y^(n) in the expansion of {(1+x)(1+...

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  16. If (1)/(1!(n-1)!) + (1)/(3!(n-3)!) + (1)/(5!(n-5)!) +…. =

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  17. If sum(r =0)^(n) ((r+2)/(r+1)) *""^(n)C(r ) =(255)/(6). Find n.

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  18. Show that 1sum(r =0)^(50) (""^(100)C( r))*(""^(200)C(150+r ))=""^(300)...

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  19. Prove that sum(k=1)^(n-r ) ""^(n-k)C(r )= ""^(n)C( r+1) .

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  20. Show that C(0) +(C(0) +C(1))+(C(0)+C(1)+C(2)) +…+(C(0) +C(1)+…+C(n)) =...

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